Daily Papers

Recent progress in dense SLAM has primarily targeted monocular setups, often at the expense of robustness and geometric coverage. We present MCGS-SLAM, the first purely RGB-based multi-camera SLAM system built on 3D Gaussian Splatting (3DGS). Unlike prior methods relying on sparse maps or inertial data, MCGS-SLAM fuses dense RGB inputs from multiple viewpoints into a unified, continuously optimized Gaussian map. A multi-camera bundle adjustment (MCBA) jointly refines poses and depths via dense photometric and geometric residuals, while a scale consistency module enforces metric alignment across views using low-rank priors. The system supports RGB input and maintains real-time performance at large scale. Experiments on synthetic and real-world datasets show that MCGS-SLAM consistently yields accurate trajectories and photorealistic reconstructions, usually outperforming monocular baselines. Notably, the wide field of view from multi-camera input enables reconstruction of side-view regions that monocular setups miss, critical for safe autonomous operation. These results highlight the promise of multi-camera Gaussian Splatting SLAM for high-fidelity mapping in robotics and autonomous driving.

The classification of mental health is challenging for a variety of reasons. For one, there is overlap between the mental health issues. In addition, the signs of mental health issues depend on the context of the situation, making classification difficult. Although fine-tuning transformers has improved the performance for mental health classification, standard cross-entropy training tends to create entangled feature spaces and fails to utilize all the information the transformers contain. We present a new framework that focuses on representations to improve mental health classification. This is done using two methods. First, layer-attentive residual aggregation which works on residual connections to to weigh and fuse representations from all transformer layers while maintaining high-level semantics. Second, supervised contrastive feature learning uses temperature-scaled supervised contrastive learning with progressive weighting to increase the geometric margin between confusable mental health problems and decrease class overlap by restructuring the feature space. With a score of 74.36\%, the proposed method is the best performing on the SWMH benchmark and outperforms models that are domain-specialized, such as MentalBERT and MentalRoBERTa by margins of (3.25\% - 2.2\%) and 2.41 recall points over the highest achieving model. These findings show that domain-adaptive pretraining for mental health text classification can be surpassed by carefully designed representation geometry and layer-aware residual integration, which also provide enhanced interpretability through learnt layer importance.

Video diffusion models lack explicit geometric supervision during training, leading to inconsistency artifacts such as object deformation, spatial drift, and depth violations in generated videos. To address this limitation, we propose a geometry-based reward model that leverages pretrained geometric foundation models to evaluate multi-view consistency through cross-frame reprojection error. Unlike previous geometric metrics that measure inconsistency in pixel space, where pixel intensity may introduce additional noise, our approach conducts error computation in a pointwise fashion, yielding a more physically grounded and robust error metric. Furthermore, we introduce a geometry-aware sampling strategy that filters out low-texture and non-semantic regions, focusing evaluation on geometrically meaningful areas with reliable correspondences to improve robustness. We apply this reward model to align video diffusion models through two complementary pathways: post-training of a bidirectional model via SFT or Reinforcement Learning and inference-time optimization of a Causal Video Model (e.g., Streaming video generator) via test-time scaling with our reward as a path verifier. Experimental results validate the effectiveness of our design, demonstrating that our geometry-based reward provides superior robustness compared to other variants. By enabling efficient inference-time scaling, our method offers a practical solution for enhancing open-source video models without requiring extensive computational resources for retraining.

The rapid development of Large Multimodal Models (LMMs) has led to remarkable progress in 2D visual understanding; however, extending these capabilities to 3D scene understanding remains a significant challenge. Existing approaches predominantly rely on text-only supervision, which fails to provide the geometric constraints required for learning robust 3D spatial representations. In this paper, we introduce Reg3D, a novel Reconstructive Geometry Instruction Tuning framework that addresses this limitation by incorporating geometry-aware supervision directly into the training process. Our key insight is that effective 3D understanding necessitates reconstructing underlying geometric structures rather than merely describing them. Unlike existing methods that inject 3D information solely at the input level, Reg3D adopts a dual-supervision paradigm that leverages 3D geometric information both as input and as explicit learning targets. Specifically, we design complementary object-level and frame-level reconstruction tasks within a dual-encoder architecture, enforcing geometric consistency to encourage the development of spatial reasoning capabilities. Extensive experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements, establishing a new training paradigm for spatially aware multimodal models.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely attribute this phenomenon to optimization instability or vanishing gradients, yet such accounts fail to explain why collapse persists even under modern normalization and initialization schemes. In this paper, we argue that the collapse of deep Transformers is fundamentally a geometric problem. Standard residual updates implicitly assume that feature accumulation is always beneficial, but offer no mechanism to constrain update directions or to erase outdated information. As depth increases, this leads to systematic drift off the semantic manifold and monotonic feature accumulation, causing representational degeneracy. We propose a unified geometric framework that addresses these failures through two orthogonal principles. First, manifold-constrained hyper-connections restrict residual updates to valid local tangent directions, preventing uncontrolled manifold drift. Second, deep delta learning introduces data-dependent, non-monotonic updates that enable reflection and erasure of redundant features rather than their unconditional accumulation. Together, these mechanisms decouple the direction and sign of feature updates, yielding a stable geometric evolution across depth. We term the resulting architecture the Manifold-Geometric Transformer (MGT). Our analysis predicts that enforcing geometric validity while allowing dynamic erasure is essential for avoiding rank collapse in ultra-deep networks. We outline an evaluation protocol for Transformers exceeding 100 layers to test the hypothesis that geometry, rather than depth itself, is the key limiting factor in deep representation learning.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a significant challenge, due to its rendering-based optimization process and entangled learning of appearance and geometry with photometric losses. In this paper, we present a novel framework, i.e, GURecon, which establishes a geometric uncertainty field for the neural surface based on geometric consistency. Different from existing methods that rely on rendering-based measurement, GURecon models a continuous 3D uncertainty field for the reconstructed surface, and is learned by an online distillation approach without introducing real geometric information for supervision. Moreover, in order to mitigate the interference of illumination on geometric consistency, a decoupled field is learned and exploited to finetune the uncertainty field. Experiments on various datasets demonstrate the superiority of GURecon in modeling 3D geometric uncertainty, as well as its plug-and-play extension to various neural surface representations and improvement on downstream tasks such as incremental reconstruction. The code and supplementary material are available on the project website: https://zju3dv.github.io/GURecon/.

We study the geometric structure of layer updates in deep language models. Rather than analyzing what information is encoded in intermediate representations, we ask how representations change from one layer to the next. We show that layerwise updates admit a decomposition into a dominant tokenwise component and a residual that is not captured by restricted tokenwise function classes. Across multiple architectures, including Transformers and state-space models, we find that the full layer update is almost perfectly aligned with the tokenwise component, while the residual exhibits substantially weaker alignment, larger angular deviation, and significantly lower projection onto the dominant tokenwise subspace. This indicates that the residual is not merely a small correction, but a geometrically distinct component of the transformation. This geometric separation has functional consequences: approximation error under the restricted tokenwise model is strongly associated with output perturbation, with Spearman correlations often exceeding 0.7 and reaching up to 0.95 in larger models. Together, these results suggest that most layerwise updates behave like structured reparameterizations along a dominant direction, while functionally significant computation is concentrated in a geometrically distinct residual component. Our framework provides a simple, architecture-agnostic method for probing the geometric and functional structure of layer updates in modern language models.

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce Test3R, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets (I_1,I_2,I_3), Test3R generates reconstructions from pairs (I_1,I_2) and (I_1,I_3). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image I_1. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

Recent advances in dense 3D reconstruction have led to significant progress, yet achieving accurate unified geometric prediction remains a major challenge. Most existing methods are limited to predicting a single geometry quantity from input images. However, geometric quantities such as depth, surface normals, and point maps are inherently correlated, and estimating them in isolation often fails to ensure consistency, thereby limiting both accuracy and practical applicability. This motivates us to explore a unified framework that explicitly models the structural coupling among different geometric properties to enable joint regression. In this paper, we present Dens3R, a 3D foundation model designed for joint geometric dense prediction and adaptable to a wide range of downstream tasks. Dens3R adopts a two-stage training framework to progressively build a pointmap representation that is both generalizable and intrinsically invariant. Specifically, we design a lightweight shared encoder-decoder backbone and introduce position-interpolated rotary positional encoding to maintain expressive power while enhancing robustness to high-resolution inputs. By integrating image-pair matching features with intrinsic invariance modeling, Dens3R accurately regresses multiple geometric quantities such as surface normals and depth, achieving consistent geometry perception from single-view to multi-view inputs. Additionally, we propose a post-processing pipeline that supports geometrically consistent multi-view inference. Extensive experiments demonstrate the superior performance of Dens3R across various dense 3D prediction tasks and highlight its potential for broader applications.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

