3D Geometry

Despite the remarkable prowess of Vision-Language Models (VLMs) in general multimodal tasks, they remain fundamentally flat'' when reasoning about the physical world. We argue that this spatial bottleneck stems from a profound dimensional mismatch: while VLMs are trained to interpret 2D projections, true spatial reasoning demands the recovery of latent 3D geometry and temporal continuity. To conquer this high-dimensional complexity, we advocate a shift from monolithic learning to a divide and conquer'' paradigm. We present FactoSR, a factorized reinforcement learning framework that explicitly interpret the dimensions collapsed by visual projection. At its core, FactoSR decomposes the monolithic problem of world-consistent reasoning into three orthogonal, geometric sub-objectives: planar correspondence ($XY$), depth consistency ($Z$), and temporal reversibility ($T$). By optimizing these verifiable constraints within a unified policy learning mechanism, we effectively transform an ill-posed projection recovery problem into a series of tangible reasoning steps. Extensive evaluations on multi-view and video benchmarks demonstrate that this elegant decomposition yields substantial gains in 3D and 4D reasoning, achieving a 5.9% boost on VSI-Bench and 4.5% on All-Angles-Bench. Our findings suggest that reinforcing explicit, factorized 4D consistency is a critical step toward evolving VLMs into robust, world-aware reasoners.

We present PointGT, a point-based 3D representation that enables simultaneous editing of object geometry and appearance. Existing reconstruction and view synthesis techniques produce volumetric 3D representations that are high-quality and photorealistic, but are difficult to edit. In particular, recent efforts to enable texture editing for 3D Gaussian Splatting representations are not compatible with geometry edits and deformations. Our method combines a point-based representation that is well-suited for geometry deformations with a learned UV mapping technique that enables high-resolution texture editing. We show that PointGT enables fine-grained editing of both geometry and texture in point-based neural representations with high rendering quality.

Dense 3D reconstruction is critical for clinical endoscopic navigation and documentation. While Gaussian Splatting SLAM systems show promise in this domain, they fundamentally rely on strict multi-view photometric consistency. In routine procedures, this assumption is severely violated by intermittent optical degradations like moving debris and water flushing. Standard systems erroneously fuse these cameraattached artifacts into the persistent 3D geometry, causing severe tracking drift and irreversible map corruption. To address this limitation, we propose EndoMD-SLAM, a framework designed to maintain stability under optical degradation through specialized tracking and mapping mechanisms. On the tracking side, a memory-driven gating mechanism detects unreliable observations to suspend map updates and utilizes historical keyframes for drift-aware relocalization. On the mapping side, a self-supervised static-transient decomposition isolates visual contaminants into a dedicated transient field. This explicit separation prevents artifacts from structurally entangling with the persistent anatomical map. We curate a degradationfocused benchmark from colonoscopy videos to systematically evaluate these failure modes. Extensive experiments show that while standard baselines fail under severe optical degradation, EndoMD-SLAM preserves geometric integrity, reducing absolute trajectory error by 91% and improving rendering fidelity by 9.9 dB PSNR.

We propose a convolutional neural shading (CNS), a novel pipeline to reconstruct high-quality 3D shapes from multi-view images. Several recent studies have used neural radiance fields and other neural differentiable rendering methods to understand 3D geometry. However, these approaches rely on single-point geometric information, such as positions and normals of the surface, leading to a lack of detailed local geometry. Our approach addresses the inherent limitations of single-point information by leveraging a neural shader to capture variations even in dark and textureless regions with a convolutional neural shader, resulting in far more accurate geometry predictions. Additionally, our method mitigates surface irregularities at image boundaries by introducing a fine-detail displacement network, which utilizes spatial information of surface geometry and learns fine displacement details by correlating neighboring values in the rendering coordinates. Through extensive experiments, our proposed method has demonstrated significant quality improvements in the reconstructed shapes and rendered images over current state-of-the-art methods.

Existing image manipulation localization (IML) methods rely heavily on 2D forensic cues, such as low-level artifacts, noise traces, and semantic inconsistencies in the manipulated image. While effective in many cases, these cues become much less discriminative when manipulated regions are well blended with their surrounding context in appearance. In such cases, a manipulated region may remain locally appearance-consistent, but still violate the geometric structure of the surrounding scene. This limitation motivates us to go beyond purely 2D evidence and introduce geometric reasoning into IML. To this end, we leverage monocular reconstruction to obtain auxiliary geometric cues, including depth and surface normals. However, a key challenge lies in the fact that reconstructed geometry on manipulated images is inherently noisy and cannot be used naively. Rather than treating depth and normals as direct evidence, we estimate their reliability and exploit them selectively for localization. Based on this principle, we design a geometry-aware framework (GFrame) that fuses reliable geometric cues with RGB features and propagates them across scales to improve fine-grained localization. Extensive experiments show that the proposed method achieves excellent performance under limited budget constraints. These results indicate that reliable 3D geometry provides complementary forensic evidence beyond traditional 2D cues for IML. Related code will be released.