Text-to-3D generation has achieved significant success by incorporating powerful 2D diffusion models, but insufficient 3D prior knowledge also leads to the inconsistency of 3D geometry. Recently, since large-scale multi-view datasets have been released, fine-tuning the diffusion model on the multi-view datasets becomes a mainstream to solve the 3D inconsistency problem. However, it has confronted with fundamental difficulties regarding the limited quality and diversity of 3D data, compared with 2D data. To sidestep these trade-offs, we explore a retrieval-augmented approach tailored for score distillation, dubbed RetDream. We postulate that both expressiveness of 2D diffusion models and geometric consistency of 3D assets can be fully leveraged by employing the semantically relevant assets directly within the optimization process. To this end, we introduce novel framework for retrieval-based quality enhancement in text-to-3D generation. We leverage the retrieved asset to incorporate its geometric prior in the variational objective and adapt the diffusion model's 2D prior toward view consistency, achieving drastic improvements in both geometry and fidelity of generated scenes. We conduct extensive experiments to demonstrate that RetDream exhibits superior quality with increased geometric consistency. Project page is available at https://ku-cvlab.github.io/RetDream/.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Since a building's floorplans are easily accessible, consistent over time, and inherently robust to changes in visual appearance, self-localization within the floorplan has attracted researchers' interest. However, since floorplans are minimalist representations of a building's structure, modal and geometric differences between visual perceptions and floorplans pose challenges to this task. While existing methods cleverly utilize 2D geometric features and pose filters to achieve promising performance, they fail to address the localization errors caused by frequent visual changes and view occlusions due to variously shaped 3D objects. To tackle these issues, this paper views the 2D Floorplan Localization (FLoc) problem from a higher dimension by injecting 3D geometric priors into the visual FLoc algorithm. For the 3D geometric prior modeling, we first model geometrically aware view invariance using multi-view constraints, i.e., leveraging imaging geometric principles to provide matching constraints between multiple images that see the same points. Then, we further model the view-scene aligned geometric priors, enhancing the cross-modal geometry-color correspondences by associating the scene's surface reconstruction with the RGB frames of the sequence. Both 3D priors are modeled through self-supervised contrastive learning, thus no additional geometric or semantic annotations are required. These 3D priors summarized in extensive realistic scenes bridge the modal gap while improving localization success without increasing the computational burden on the FLoc algorithm. Sufficient comparative studies demonstrate that our method significantly outperforms state-of-the-art methods and substantially boosts the FLoc accuracy. All data and code will be released after the anonymous review.

Recent advances in data-driven geometric multi-view 3D reconstruction foundation models (e.g., DUSt3R) have shown remarkable performance across various 3D vision tasks, facilitated by the release of large-scale, high-quality 3D datasets. However, as we observed, constrained by their matching-based principles, the reconstruction quality of existing models suffers significant degradation in challenging regions with limited matching cues, particularly in weakly textured areas and low-light conditions. To mitigate these limitations, we propose to harness the inherent robustness of monocular geometry estimation to compensate for the inherent shortcomings of matching-based methods. Specifically, we introduce a monocular-guided refinement module that integrates monocular geometric priors into multi-view reconstruction frameworks. This integration substantially enhances the robustness of multi-view reconstruction systems, leading to high-quality feed-forward reconstructions. Comprehensive experiments across multiple benchmarks demonstrate that our method achieves substantial improvements in both mutli-view camera pose estimation and point cloud accuracy.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Recent advances in discriminative and generative pretraining have yielded geometry estimation models with strong generalization capabilities. While discriminative monocular geometry estimation methods rely on large-scale fine-tuning data to achieve zero-shot generalization, several generative-based paradigms show the potential of achieving impressive generalization performance on unseen scenes by leveraging pre-trained diffusion models and fine-tuning on even a small scale of synthetic training data. Frustratingly, these models are trained with different recipes on different datasets, making it hard to find out the critical factors that determine the evaluation performance. Besides, current geometry evaluation benchmarks have two main drawbacks that may prevent the development of the field, i.e., limited scene diversity and unfavorable label quality. To resolve the above issues, (1) we build fair and strong baselines in a unified codebase for evaluating and analyzing the geometry estimation models; (2) we evaluate monocular geometry estimators on more challenging benchmarks for geometry estimation task with diverse scenes and high-quality annotations. Our results reveal that pre-trained using large data, discriminative models such as DINOv2, can outperform generative counterparts with a small amount of high-quality synthetic data under the same training configuration, which suggests that fine-tuning data quality is a more important factor than the data scale and model architecture. Our observation also raises a question: if simply fine-tuning a general vision model such as DINOv2 using a small amount of synthetic depth data produces SOTA results, do we really need complex generative models for depth estimation? We believe this work can propel advancements in geometry estimation tasks as well as a wide range of downstream applications.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Recent advances in neural reconstruction using posed image sequences have made remarkable progress. However, due to the lack of depth information, existing volumetric-based techniques simply duplicate 2D image features of the object surface along the entire camera ray. We contend this duplication introduces noise in empty and occluded spaces, posing challenges for producing high-quality 3D geometry. Drawing inspiration from traditional multi-view stereo methods, we propose an end-to-end 3D neural reconstruction framework CVRecon, designed to exploit the rich geometric embedding in the cost volumes to facilitate 3D geometric feature learning. Furthermore, we present Ray-contextual Compensated Cost Volume (RCCV), a novel 3D geometric feature representation that encodes view-dependent information with improved integrity and robustness. Through comprehensive experiments, we demonstrate that our approach significantly improves the reconstruction quality in various metrics and recovers clear fine details of the 3D geometries. Our extensive ablation studies provide insights into the development of effective 3D geometric feature learning schemes. Project page: https://cvrecon.ziyue.cool/

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we explore the possibility that one can uncover useful geometric inductive biases by studying how training molds the Riemannian geometry induced by unconstrained neural network feature maps. We first show that at infinite width, neural networks with random parameters induce highly symmetric metrics on input space. This symmetry is broken by feature learning: networks trained to perform classification tasks learn to magnify local areas along decision boundaries. This holds in deep networks trained on high-dimensional image classification tasks, and even in self-supervised representation learning. These results begin to elucidate how training shapes the geometry induced by unconstrained neural network feature maps, laying the groundwork for an understanding of this richly nonlinear form of feature learning.

Geometric models like DUSt3R have shown great advances in understanding the geometry of a scene from pairs of photos. However, they fail when the inputs are from vastly different viewpoints (e.g., aerial vs. ground) or modalities (e.g., photos vs. abstract drawings) compared to what was observed during training. This paper addresses a challenging version of this problem: predicting correspondences between ground-level photos and floor plans. Current datasets for joint photo--floor plan reasoning are limited, either lacking in varying modalities (VIGOR) or lacking in correspondences (WAFFLE). To address these limitations, we introduce a new dataset, C3, created by first reconstructing a number of scenes in 3D from Internet photo collections via structure-from-motion, then manually registering the reconstructions to floor plans gathered from the Internet, from which we can derive correspondence between images and floor plans. C3 contains 90K paired floor plans and photos across 597 scenes with 153M pixel-level correspondences and 85K camera poses. We find that state-of-the-art correspondence models struggle on this task. By training on our new data, we can improve on the best performing method by 34% in RMSE. We also identify open challenges in cross-modal geometric reasoning that our dataset aims to help address.

Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by comparing them with reference images. To bridge this gap, we introduce the CAD review task to automatically detect and correct potential errors, ensuring consistency between the constructed 3D objects and reference images. However, recent advanced multimodal large language models (MLLMs) struggle to recognize multiple geometric components and perform spatial geometric operations within the CAD program, leading to inaccurate reviews. In this paper, we propose the CAD program repairer (ReCAD) framework to effectively detect program errors and provide helpful feedback on error correction. Additionally, we create a dataset, CADReview, consisting of over 20K program-image pairs, with diverse errors for the CAD review task. Extensive experiments demonstrate that our ReCAD significantly outperforms existing MLLMs, which shows great potential in design applications.

Vision-language models (VLM) excel at general understanding yet remain weak at dynamic spatial reasoning (DSR), i.e., reasoning about the evolvement of object geometry and relationship in 3D space over time, largely due to the scarcity of scalable 4D-aware training resources. To bridge this gap across aspects of dataset, benchmark and model, we introduce DSR Suite. First, we propose an automated pipeline that generates multiple-choice question-answer pairs from in-the-wild videos for DSR. By leveraging modern vision foundation models, the pipeline extracts rich geometric and motion information, including camera poses, local point clouds, object masks, orientations, and 3D trajectories. These geometric cues enable the construction of DSR-Train for learning and further human-refined DSR-Bench for evaluation. Compared with previous works, our data emphasize (i) in-the-wild video sources, (ii) object- and scene-level 3D requirements, (iii) viewpoint transformations, (iv) multi-object interactions, and (v) fine-grained, procedural answers. Beyond data, we propose a lightweight Geometry Selection Module (GSM) to seamlessly integrate geometric priors into VLMs, which condenses question semantics and extracts question-relevant knowledge from pretrained 4D reconstruction priors into a compact set of geometry tokens. This targeted extraction avoids overwhelming the model with irrelevant knowledge. Experiments show that integrating DSR-Train and GSM into Qwen2.5-VL-7B significantly enhances its dynamic spatial reasoning capability, while maintaining accuracy on general video understanding benchmarks.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

Understanding what semantic information persists after object removal is critical for privacy-preserving 3D reconstruction and editable scene representations. In this work, we introduce a novel benchmark and evaluation framework to measure semantic residuals, the unintended semantic traces left behind, after object removal in 3D Gaussian Splatting. We conduct experiments across a diverse set of indoor and outdoor scenes, showing that current methods can preserve semantic information despite the absence of visual geometry. We also release Remove360, a dataset of pre/post-removal RGB images and object-level masks captured in real-world environments. While prior datasets have focused on isolated object instances, Remove360 covers a broader and more complex range of indoor and outdoor scenes, enabling evaluation of object removal in the context of full-scene representations. Given ground truth images of a scene before and after object removal, we assess whether we can truly eliminate semantic presence, and if downstream models can still infer what was removed. Our findings reveal critical limitations in current 3D object removal techniques and underscore the need for more robust solutions capable of handling real-world complexity. The evaluation framework is available at github.com/spatial-intelligence-ai/Remove360.git. Data are available at huggingface.co/datasets/simkoc/Remove360.

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the rectification performance. To this end, we present DocGeoNet for document image rectification by introducing explicit geometric representation. Technically, two typical attributes of the document image are involved in the proposed geometric representation learning, i.e., 3D shape and textlines. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image while overlooking the local structure. On the other hand, textlines complementarily provide explicit geometric constraints for local patterns. The learned geometric representation effectively bridges the distorted image and the ground truth one. Extensive experiments show the effectiveness of our framework and demonstrate the superiority of our DocGeoNet over state-of-the-art methods on both the DocUNet Benchmark dataset and our proposed DIR300 test set. The code is available at https://github.com/fh2019ustc/DocGeoNet.

Prior ReLoc3R achieves breakthrough performance with fast 25ms inference and state-of-the-art regression accuracy, yet our analysis reveals subtle geometric inconsistencies in its internal representations that prevent reaching the precision ceiling of correspondence-based methods like MASt3R (which require 300ms per pair). In this work, we present GeLoc3r, a novel approach to relative camera pose estimation that enhances pose regression methods through Geometric Consistency Regularization (GCR). GeLoc3r overcomes the speed-accuracy dilemma by training regression networks to produce geometrically consistent poses without inference-time geometric computation. During training, GeLoc3r leverages ground-truth depth to generate dense 3D-2D correspondences, weights them using a FusionTransformer that learns correspondence importance, and computes geometrically-consistent poses via weighted RANSAC. This creates a consistency loss that transfers geometric knowledge into the regression network. Unlike FAR method which requires both regression and geometric solving at inference, GeLoc3r only uses the enhanced regression head at test time, maintaining ReLoc3R's fast speed and approaching MASt3R's high accuracy. On challenging benchmarks, GeLoc3r consistently outperforms ReLoc3R, achieving significant improvements including 40.45% vs. 34.85% AUC@5° on the CO3Dv2 dataset (16% relative improvement), 68.66% vs. 66.70% AUC@5° on RealEstate10K, and 50.45% vs. 49.60% on MegaDepth1500. By teaching geometric consistency during training rather than enforcing it at inference, GeLoc3r represents a paradigm shift in how neural networks learn camera geometry, achieving both the speed of regression and the geometric understanding of correspondence methods.

Feed-forward 3D reconstruction models are efficient but rigid: once trained, they perform inference in a zero-shot manner and cannot adapt to the test scene. As a result, visually plausible reconstructions often contain errors, particularly under occlusions, specularities, and ambiguous cues. To address this, we introduce Free Geometry, a framework that enables feed-forward 3D reconstruction models to self-evolve at test time without any 3D ground truth. Our key insight is that, when the model receives more views, it produces more reliable and view-consistent reconstructions. Leveraging this property, given a testing sequence, we mask a subset of frames to construct a self-supervised task. Free Geometry enforces cross-view feature consistency between representations from full and partial observations, while maintaining the pairwise relations implied by the held-out frames. This self-supervision allows for fast recalibration via lightweight LoRA updates, taking less than 2 minutes per dataset on a single GPU. Our approach consistently improves state-of-the-art foundation models, including Depth Anything 3 and VGGT, across 4 benchmark datasets, yielding an average improvement of 3.73% in camera pose accuracy and 2.88% in point map prediction. Code is available at https://github.com/hiteacherIamhumble/Free-Geometry .

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

3D Gaussians have recently emerged as an effective scene representation for real-time splatting and accurate novel-view synthesis, motivating several works to adapt multi-view structure prediction networks to regress per-pixel 3D Gaussians from images. However, most prior work extends these networks to predict additional Gaussian parameters -- orientation, scale, opacity, and appearance -- while relying almost exclusively on view-synthesis supervision. We show that a view-synthesis loss alone is insufficient to recover geometrically meaningful splats in this setting. We analyze and address the ambiguities of learning 3D Gaussian splats under self-supervision for pose-free generalizable splatting, and introduce G3Splat, which enforces geometric priors to obtain geometrically consistent 3D scene representations. Trained on RE10K, our approach achieves state-of-the-art performance in (i) geometrically consistent reconstruction, (ii) relative pose estimation, and (iii) novel-view synthesis. We further demonstrate strong zero-shot generalization on ScanNet, substantially outperforming prior work in both geometry recovery and relative pose estimation. Code and pretrained models are released on our project page (https://m80hz.github.io/g3splat/).

The grand vision of enabling persistent, large-scale 3D visual geometry understanding is shackled by the irreconcilable demands of scalability and long-term stability. While offline models like VGGT achieve inspiring geometry capability, their batch-based nature renders them irrelevant for live systems. Streaming architectures, though the intended solution for live operation, have proven inadequate. Existing methods either fail to support truly infinite-horizon inputs or suffer from catastrophic drift over long sequences. We shatter this long-standing dilemma with InfiniteVGGT, a causal visual geometry transformer that operationalizes the concept of a rolling memory through a bounded yet adaptive and perpetually expressive KV cache. Capitalizing on this, we devise a training-free, attention-agnostic pruning strategy that intelligently discards obsolete information, effectively ``rolling'' the memory forward with each new frame. Fully compatible with FlashAttention, InfiniteVGGT finally alleviates the compromise, enabling infinite-horizon streaming while outperforming existing streaming methods in long-term stability. The ultimate test for such a system is its performance over a truly infinite horizon, a capability that has been impossible to rigorously validate due to the lack of extremely long-term, continuous benchmarks. To address this critical gap, we introduce the Long3D benchmark, which, for the first time, enables a rigorous evaluation of continuous 3D geometry estimation on sequences about 10,000 frames. This provides the definitive evaluation platform for future research in long-term 3D geometry understanding. Code is available at: https://github.com/AutoLab-SAI-SJTU/InfiniteVGGT

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

We present NeRF-Det, a novel method for indoor 3D detection with posed RGB images as input. Unlike existing indoor 3D detection methods that struggle to model scene geometry, our method makes novel use of NeRF in an end-to-end manner to explicitly estimate 3D geometry, thereby improving 3D detection performance. Specifically, to avoid the significant extra latency associated with per-scene optimization of NeRF, we introduce sufficient geometry priors to enhance the generalizability of NeRF-MLP. Furthermore, we subtly connect the detection and NeRF branches through a shared MLP, enabling an efficient adaptation of NeRF to detection and yielding geometry-aware volumetric representations for 3D detection. Our method outperforms state-of-the-arts by 3.9 mAP and 3.1 mAP on the ScanNet and ARKITScenes benchmarks, respectively. We provide extensive analysis to shed light on how NeRF-Det works. As a result of our joint-training design, NeRF-Det is able to generalize well to unseen scenes for object detection, view synthesis, and depth estimation tasks without requiring per-scene optimization. Code is available at https://github.com/facebookresearch/NeRF-Det.

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Recent advances in 3D reconstruction have achieved remarkable progress in high-quality scene capture from dense multi-view imagery, yet struggle when input views are limited. Various approaches, including regularization techniques, semantic priors, and geometric constraints, have been implemented to address this challenge. Latest diffusion-based methods have demonstrated substantial improvements by generating novel views from new camera poses to augment training data, surpassing earlier regularization and prior-based techniques. Despite this progress, we identify three critical limitations in these state-of-the-art approaches: inadequate coverage beyond known view peripheries, geometric inconsistencies across generated views, and computationally expensive pipelines. We introduce GaMO (Geometry-aware Multi-view Outpainter), a framework that reformulates sparse-view reconstruction through multi-view outpainting. Instead of generating new viewpoints, GaMO expands the field of view from existing camera poses, which inherently preserves geometric consistency while providing broader scene coverage. Our approach employs multi-view conditioning and geometry-aware denoising strategies in a zero-shot manner without training. Extensive experiments on Replica and ScanNet++ demonstrate state-of-the-art reconstruction quality across 3, 6, and 9 input views, outperforming prior methods in PSNR and LPIPS, while achieving a 25times speedup over SOTA diffusion-based methods with processing time under 10 minutes. Project page: https://yichuanh.github.io/GaMO/

Recent developments in Multimodal Large Language Models (MLLMs) have significantly improved Vision-Language (VL) reasoning in 2D domains. However, extending these capabilities to 3D scene understanding remains a major challenge. Existing 3D Multimodal Large Language Models (3D-MLLMs) often depend on 3D data inputs, which limits scalability and generalization. To address this limitation, we propose Vid-LLM, a video-based 3D-MLLM that directly processes video inputs without requiring external 3D data, making it practical for real-world deployment. In our method, the geometric prior are directly used to improve the performance of the sceen perception. To integrate the geometric cues into the MLLM compactly, we design a Cross-Task Adapter (CTA) module to align the 3D geometric priors with the vision-language representations. To ensure geometric consistency and integrity, we introduce a Metric Depth Model that recovers real-scale geometry from the reconstruction outputs. Finally, the model is fine-tuned with a two-stage distillation optimization strategy, realizing fast convergence and stabilizes training. Extensive experiments across diverse benchmarks verified the effectiveness of our method on 3D Question Answering, 3D Dense Captioning and 3D Visual Grounding tasks, demonstrating the superior multi-task capabilities.