Monocular geometry estimation has recently achieved impressive performance across diverse scenes. However, state-of-the-art models still face notable distortion in local 3D structure, especially in fine details, like thin structures and small objects. We attribute this limitation to an architectural mismatch: most current models decode 3D geometry within a 2D parameterization, where feature interactions are governed by image-plane proximity rather than true 3D spatial relationships. This inadvertently mixes features from geometrically distant surfaces, resulting in over-smoothed geometry particularly around thin or elongated structure. In this paper, we propose MoGe-3, a fine-detail monocular geometry estimation model with Self-Guided Sparse 3D Refinement (SSR) that lifts monocular geometry modeling from 2D image space to 3D space for high-fidelity metric-scale point maps. MoGe-3 lifts the coarse point map from a foundation base model onto a sparse voxel shell and refines it via SSR. The SSR employs sparse convolutions that aggregate features based on 3D spatial locality, avoiding feature mixing across depth discontinuities. Extensive experiments on diverse datasets demonstrate that MoGe-3 significantly outperforms existing approaches in recovering fine detailed 3D geometry across both quantitative metrics and qualitative visualizations. Project page: https://qft-333.github.io/moge3page/

Autonomous driving requires both safe and efficient planning decisions in dynamic 3D environments. Although recent Vision/Video-Action models learn policies directly from visual observations and scale well with advances in vision transformers and large-scale training data, they often lack explicit geometric grounding and future-aware spatial guidance, limiting their ability to balance collision avoidance and driving progress. In this work, we propose GeoWorldAD, a geometry world action model that grounds trajectory planning in ego-aligned 3D space and anticipates short-horizon scene evolution with latent future geometry tokens. Present geometry provides essential spatial constraints for safe planning, while future geometry reveals how surrounding agents and ego-centric free space may evolve, reducing overly conservative decisions without sacrificing safety. To efficiently exploit these geometric cues, GeoWorldAD progressively aggregates multi-scale present geometry and latent future geometry through iterative trajectory refinement. Experiments on NAVSIM v1 and v2 demonstrate state-of-the-art performance, highlighting the effectiveness of explicit 3D geometry grounding and future geometry world modeling for safe and efficient autonomous driving.

3D geometric tooth alignment planning, which determines sequential trajectories from initial malocclusion to the final target alignment, is a cornerstone of modern digital orthodontics. This paper presents a novel deep reinforcement learning (DRL) framework to automate the generation of these alignment paths. We formulate the planning process as a Markov Decision Process (MDP) to capture its sequential decision-making nature, focusing on optimizing geometric trajectories while integrating essential spatial constraints, such as inter-dental collision avoidance and path efficiency. The proposed method leverages the Deep Deterministic Policy Gradient (DDPG) algorithm, enhanced by three key innovations: (1) a Transformer-based agent to model complex spatial interactions between teeth and manage high-dimensional state-action spaces; (2) a dynamic masking scheme that restricts movement to a sparse subset of teeth per step, better reflecting the clinical logic of sequential alignment; and (3) a two-stage curriculum learning strategy that gradually increases task difficulty to ensure training stability and efficient path discovery. We evaluate our approach on a dataset of 10K expert-designed treatment plans based on clinical data. Experimental results demonstrate that our method outperforms existing baselines in terms of path safety and geometric efficiency, providing a robust and automated solution for 3D geometric orthodontic alignment planning.

We introduce a novel mathematical framework for analyzing and generating complex tree-shaped 3D objects, such as botanical trees and plants, which deform both in their 3D geometry and branching structure. Unlike previous works, which either consider only the skeletal structure of tree-like objects or approximate their 3D geometry using branch thickness, the proposed framework accurately models both the 3D geometry of the tree branches and the way they are interconnected. In this paper, we first generalize the Square Root Normal Fields (SRNF) representation, originally proposed for the statistical analysis of genus-0 surfaces, to tree-shaped 3D objects. We then treat tree-shaped 3D objects as points on a novel Riemannian tree-shape space equipped with a novel Riemannian metric that measures the amount of surface bending and stretching, and structural changes one needs to apply to one 3D tree-shape to align it with another. This way, deformations become trajectories in this novel tree-shape space. We analyze the theoretical properties of this novel tree-shape space and the corresponding metric and develop algorithms for computing point-wise and branch-wise correspondences and geodesic paths between complex 3D trees. We finally show how to use these building blocks for (1) computing statistical summaries, \ie means and modes of variation, of collections of tree-shaped 3D objects, and (2) synthesizing novel tree-shaped 3D objects by sampling from probability distributions fitted to a population of tree-shaped 3D objects. We demonstrate the performance and utility of the proposed framework on real and synthetic plants and botanical trees and show that it significantly outperforms the state-of-the-art.