The growing demand for Embodied AI and VR applications has highlighted the need for synthesizing high-quality 3D indoor scenes from sparse inputs. However, existing approaches struggle to infer massive amounts of missing geometry in large unseen areas while maintaining global consistency, often producing locally plausible but globally inconsistent reconstructions. We present Rein3D, a framework that reconstructs full 360-degree indoor environments by coupling explicit 3D Gaussian Splatting (3DGS) with temporally coherent priors from video diffusion models. Our approach follows a "restore-and-refine" paradigm: we employ a radial exploration strategy to render imperfect panoramic videos along trajectories starting from the origin, effectively uncovering occluded regions from a coarse 3DGS initialization. These sequences are restored by a panoramic video-to-video diffusion model and further enhanced via video super-resolution to synthesize high-fidelity geometry and textures. Finally, these refined videos serve as pseudo-ground truths to update the global 3D Gaussian field. To support this task, we construct PanoV2V-15K, a dataset of over 15K paired clean and degraded panoramic videos for diffusion-based scene restoration. Experiments demonstrate that Rein3D produces photorealistic and globally consistent 3D scenes and significantly improves long-range camera exploration compared with existing baselines.

Large-scale video diffusion models achieve impressive visual quality, yet often fail to preserve geometric consistency. Prior approaches improve consistency either by augmenting the generator with additional modules or applying geometry-aware alignment. However, architectural modifications can compromise the generalization of internet-scale pretrained models, while existing alignment methods are limited to static scenes and rely on RGB-space rewards that require repeated VAE decoding, incurring substantial compute overhead and failing to generalize to highly dynamic real-world scenes. To preserve the pretrained capacity while improving geometric consistency, we propose VGGRPO (Visual Geometry GRPO), a latent geometry-guided framework for geometry-aware video post-training. VGGRPO introduces a Latent Geometry Model (LGM) that stitches video diffusion latents to geometry foundation models, enabling direct decoding of scene geometry from the latent space. By constructing LGM from a geometry model with 4D reconstruction capability, VGGRPO naturally extends to dynamic scenes, overcoming the static-scene limitations of prior methods. Building on this, we perform latent-space Group Relative Policy Optimization with two complementary rewards: a camera motion smoothness reward that penalizes jittery trajectories, and a geometry reprojection consistency reward that enforces cross-view geometric coherence. Experiments on both static and dynamic benchmarks show that VGGRPO improves camera stability, geometry consistency, and overall quality while eliminating costly VAE decoding, making latent-space geometry-guided reinforcement an efficient and flexible approach to world-consistent video generation.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly competitive baseline results from combining popular clustering algorithms with recent improvements in 3D geometry estimation. However, such purely geometric methods are understandably oblivious to plane semantics, which are crucial to discerning distinct planes. To overcome this limitation, we propose a method that predicts multi-view consistent plane embeddings that complement geometry when clustering points into planes. We show through extensive evaluation on the ScanNetV2 dataset that our new method outperforms existing approaches and our strong geometric baseline for the task of plane estimation.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Efficiently synthesizing novel views from sparse inputs while maintaining accuracy remains a critical challenge in 3D reconstruction. While advanced techniques like radiance fields and 3D Gaussian Splatting achieve rendering quality and impressive efficiency with dense view inputs, they suffer from significant geometric reconstruction errors when applied to sparse input views. Moreover, although recent methods leverage monocular depth estimation to enhance geometric learning, their dependence on single-view estimated depth often leads to view inconsistency issues across different viewpoints. Consequently, this reliance on absolute depth can introduce inaccuracies in geometric information, ultimately compromising the quality of scene reconstruction with Gaussian splats. In this paper, we present RDG-GS, a novel sparse-view 3D rendering framework with Relative Depth Guidance based on 3D Gaussian Splatting. The core innovation lies in utilizing relative depth guidance to refine the Gaussian field, steering it towards view-consistent spatial geometric representations, thereby enabling the reconstruction of accurate geometric structures and capturing intricate textures. First, we devise refined depth priors to rectify the coarse estimated depth and insert global and fine-grained scene information to regular Gaussians. Building on this, to address spatial geometric inaccuracies from absolute depth, we propose relative depth guidance by optimizing the similarity between spatially correlated patches of depth and images. Additionally, we also directly deal with the sparse areas challenging to converge by the adaptive sampling for quick densification. Across extensive experiments on Mip-NeRF360, LLFF, DTU, and Blender, RDG-GS demonstrates state-of-the-art rendering quality and efficiency, making a significant advancement for real-world application.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

Robust 3D geometry estimation from videos is critical for applications such as autonomous navigation, SLAM, and 3D scene reconstruction. Recent methods like DUSt3R demonstrate that regressing dense pointmaps from image pairs enables accurate and efficient pose-free reconstruction. However, existing RGB-only approaches struggle under real-world conditions involving dynamic objects and extreme illumination, due to the inherent limitations of conventional cameras. In this paper, we propose EAG3R, a novel geometry estimation framework that augments pointmap-based reconstruction with asynchronous event streams. Built upon the MonST3R backbone, EAG3R introduces two key innovations: (1) a retinex-inspired image enhancement module and a lightweight event adapter with SNR-aware fusion mechanism that adaptively combines RGB and event features based on local reliability; and (2) a novel event-based photometric consistency loss that reinforces spatiotemporal coherence during global optimization. Our method enables robust geometry estimation in challenging dynamic low-light scenes without requiring retraining on night-time data. Extensive experiments demonstrate that EAG3R significantly outperforms state-of-the-art RGB-only baselines across monocular depth estimation, camera pose tracking, and dynamic reconstruction tasks.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

From a single image, visual cues can help deduce intrinsic and extrinsic camera parameters like the focal length and the gravity direction. This single-image calibration can benefit various downstream applications like image editing and 3D mapping. Current approaches to this problem are based on either classical geometry with lines and vanishing points or on deep neural networks trained end-to-end. The learned approaches are more robust but struggle to generalize to new environments and are less accurate than their classical counterparts. We hypothesize that they lack the constraints that 3D geometry provides. In this work, we introduce GeoCalib, a deep neural network that leverages universal rules of 3D geometry through an optimization process. GeoCalib is trained end-to-end to estimate camera parameters and learns to find useful visual cues from the data. Experiments on various benchmarks show that GeoCalib is more robust and more accurate than existing classical and learned approaches. Its internal optimization estimates uncertainties, which help flag failure cases and benefit downstream applications like visual localization. The code and trained models are publicly available at https://github.com/cvg/GeoCalib.

Recent advancements in neural visual geometry, including transformer-based models such as VGGT and Pi3, have achieved impressive accuracy on 3D reconstruction tasks. However, their reliance on full attention makes them fundamentally limited by GPU memory capacity, preventing them from scaling to large, unordered image collections. We introduce MERG3R, a training-free divide-and-conquer framework that enables geometric foundation models to operate far beyond their native memory limits. MERG3R first reorders and partitions unordered images into overlapping, geometrically diverse subsets that can be reconstructed independently. It then merges the resulting local reconstructions through an efficient global alignment and confidence-weighted bundle adjustment procedure, producing a globally consistent 3D model. Our framework is model-agnostic and can be paired with existing neural geometry models. Across large-scale datasets, including 7-Scenes, NRGBD, Tanks & Temples, and Cambridge Landmarks, MERG3R consistently improves reconstruction accuracy, memory efficiency, and scalability, enabling high-quality reconstruction when the dataset exceeds memory capacity limits.

Recent advances in scene understanding benefit a lot from depth maps because of the 3D geometry information, especially in complex conditions (e.g., low light and overexposed). Existing approaches encode depth maps along with RGB images and perform feature fusion between them to enable more robust predictions. Taking into account that depth can be regarded as a geometry supplement for RGB images, a straightforward question arises: Do we really need to explicitly encode depth information with neural networks as done for RGB images? Based on this insight, in this paper, we investigate a new way to learn RGBD feature representations and present DFormerv2, a strong RGBD encoder that explicitly uses depth maps as geometry priors rather than encoding depth information with neural networks. Our goal is to extract the geometry clues from the depth and spatial distances among all the image patch tokens, which will then be used as geometry priors to allocate attention weights in self-attention. Extensive experiments demonstrate that DFormerv2 exhibits exceptional performance in various RGBD semantic segmentation benchmarks. Code is available at: https://github.com/VCIP-RGBD/DFormer.

Geometric foundation models show promise in 3D reconstruction, yet their progress is severely constrained by the scarcity of diverse, large-scale 3D annotations. While Internet videos offer virtually unlimited raw data, utilizing them as a scaling source for geometric learning is challenging due to the absence of ground-truth geometry and the presence of observational noise. To address this, we propose SAGE, a framework for Scalable Adaptation of GEometric foundation models from raw video streams. SAGE leverages a hierarchical mining pipeline to transform videos into training trajectories and hybrid supervision: (1) Informative training trajectory selection; (2) Sparse Geometric Anchoring via SfM point clouds for global structural guidance; and (3) Dense Differentiable Consistency via 3D Gaussian rendering for multi-view constraints. To prevent catastrophic forgetting, we introduce a regularization strategy using anchor data. Extensive experiments show that SAGE significantly enhances zero-shot generalization, reducing Chamfer Distance by 20-42% on unseen benchmarks (7Scenes, TUM-RGBD, Matterport3D) compared to state-of-the-art baselines. To our knowledge, SAGE pioneers the adaptation of geometric foundation models via Internet video, establishing a scalable paradigm for general-purpose 3D learning.

Vision-Language Models (VLMs) have shown remarkable capabilities in spatial reasoning, yet they remain fundamentally limited to qualitative precision and lack the computational precision required for real-world robotics. Current approaches fail to leverage metric cues from depth sensors and camera calibration, instead reducing geometric problems to pattern recognition tasks that cannot deliver the centimeter-level accuracy essential for robotic manipulation. We present TIGeR (Tool-Integrated Geometric Reasoning), a novel framework that transforms VLMs from perceptual estimators to geometric computers by enabling them to generate and execute precise geometric computations through external tools. Rather than attempting to internalize complex geometric operations within neural networks, TIGeR empowers models to recognize geometric reasoning requirements, synthesize appropriate computational code, and invoke specialized libraries for exact calculations. To support this paradigm, we introduce TIGeR-300K, a comprehensive tool-invocation-oriented dataset covering point transformations, pose estimation, and spatial compatibility verification, complete with tool invocation sequences and intermediate computations. Through a two-stage training pipeline combining supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT) with our proposed hierarchical reward design, TIGeR achieves SOTA performance on geometric reasoning benchmarks while demonstrating centimeter-level precision in real-world robotic manipulation tasks.

Multi-view transformers such as DUSt3R are revolutionizing 3D vision by solving 3D tasks in a feed-forward manner. However, contrary to previous optimization-based pipelines, the inner mechanisms of multi-view transformers are unclear. Their black-box nature makes further improvements beyond data scaling challenging and complicates usage in safety- and reliability-critical applications. Here, we present an approach for probing and visualizing 3D representations from the residual connections of the multi-view transformers' layers. In this manner, we investigate a variant of the DUSt3R model, shedding light on the development of its latent state across blocks, the role of the individual layers, and suggest how it differs from methods with stronger inductive biases of explicit global pose. Finally, we show that the investigated variant of DUSt3R estimates correspondences that are refined with reconstructed geometry. The code used for the analysis is available at https://github.com/JulienGaubil/und3rstand .

We present an algorithm for reconstructing dense, geometrically consistent depth for all pixels in a monocular video. We leverage a conventional structure-from-motion reconstruction to establish geometric constraints on pixels in the video. Unlike the ad-hoc priors in classical reconstruction, we use a learning-based prior, i.e., a convolutional neural network trained for single-image depth estimation. At test time, we fine-tune this network to satisfy the geometric constraints of a particular input video, while retaining its ability to synthesize plausible depth details in parts of the video that are less constrained. We show through quantitative validation that our method achieves higher accuracy and a higher degree of geometric consistency than previous monocular reconstruction methods. Visually, our results appear more stable. Our algorithm is able to handle challenging hand-held captured input videos with a moderate degree of dynamic motion. The improved quality of the reconstruction enables several applications, such as scene reconstruction and advanced video-based visual effects.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

Open-vocabulary 3D object detection aims to localize and recognize objects beyond a fixed training taxonomy. In multi-view RGB settings, recent approaches often decouple geometry-based instance construction from semantic labeling, generating class-agnostic fragments and assigning open-vocabulary categories post hoc. While flexible, such decoupling leaves instance construction governed primarily by geometric consistency, without semantic constraints during merging. When geometric evidence is view-dependent and incomplete, this geometry-only merging can lead to irreversible association errors, including over-merging of distinct objects or fragmentation of a single instance. We propose Group3D, a multi-view open-vocabulary 3D detection framework that integrates semantic constraints directly into the instance construction process. Group3D maintains a scene-adaptive vocabulary derived from a multimodal large language model (MLLM) and organizes it into semantic compatibility groups that encode plausible cross-view category equivalence. These groups act as merge-time constraints: 3D fragments are associated only when they satisfy both semantic compatibility and geometric consistency. This semantically gated merging mitigates geometry-driven over-merging while absorbing multi-view category variability. Group3D supports both pose-known and pose-free settings, relying only on RGB observations. Experiments on ScanNet and ARKitScenes demonstrate that Group3D achieves state-of-the-art performance in multi-view open-vocabulary 3D detection, while exhibiting strong generalization in zero-shot scenarios. The project page is available at https://ubin108.github.io/Group3D/.

Decompositional reconstruction of 3D scenes, with complete shapes and detailed texture of all objects within, is intriguing for downstream applications but remains challenging, particularly with sparse views as input. Recent approaches incorporate semantic or geometric regularization to address this issue, but they suffer significant degradation in underconstrained areas and fail to recover occluded regions. We argue that the key to solving this problem lies in supplementing missing information for these areas. To this end, we propose DP-Recon, which employs diffusion priors in the form of Score Distillation Sampling (SDS) to optimize the neural representation of each individual object under novel views. This provides additional information for the underconstrained areas, but directly incorporating diffusion prior raises potential conflicts between the reconstruction and generative guidance. Therefore, we further introduce a visibility-guided approach to dynamically adjust the per-pixel SDS loss weights. Together these components enhance both geometry and appearance recovery while remaining faithful to input images. Extensive experiments across Replica and ScanNet++ demonstrate that our method significantly outperforms SOTA methods. Notably, it achieves better object reconstruction under 10 views than the baselines under 100 views. Our method enables seamless text-based editing for geometry and appearance through SDS optimization and produces decomposed object meshes with detailed UV maps that support photorealistic Visual effects (VFX) editing. The project page is available at https://dp-recon.github.io/.

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing a complementary process of Reinforcement Learning with Verifiable Rewards (RLVR) into the data generation pipeline. By adopting RLVR to refine captions for geometric images synthesized from 50 basic geometric relations and using reward signals derived from mathematical problem-solving tasks, our pipeline successfully captures the key features of geometry problem-solving. This enables better task generalization and yields non-trivial improvements. Furthermore, even in out-of-distribution scenarios, the generated dataset enhances the general reasoning capabilities of multimodal large language models, yielding accuracy improvements of 2.8%-4.8% in statistics, arithmetic, algebraic, and numerical tasks with non-geometric input images of MathVista and MathVerse, along with 2.4%-3.9% improvements in Art, Design, Tech, and Engineering tasks in MMMU.

3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but can face catastrophic failures due to the reliance on accurate pixel correspondence across views. The latter was proffered to mitigate these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly generalize to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network. Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. Here, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets.

Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained accuracy due to the absence of explicit multi-view constraints. We introduce the Geometry-Grounded Point Transformer (GGPT), a framework that augments feed-forward reconstruction with reliable sparse geometric guidance. We first propose an improved Structure-from-Motion pipeline based on dense feature matching and lightweight geometric optimisation to efficiently estimate accurate camera poses and partial 3D point clouds from sparse input views. Building on this foundation, we propose a geometry-guided 3D point transformer that refines dense point maps under explicit partial-geometry supervision using an optimised guidance encoding. Extensive experiments demonstrate that our method provides a principled mechanism for integrating geometric priors with dense feed-forward predictions, producing reconstructions that are both geometrically consistent and spatially complete, recovering fine structures and filling gaps in textureless areas. Trained solely on ScanNet++ with VGGT predictions, GGPT generalises across architectures and datasets, substantially outperforming state-of-the-art feed-forward 3D reconstruction models in both in-domain and out-of-domain settings.