Estimating 3D geometry in underwater environments presents unique challenges due to light attenuation, scattering, and the absence of large-scale, high-quality 3D annotations. Pioneering methods rely on massive dense annotations that are impractical in underwater settings. In this paper, we propose Wat3R, a cross-domain semi-supervised learning framework designed to adapt feed-forward 3D reconstruction models from air to underwater scenes. Uniquely, our method eliminates the need for any annotated underwater data following a teacher-student architecture, that learns robust geometry representations merely on abundant unlabeled real underwater video footage. We also design a cross-view consistency loss that leverages geometric cues from other views to compensate for the information degradation in the current view caused by water attenuation and scattering. Furthermore, considering the lack of comprehensive evaluation benchmarks, we construct Water3D, a diverse dataset covering various water bodies and underwater scenarios, designed for geometric task evaluation. Experimental results demonstrate that Wat3R outperforms current state-of-the-art methods in underwater multi-view depth estimation and point cloud reconstruction. The dataset and code are available at https://github.com/LSXI7/Wat3R .

Recently, Vision-Language-Action (VLA) models have demonstrated strong generalization across diverse tasks. However, effective robotic manipulation in physical environments fundamentally requires geometric understanding and spatial reasoning. While some VLA approaches attempt to incorporate 3D information, they are constrained by limited data availability and geometric information loss in current 3D encoding pipelines, and fail to jointly capture 3D geometry and temporally structured actions in dynamic environments. To address these limitations, we introduce Lift3D-VLA, a unified VLA framework that equips models with explicit 3D point cloud reasoning and enables temporally coherent action generation. First, building upon our previous work Lift3D, an enhanced 2D model-lifting strategy is proposed to geometrically align 3D points with pretrained 2D positional embeddings. This design enables direct point-cloud encoding within the VLA vision encoder while minimizing spatial information loss. Based on explicit 3D inputs, we propose Geometry-Centric Masked Autoencoding (GC-MAE), a dual-objective self-supervised framework that reconstructs the current point cloud while predicting its future geometric evolution. This formulation allows the 2D vision encoder to internalize both 3D structure and physical dynamics. To fully exploit 3D representations, we further design layer-wise temporal action modeling, which leverages multiple layers of the LLM to collaboratively predict action chunks, enabling temporally consistent predictions. Across 22 simulated tasks and 8 real-world manipulation tasks, Lift3D-VLA achieves 10.8% and 11.1% higher mean success rates on MetaWorld and RLBench than the best-performing prior VLA methods, and outperforms the strongest real-world baseline by 4 percentage points, while exhibiting stronger generalization to out-of-distribution perturbations.

While garments are essential for realistic digital humans, their topological variety makes them much harder to model than parametric bodies. Traditional tailoring relies on 2D sewing patterns, yet bridging these patterns to 3D geometry currently requires physical simulations. We present Stitched Embeddings, the first simulation-free framework to unify 3D garment reconstruction and sewing pattern inference within a single bidirectional latent space. By leveraging the geometric priors of a pretrained 3D foundation model, our approach overcomes the data scarcity typically associated with high-quality garment modeling. We propose to use the BoxMesh as a critical intermediate representation to align 2D panels into 3D configurations without the computational overhead of a simulator. This architecture achieves state-of-the-art accuracy in pattern reconstruction while significantly improving efficiency. Furthermore, our differentiable pipeline enables novel applications, including pattern recovery from meshes and 3D editing from 2D patterns. Finally, this work provides a scalable link between neural 3D vision and the physical garment manufacturing pipeline. Project Page: https://andreus00.github.io/stitchedembeddings

Identifying and grounding precise geometric entities, such as edges, planar regions, and curved surfaces within 3D objects, is foundational to computer-aided design (CAD), robotic manipulation, and scientific simulation. Although modern Vision Language Models (VLMs) have advanced referring segmentation (RIS) in the image domain, extending such language-driven localization to structured 3D geometry is substantially harder. The 3D object appearance is highly sensitive to viewpoints; a single perspective may render a target entity clearly observable, while another may suffer from severe occlusion or foreshortening. In this work, we attempt to solve these challenges with MV-GEL (Multi-View Geometric Entity Localization), a framework for localizing fine-grained geometric entities on polygon meshes from natural language queries. Our key insight is that reliable CAD entity (i.e., faces, edges or solids) localization depends on selecting views that make the queried entity maximally interpretable. We introduce GELviews, a prompt-conditioned ranking module that prioritizes viewpoints based on language prompted observability of geometric CAD entities. Selected views are processed by a VLM-based reasoning segmentation backbone, and predicted masks are lifted to the corresponding meshes via geometry-aware ray casting. Our framework is completely CAD agnostic and relies only on 3D meshes. Experiments show up to a 1.7X improvement in face-level IoU and over 4.5X gains in edge-level F1 compared to vanilla baselines, substantially outperforming CLIP-based and random view sampling, particularly for thin and view-sensitive structures.The dataset, code and trained checkpoints are available at https://github.com/kbali1297/MV-GEL.

Monocular 3D lane detection plays a critical role in autonomous driving, yet recovering reliable 3D geometry from a single image remains challenging due to inherent depth ambiguity. Prior methods project image features into Bird's-Eye-View (BEV) space under a flat-ground assumption, causing geometric distortion on real-world roads. Recent methods instead predict explicit height maps to capture non-planar surfaces, but still rely on sparse anchor-based regression and exploit the recovered geometry merely for spatial transformation rather than semantic understanding. To overcome these limitations, we propose HSDF-Lane, which implicitly models the road surface as a Height-aligned Signed Distance Field (HSDF) over a densely sampled 3D feature volume. Through differentiable rendering, the HSDF jointly produces an accurate height map and surface-aligned features. We further introduce Lane-aware Semantic Positional Encoding (LSPE), which injects a lane-existence prior derived from the surface-aligned features into the transformer queries, coupling geometric structure with semantic guidance. Extensive experiments on the OpenLane benchmark show that HSDF-Lane achieves state-of-the-art performance in both 3D lane detection and height map estimation.

Text-driven Referring Video Object Segmentation (RVOS) aims to locate and segment target objects in videos given natural language. However, existing models are typically trained on 2D image or video datasets with naive segmentation losses, which overlooks the geometric consistency across frames and leads to weak spatial understanding. In this paper, we propose Geometry-enhanced Language-guided Video segmentation (GeoLaV), a two-stage framework that distills 3D geometric knowledge from images to enhance text-driven video segmentation. In the first stage, we perform monocular geometry pretraining with monocular novel-view synthesis, enabling the model to acquire geometry-consistent visual representations via spatial alignment on large-scale single-image datasets. In the second stage, we introduce geometry-aware distillation and fine-tune the model on video segmentation datasets, transferring 3D structural knowledge from a general 3D prior model. This process reinforces 3D awareness and improves both spatiotemporal coherence and language grounding in segmentation. Extensive experiments show that our method using only image segmentation data already provides notable zero-shot generalization in RVOS. When combined with geometry-aware distillation for fine-tuning on videos, our method achieves state-of-the-art performance across multiple RVOS benchmarks. The code is available at https://github.com/Tony1882880/GeoLaV.

In this paper, we present a novel geometry-aware style transfer framework for 3D Gaussian splatting (3DGS) that simultaneously transfers appearance attributes and geometric structures. Unlike prior works that primarily focus on color-based stylization and often overlook structural adaptation, our method explicitly incorporates geometry adaptation through a decoupled optimization scheme that alternately updates color and geometry parameters. This strategy alleviates potential interference between color and geometry updates, leading to stable and consistent scene-level geometry transformation. The decoupled optimization is enabled by the proposed geometry-aware contrastive feature matching (GCFM). GCFM integrates RGB, depth, and edge cues into a contrastive objective and is employed in both optimization phases to effectively transfer structural characteristics from style images to Gaussian primitives. Extensive experiments show that our approach achieves superior performance in both qualitative fidelity and quantitative metrics, significantly outperforming existing 3DGS-based stylization methods. Our code is available at \href{https://github.com/oweixx/gast}{https://github.com/oweixx/gast}.