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Recovering high-quality depth maps from compressed sources has gained significant attention due to the limitations of consumer-grade depth cameras and the bandwidth restrictions during data transmission. However, current methods still suffer from two challenges. First, bit-depth compression produces a uniform depth representation in regions with subtle variations, hindering the recovery of detailed information. Second, densely distributed random noise reduces the accuracy of estimating the global geometric structure of the scene. To address these challenges, we propose a novel framework, termed geometry-decoupled network (GDNet), for compressed depth map super-resolution that decouples the high-quality depth map reconstruction process by handling global and detailed geometric features separately. To be specific, we propose the fine geometry detail encoder (FGDE), which is designed to aggregate fine geometry details in high-resolution low-level image features while simultaneously enriching them with complementary information from low-resolution context-level image features. In addition, we develop the global geometry encoder (GGE) that aims at suppressing noise and extracting global geometric information effectively via constructing compact feature representation in a low-rank space. We conduct experiments on multiple benchmark datasets, demonstrating that our GDNet significantly outperforms current methods in terms of geometric consistency and detail recovery. In the ECCV 2024 AIM Compressed Depth Upsampling Challenge, our solution won the 1st place award. Our codes are available at: https://github.com/Ian0926/GDNet.

This paper concerns the research problem of point cloud registration to find the rigid transformation to optimally align the source point set with the target one. Learning robust point cloud registration models with deep neural networks has emerged as a powerful paradigm, offering promising performance in predicting the global geometric transformation for a pair of point sets. Existing methods firstly leverage an encoder to regress a latent shape embedding, which is then decoded into a shape-conditioned transformation via concatenation-based conditioning. However, different regions of a 3D shape vary in their geometric structures which makes it more sense that we have a region-conditioned transformation instead of the shape-conditioned one. In this paper we present a Region-Aware point cloud Registration, denoted as RAR, to predict transformation for pairwise point sets in the self-supervised learning fashion. More specifically, we develop a novel region-aware decoder (RAD) module that is formed with an implicit neural region representation parameterized by neural networks. The implicit neural region representation is learned with a self-supervised 3D shape reconstruction loss without the need for region labels. Consequently, the region-aware decoder (RAD) module guides the training of the region-aware transformation (RAT) module and region-aware weight (RAW) module, which predict the transforms and weights for different regions respectively. The global geometric transformation from source point set to target one is then formed by the weighted fusion of region-aware transforms. Compared to the state-of-the-art approaches, our experiments show that our RAR achieves superior registration performance over various benchmark datasets (e.g. ModelNet40).

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

Given a monocular video, the goal of video re-rendering is to generate views of the scene from a novel camera trajectory. Existing methods face two distinct challenges. Geometrically unconditioned models lack spatial awareness, leading to drift and deformation under viewpoint changes. On the other hand, geometrically-conditioned models depend on estimated depth and explicit reconstruction, making them susceptible to depth inaccuracies and calibration errors. We propose to address these challenges by using the implicit geometric knowledge embedded in the latent space of a large 4D reconstruction model to condition the video generation process. These latents capture scene structure in a continuous space without explicit reconstruction. Therefore, they provide a flexible representation that allows the pretrained diffusion prior to regularize errors more effectively. By jointly conditioning on these latents and source camera poses, we demonstrate that our model achieves state-of-the-art results on the video re-rendering task. Project webpage is https://lavr-4d-scene-rerender.github.io/

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

Recovering pixel-wise geometric properties from a single image is fundamentally ill-posed due to appearance ambiguity and non-injective mappings between 2D observations and 3D structures. While discriminative regression models achieve strong performance through large-scale supervision, their success is bounded by the scale, quality and diversity of available data and limited physical reasoning. Recent diffusion models exhibit powerful world priors that encode geometry and semantics learned from massive image-text data, yet directly reusing their stochastic generative formulation is suboptimal for deterministic geometric inference: the former is optimized for diverse and high-fidelity image generation, whereas the latter requires stable and accurate predictions. In this work, we propose Lotus-2, a two-stage deterministic framework for stable, accurate and fine-grained geometric dense prediction, aiming to provide an optimal adaption protocol to fully exploit the pre-trained generative priors. Specifically, in the first stage, the core predictor employs a single-step deterministic formulation with a clean-data objective and a lightweight local continuity module (LCM) to generate globally coherent structures without grid artifacts. In the second stage, the detail sharpener performs a constrained multi-step rectified-flow refinement within the manifold defined by the core predictor, enhancing fine-grained geometry through noise-free deterministic flow matching. Using only 59K training samples, less than 1% of existing large-scale datasets, Lotus-2 establishes new state-of-the-art results in monocular depth estimation and highly competitive surface normal prediction. These results demonstrate that diffusion models can serve as deterministic world priors, enabling high-quality geometric reasoning beyond traditional discriminative and generative paradigms.

Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face notable computational challenges in maintaining cross-view consistency and generating high-resolution outputs. To address these issues, we propose the Geometry-guided Multi-View Diffusion Model, which incorporates mechanisms for extracting multi-view geometric information and adjusting the intensity of geometric features to generate images that are both consistent across views and rich in detail. Specifically, we design a multi-view geometry information extraction module that leverages depth maps, normal maps, and foreground segmentation masks to construct a shared geometric structure, ensuring shape and structural consistency across different views. To enhance consistency and detail restoration during generation, we develop a decoupled geometry-enhanced attention mechanism that strengthens feature focus on key geometric details, thereby improving overall image quality and detail preservation. Furthermore, we apply an adaptive learning strategy that fine-tunes the model to better capture spatial relationships and visual coherence between the generated views, ensuring realistic results. Our model also incorporates an iterative refinement process that progressively improves the output quality through multiple stages of image generation. Finally, a dynamic geometry information intensity adjustment mechanism is proposed to adaptively regulate the influence of geometric data, optimizing overall quality while ensuring the naturalness of generated images. More details can be found on the project page: https://sobeymil.github.io/GeoMVD.com.

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

In this work, we introduce CAD-Coder, a novel framework that reformulates text-to-CAD as the generation of CadQuery scripts - a Python-based, parametric CAD language. This representation enables direct geometric validation, a richer modeling vocabulary, and seamless integration with existing LLMs. To further enhance code validity and geometric fidelity, we propose a two-stage learning pipeline: (1) supervised fine-tuning on paired text-CadQuery data, and (2) reinforcement learning with Group Reward Policy Optimization (GRPO), guided by a CAD-specific reward comprising both a geometric reward (Chamfer Distance) and a format reward. We also introduce a chain-of-thought (CoT) planning process to improve model reasoning, and construct a large-scale, high-quality dataset of 110K text-CadQuery-3D model triplets and 1.5K CoT samples via an automated pipeline. Extensive experiments demonstrate that CAD-Coder enables LLMs to generate diverse, valid, and complex CAD models directly from natural language, advancing the state of the art of text-to-CAD generation and geometric reasoning.

6D pose estimation of rigid objects is a long-standing and challenging task in computer vision. Recently, the emergence of deep learning reveals the potential of Convolutional Neural Networks (CNNs) to predict reliable 6D poses. Given that direct pose regression networks currently exhibit suboptimal performance, most methods still resort to traditional techniques to varying degrees. For example, top-performing methods often adopt an indirect strategy by first establishing 2D-3D or 3D-3D correspondences followed by applying the RANSAC-based PnP or Kabsch algorithms, and further employing ICP for refinement. Despite the performance enhancement, the integration of traditional techniques makes the networks time-consuming and not end-to-end trainable. Orthogonal to them, this paper introduces a fully learning-based object pose estimator. In this work, we first perform an in-depth investigation of both direct and indirect methods and propose a simple yet effective Geometry-guided Direct Regression Network (GDRN) to learn the 6D pose from monocular images in an end-to-end manner. Afterwards, we introduce a geometry-guided pose refinement module, enhancing pose accuracy when extra depth data is available. Guided by the predicted coordinate map, we build an end-to-end differentiable architecture that establishes robust and accurate 3D-3D correspondences between the observed and rendered RGB-D images to refine the pose. Our enhanced pose estimation pipeline GDRNPP (GDRN Plus Plus) conquered the leaderboard of the BOP Challenge for two consecutive years, becoming the first to surpass all prior methods that relied on traditional techniques in both accuracy and speed. The code and models are available at https://github.com/shanice-l/gdrnpp_bop2022.

We present WorldMirror, an all-in-one, feed-forward model for versatile 3D geometric prediction tasks. Unlike existing methods constrained to image-only inputs or customized for a specific task, our framework flexibly integrates diverse geometric priors, including camera poses, intrinsics, and depth maps, while simultaneously generating multiple 3D representations: dense point clouds, multi-view depth maps, camera parameters, surface normals, and 3D Gaussians. This elegant and unified architecture leverages available prior information to resolve structural ambiguities and delivers geometrically consistent 3D outputs in a single forward pass. WorldMirror achieves state-of-the-art performance across diverse benchmarks from camera, point map, depth, and surface normal estimation to novel view synthesis, while maintaining the efficiency of feed-forward inference. Code and models will be publicly available soon.

In the field of monocular 3D detection, it is common practice to utilize scene geometric clues to enhance the detector's performance. However, many existing works adopt these clues explicitly such as estimating a depth map and back-projecting it into 3D space. This explicit methodology induces sparsity in 3D representations due to the increased dimensionality from 2D to 3D, and leads to substantial information loss, especially for distant and occluded objects. To alleviate this issue, we propose MonoNeRD, a novel detection framework that can infer dense 3D geometry and occupancy. Specifically, we model scenes with Signed Distance Functions (SDF), facilitating the production of dense 3D representations. We treat these representations as Neural Radiance Fields (NeRF) and then employ volume rendering to recover RGB images and depth maps. To the best of our knowledge, this work is the first to introduce volume rendering for M3D, and demonstrates the potential of implicit reconstruction for image-based 3D perception. Extensive experiments conducted on the KITTI-3D benchmark and Waymo Open Dataset demonstrate the effectiveness of MonoNeRD. Codes are available at https://github.com/cskkxjk/MonoNeRD.

We present Wid3R, a feed-forward neural network for visual geometry reconstruction that supports wide field-of-view camera models. Prior methods typically assume that input images are rectified or captured with pinhole cameras, since both their architectures and training datasets are tailored to perspective images only. These assumptions limit their applicability in real-world scenarios that use fisheye or panoramic cameras and often require careful calibration and undistortion. In contrast, Wid3R is a generalizable multi-view 3D estimation method that can model wide field-of-view camera types. Our approach leverages a ray representation with spherical harmonics and a novel camera model token within the network, enabling distortion-aware 3D reconstruction. Furthermore, Wid3R is the first multi-view foundation model to support feed-forward 3D reconstruction directly from 360 imagery. It demonstrates strong zero-shot robustness and consistently outperforms prior methods, achieving improvements of up to +77.33 on Stanford2D3D.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

Neural multivariate regression underpins a wide range of domains such as control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit generalization in classification, we find that analogous collapse in regression consistently degrades performance. To explain this contrast, we analyze models through the lens of intrinsic dimension. Across control tasks and synthetic datasets, we estimate the intrinsic dimension of last-layer features (ID_H) and compare it with that of the regression targets (ID_Y). Collapsed models exhibit ID_H < ID_Y, leading to over-compression and poor generalization, whereas non-collapsed models typically maintain ID_H > ID_Y. For the non-collapsed models, performance with respect to ID_H depends on the data quantity and noise levels. From these observations, we identify two regimes (over-compressed and under-compressed) that determine when expanding or reducing feature dimensionality improves performance. Our results provide new geometric insights into neural regression and suggest practical strategies for enhancing generalization.

We introduce GeoWizard, a new generative foundation model designed for estimating geometric attributes, e.g., depth and normals, from single images. While significant research has already been conducted in this area, the progress has been substantially limited by the low diversity and poor quality of publicly available datasets. As a result, the prior works either are constrained to limited scenarios or suffer from the inability to capture geometric details. In this paper, we demonstrate that generative models, as opposed to traditional discriminative models (e.g., CNNs and Transformers), can effectively address the inherently ill-posed problem. We further show that leveraging diffusion priors can markedly improve generalization, detail preservation, and efficiency in resource usage. Specifically, we extend the original stable diffusion model to jointly predict depth and normal, allowing mutual information exchange and high consistency between the two representations. More importantly, we propose a simple yet effective strategy to segregate the complex data distribution of various scenes into distinct sub-distributions. This strategy enables our model to recognize different scene layouts, capturing 3D geometry with remarkable fidelity. GeoWizard sets new benchmarks for zero-shot depth and normal prediction, significantly enhancing many downstream applications such as 3D reconstruction, 2D content creation, and novel viewpoint synthesis.

Reconstructing 3D scenes using 3D Gaussian Splatting (3DGS) from sparse views is an ill-posed problem due to insufficient information, often resulting in noticeable artifacts. While recent approaches have sought to leverage generative priors to complete information for under-constrained regions, they struggle to generate content that remains consistent with input observations. To address this challenge, we propose GSFixer, a novel framework designed to improve the quality of 3DGS representations reconstructed from sparse inputs. The core of our approach is the reference-guided video restoration model, built upon a DiT-based video diffusion model trained on paired artifact 3DGS renders and clean frames with additional reference-based conditions. Considering the input sparse views as references, our model integrates both 2D semantic features and 3D geometric features of reference views extracted from the visual geometry foundation model, enhancing the semantic coherence and 3D consistency when fixing artifact novel views. Furthermore, considering the lack of suitable benchmarks for 3DGS artifact restoration evaluation, we present DL3DV-Res which contains artifact frames rendered using low-quality 3DGS. Extensive experiments demonstrate our GSFixer outperforms current state-of-the-art methods in 3DGS artifact restoration and sparse-view 3D reconstruction. Project page: https://github.com/GVCLab/GSFixer.

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

Absolute Pose Regression (APR) methods use deep neural networks to directly regress camera poses from RGB images. However, the predominant APR architectures only rely on 2D operations during inference, resulting in limited accuracy of pose estimation due to the lack of 3D geometry constraints or priors. In this work, we propose a test-time refinement pipeline that leverages implicit geometric constraints using a robust feature field to enhance the ability of APR methods to use 3D information during inference. We also introduce a novel Neural Feature Synthesizer (NeFeS) model, which encodes 3D geometric features during training and directly renders dense novel view features at test time to refine APR methods. To enhance the robustness of our model, we introduce a feature fusion module and a progressive training strategy. Our proposed method achieves state-of-the-art single-image APR accuracy on indoor and outdoor datasets.

Camera redirection aims to replay a dynamic scene from a single monocular video under a user-specified camera trajectory. However, large-angle redirection is inherently ill-posed: a monocular video captures only a narrow spatio-temporal view of a dynamic 3D scene, providing highly partial observations of the underlying 4D world. The key challenge is therefore to recover a complete and coherent representation from this limited input, with consistent geometry and motion. While recent diffusion-based methods achieve impressive results, they often break down under large-angle viewpoint changes far from the original trajectory, where missing visual grounding leads to severe geometric ambiguity and temporal inconsistency. To address this, we present FreeOrbit4D, an effective training-free framework that tackles this geometric ambiguity by recovering a geometry-complete 4D proxy as structural grounding for video generation. We obtain this proxy by decoupling foreground and background reconstructions: we unproject the monocular video into a static background and geometry-incomplete foreground point clouds in a unified global space, then leverage an object-centric multi-view diffusion model to synthesize multi-view images and reconstruct geometry-complete foreground point clouds in canonical object space. By aligning the canonical foreground point cloud to the global scene space via dense pixel-synchronized 3D--3D correspondences and projecting the geometry-complete 4D proxy onto target camera viewpoints, we provide geometric scaffolds that guide a conditional video diffusion model. Extensive experiments show that FreeOrbit4D produces more faithful redirected videos under challenging large-angle trajectories, and our geometry-complete 4D proxy further opens a potential avenue for practical applications such as edit propagation and 4D data generation. Project page and code will be released soon.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

We propose a system for rearranging objects in a scene to achieve a desired object-scene placing relationship, such as a book inserted in an open slot of a bookshelf. The pipeline generalizes to novel geometries, poses, and layouts of both scenes and objects, and is trained from demonstrations to operate directly on 3D point clouds. Our system overcomes challenges associated with the existence of many geometrically-similar rearrangement solutions for a given scene. By leveraging an iterative pose de-noising training procedure, we can fit multi-modal demonstration data and produce multi-modal outputs while remaining precise and accurate. We also show the advantages of conditioning on relevant local geometric features while ignoring irrelevant global structure that harms both generalization and precision. We demonstrate our approach on three distinct rearrangement tasks that require handling multi-modality and generalization over object shape and pose in both simulation and the real world. Project website, code, and videos: https://anthonysimeonov.github.io/rpdiff-multi-modal/

Multimodal Large Language Models (MLLMs) struggle with complex geometric reasoning, largely because "black box" outcome-based supervision fails to distinguish between lucky guesses and rigorous deduction. To address this, we introduce a paradigm shift towards subgoal-level evaluation and learning. We first construct GeoGoal, a benchmark synthesized via a rigorous formal verification data engine, which converts abstract proofs into verifiable numeric subgoals. This structure reveals a critical divergence between reasoning quality and outcome accuracy. Leveraging this, we propose the Sub-Goal Verifiable Reward (SGVR) framework, which replaces sparse signals with dense rewards based on the Skeleton Rate. Experiments demonstrate that SGVR not only enhances geometric performance (+9.7%) but also exhibits strong generalization, transferring gains to general math (+8.0%) and other general reasoning tasks (+2.8%), demonstrating broad applicability across diverse domains.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

Single-image room layout reconstruction aims to reconstruct the enclosed 3D structure of a room from a single image. Most previous work relies on the cuboid-shape prior. This paper considers a more general indoor assumption, i.e., the room layout consists of a single ceiling, a single floor, and several vertical walls. To this end, we first employ Convolutional Neural Networks to detect planes and vertical lines between adjacent walls. Meanwhile, estimating the 3D parameters for each plane. Then, a simple yet effective geometric reasoning method is adopted to achieve room layout reconstruction. Furthermore, we optimize the 3D plane parameters to reconstruct a geometrically consistent room layout between planes and lines. The experimental results on public datasets validate the effectiveness and efficiency of our method.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

We explore the task of geometric reconstruction of images captured from a mixture of ground and aerial views. Current state-of-the-art learning-based approaches fail to handle the extreme viewpoint variation between aerial-ground image pairs. Our hypothesis is that the lack of high-quality, co-registered aerial-ground datasets for training is a key reason for this failure. Such data is difficult to assemble precisely because it is difficult to reconstruct in a scalable way. To overcome this challenge, we propose a scalable framework combining pseudo-synthetic renderings from 3D city-wide meshes (e.g., Google Earth) with real, ground-level crowd-sourced images (e.g., MegaDepth). The pseudo-synthetic data simulates a wide range of aerial viewpoints, while the real, crowd-sourced images help improve visual fidelity for ground-level images where mesh-based renderings lack sufficient detail, effectively bridging the domain gap between real images and pseudo-synthetic renderings. Using this hybrid dataset, we fine-tune several state-of-the-art algorithms and achieve significant improvements on real-world, zero-shot aerial-ground tasks. For example, we observe that baseline DUSt3R localizes fewer than 5% of aerial-ground pairs within 5 degrees of camera rotation error, while fine-tuning with our data raises accuracy to nearly 56%, addressing a major failure point in handling large viewpoint changes. Beyond camera estimation and scene reconstruction, our dataset also improves performance on downstream tasks like novel-view synthesis in challenging aerial-ground scenarios, demonstrating the practical value of our approach in real-world applications.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

In this paper, we present a new method for multi-view geometric reconstruction. In recent years, large vision models have rapidly developed, performing excellently across various tasks and demonstrating remarkable generalization capabilities. Some works use large vision models for monocular depth estimation, which have been applied to facilitate multi-view reconstruction tasks in an indirect manner. Due to the ambiguity of the monocular depth estimation task, the estimated depth values are usually not accurate enough, limiting their utility in aiding multi-view reconstruction. We propose to incorporate SfM information, a strong multi-view prior, into the depth estimation process, thus enhancing the quality of depth prediction and enabling their direct application in multi-view geometric reconstruction. Experimental results on public real-world datasets show that our method significantly improves the quality of depth estimation compared to previous monocular depth estimation works. Additionally, we evaluate the reconstruction quality of our approach in various types of scenes including indoor, streetscape, and aerial views, surpassing state-of-the-art MVS methods. The code and supplementary materials are available at https://zju3dv.github.io/murre/ .

We present GenesisGeo, an automated theorem prover in Euclidean geometry. We have open-sourced a large-scale geometry dataset of 21.8 million geometric problems, over 3 million of which contain auxiliary constructions. Specially, we significantly accelerate the symbolic deduction engine DDARN by 120x through theorem matching, combined with a C++ implementation of its core components. Furthermore, we build our neuro-symbolic prover, GenesisGeo, upon Qwen3-0.6B-Base, which solves 24 of 30 problems (IMO silver medal level) in the IMO-AG-30 benchmark using a single model, and achieves 26 problems (IMO gold medal level) with a dual-model ensemble.

Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a highly efficient method for geometry theorem proving that runs entirely on CPUs without relying on neural network-based inference. Our initial study shows that a simple random strategy for adding auxiliary points can achieve silver-medal level human performance on IMO. Building on this, we propose HAGeo, a Heuristic-based method for adding Auxiliary constructions in Geometric deduction that solves 28 of 30 problems on the IMO-30 benchmark, achieving gold-medal level performance and surpassing AlphaGeometry, a competitive neural network-based approach, by a notable margin. To evaluate our method and existing approaches more comprehensively, we further construct HAGeo-409, a benchmark consisting of 409 geometry problems with human-assessed difficulty levels. Compared with the widely used IMO-30, our benchmark poses greater challenges and provides a more precise evaluation, setting a higher bar for geometry theorem proving.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

We introduce Temporal Residual Jacobians as a novel representation to enable data-driven motion transfer. Our approach does not assume access to any rigging or intermediate shape keyframes, produces geometrically and temporally consistent motions, and can be used to transfer long motion sequences. Central to our approach are two coupled neural networks that individually predict local geometric and temporal changes that are subsequently integrated, spatially and temporally, to produce the final animated meshes. The two networks are jointly trained, complement each other in producing spatial and temporal signals, and are supervised directly with 3D positional information. During inference, in the absence of keyframes, our method essentially solves a motion extrapolation problem. We test our setup on diverse meshes (synthetic and scanned shapes) to demonstrate its superiority in generating realistic and natural-looking animations on unseen body shapes against SoTA alternatives. Supplemental video and code are available at https://temporaljacobians.github.io/ .

Online 3D occupancy prediction provides a comprehensive spatial understanding of embodied environments. While the innovative EmbodiedOcc framework utilizes 3D semantic Gaussians for progressive indoor occupancy prediction, it overlooks the geometric characteristics of indoor environments, which are primarily characterized by planar structures. This paper introduces EmbodiedOcc++, enhancing the original framework with two key innovations: a Geometry-guided Refinement Module (GRM) that constrains Gaussian updates through plane regularization, along with a Semantic-aware Uncertainty Sampler (SUS) that enables more effective updates in overlapping regions between consecutive frames. GRM regularizes the position update to align with surface normals. It determines the adaptive regularization weight using curvature-based and depth-based constraints, allowing semantic Gaussians to align accurately with planar surfaces while adapting in complex regions. To effectively improve geometric consistency from different views, SUS adaptively selects proper Gaussians to update. Comprehensive experiments on the EmbodiedOcc-ScanNet benchmark demonstrate that EmbodiedOcc++ achieves state-of-the-art performance across different settings. Our method demonstrates improved edge accuracy and retains more geometric details while ensuring computational efficiency, which is essential for online embodied perception. The code will be released at: https://github.com/PKUHaoWang/EmbodiedOcc2.

Three-dimensional Gaussian Splatting (3DGS) has recently emerged as an efficient representation for novel-view synthesis, achieving impressive visual quality. However, in scenes dominated by large and low-texture regions, common in indoor environments, the photometric loss used to optimize 3DGS yields ambiguous geometry and fails to recover high-fidelity 3D surfaces. To overcome this limitation, we introduce PlanarGS, a 3DGS-based framework tailored for indoor scene reconstruction. Specifically, we design a pipeline for Language-Prompted Planar Priors (LP3) that employs a pretrained vision-language segmentation model and refines its region proposals via cross-view fusion and inspection with geometric priors. 3D Gaussians in our framework are optimized with two additional terms: a planar prior supervision term that enforces planar consistency, and a geometric prior supervision term that steers the Gaussians toward the depth and normal cues. We have conducted extensive experiments on standard indoor benchmarks. The results show that PlanarGS reconstructs accurate and detailed 3D surfaces, consistently outperforming state-of-the-art methods by a large margin. Project page: https://planargs.github.io

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.

3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of fragments grows, since the target shape is unknown and fragments provide weak semantic cues. Existing end-to-end approaches are prone to cascading failures due to unreliable contact reasoning, most notably inaccurate fragment adjacencies. To address this, we propose Structure-Aware Reassembly (SARe), a generative framework with SARe-Gen for Euclidean-space assembly generation and SARe-Refine for inference-time refinement, with explicit contact modeling. SARe-Gen jointly predicts fracture-surface token probabilities and an inter-fragment contact graph to localize contact regions and infer candidate adjacencies. It adopts a query-point-based conditioning scheme and extracts aligned local geometric tokens at query locations from a frozen geometry encoder, yielding queryable structural representations without additional structural pretraining. We further introduce an inference-time refinement stage, SARe-Refine. By verifying candidate contact edges with geometric-consistency checks, it selects reliable substructures and resamples the remaining uncertain regions while keeping verified parts fixed, leading to more stable and consistent assemblies in the many-fragment regime. We evaluate SARe across three settings, including synthetic fractures, simulated fractures from scanned real objects, and real physically fractured scans. The results demonstrate state-of-the-art performance, with more graceful degradation and higher success rates as the fragment count increases in challenging large-scale reassembly.

Point cloud analysis is challenging due to irregularity and unordered data structure. To capture the 3D geometries, prior works mainly rely on exploring sophisticated local geometric extractors using convolution, graph, or attention mechanisms. These methods, however, incur unfavorable latency during inference, and the performance saturates over the past few years. In this paper, we present a novel perspective on this task. We notice that detailed local geometrical information probably is not the key to point cloud analysis -- we introduce a pure residual MLP network, called PointMLP, which integrates no sophisticated local geometrical extractors but still performs very competitively. Equipped with a proposed lightweight geometric affine module, PointMLP delivers the new state-of-the-art on multiple datasets. On the real-world ScanObjectNN dataset, our method even surpasses the prior best method by 3.3% accuracy. We emphasize that PointMLP achieves this strong performance without any sophisticated operations, hence leading to a superior inference speed. Compared to most recent CurveNet, PointMLP trains 2x faster, tests 7x faster, and is more accurate on ModelNet40 benchmark. We hope our PointMLP may help the community towards a better understanding of point cloud analysis. The code is available at https://github.com/ma-xu/pointMLP-pytorch.