We present SCOPE (Scale-Consistent One-Pass Estimation of 3D Geometry), a novel approach for estimating 3D geometry from extended monocular video sequences, where existing methods struggle to maintain both geometric accuracy and temporal consistency across hundreds of frames. Our approach generates affine-invariant 3D point maps with shared parameters across entire sequences, enabling consistent scale-invariant representations. We introduce three key innovations: viewpoint-invariant geometry aligning multi-perspective points in a unified reference frame; appearance-invariant learning enforcing consistency across exponential timescales; and frequency-modulated positioning enabling extrapolation to sequences vastly exceeding training length. Experiments across diverse datasets demonstrate significant improvements, reducing relative point map error by 24.2% and temporal alignment error by 34.9% on ScanNet compared to state-of-the-art methods. Our approach handles challenging scenarios with complex camera trajectories and lighting variations while efficiently processing extended sequences in a single pass. Project page: https://scope3d.github.io/.

After the success of 3D Gaussian Splatting (3DGS) for novel view synthesis, many works have explored how to also use it for geometric surface representation. However, extracting accurate geometric information directly from 3DGS remains challenging and can often reduce the appearance rendering quality. In this work, we show that 3DGS in its default form is inheritedly unsuited to represent texture and geometry at the same time, by training with complete ground-truth texture and geometry information. We also propose a simple solution by applying a single additional geometry opacity parameter to each splat, together with an optional transparency-curated optimization pipeline. Our experiments, both with ground-truth and vision foundation model geometric input, show that this change leads to improved rendering and geometry performance on a wide variety of dataset, and especially complex scenes with transparent objects benefit significantly from our method.

Geometric analysis fundamentally distinguishes between \textit{extrinsic} and \textit{intrinsic} perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely \textbf{PRISM}, for \textbf{P}re-training, which learns isometric embeddings by \textbf{R}ecovering the \textbf{I}ntrinsic \textbf{S}urface geodesic \textbf{M}etric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.

Recent feedforward 3D reconstruction methods predict point maps and estimate global 3D geometry remarkably well. However, their predictions still exhibit inaccurate local surface geometry, which is clearly visible qualitatively but only weakly reflected in common metrics. To make these errors more explicit in evaluation, we introduce a point map normal metric that evaluates the local surface orientation induced by neighboring 3D predictions. To reduce these errors, we propose two complementary components: a point gradient matching loss that supervises depth-normalized 3D finite differences, and a Neighborhood Attention Decoder (NAD) that progressively upsamples features and uses Neighborhood Attention for local feature mixing. Across eight zero-shot monocular geometry benchmarks, our model, SurGe, achieves the best average rank for global point map AbsRel and consistently improves local point map and point map normal evaluations.

We present a dense RGB-D SLAM system using differentiable triangles as the 3D map representation. While 3D Gaussian Splatting has emerged as the leading method for novel-view synthesis, triangles remain the standard primitive for traditional rendering hardware, game engines, and downstream tasks requiring explicit geometry such as simulation, collision, and editing. Recent offline methods have demonstrated that an unstructured 'triangle soup' can be optimised into a photorealistic mesh via Delaunay triangulation across a set of posed images. Building upon this insight, we present the first dense SLAM system to employ Triangle Splatting to perform both tracking and mapping through online differentiable rendering of a triangle soup. The map can be converted into a connected mesh on-the-fly via restricted Delaunay triangulation, enabling new online capabilities such as mesh deformation and collision checking. On Replica and TUM-RGBD, our system outperforms baselines on 3D geometry, matches the camera-tracking accuracy, and enables online mesh-based scene editing.

Converting hand-drawn sketches into structured 3D geometries remains challenging due to the difficulty of representing non-Euclidean surfaces and maintaining topological consistency. Existing generative models such as GANs, NeRFs, and diffusion architectures often fail to produce editable manifolds directly usable in downstream design workflows. We present Sketch2MinSurf, a hybrid vision-language and geometric optimization framework that integrates vision-language guidance with minimal-surface theory to generate smooth and editable 3D surfaces from hand-drawn sketches. The core of our approach is a spatial-topological encoding that represents geometry as tuples of node coordinates and real/virtual edge skeletons, enabling stable topological control during generation. We further introduce the Sketch2MinSurf Structural Loss (S2MS-Loss), a reward-modulated objective that jointly constrains geometric reconstruction and topological coherence. On a test set of 100 sketches, Sketch2MinSurf achieves a topological similarity score of 0.844, outperforming existing sketch-to-shape baselines. The generated manifolds are directly editable and free from non-manifold artifacts. A public art installation at a university showcases the method's potential for human-intent-driven 3D form generation. The dataset and code are available at https://anonymous.4open.science/r/Sketch2MinSurf/.

Reconstructing coherent 3D geometry and appearance from unposed multi-view images is a fundamental yet challenging problem in computer vision. Most existing visual geometry foundation models predict explicit geometry by regressing pixel-aligned pointmaps, often suffering from redundancy and limited geometric continuity. We propose IVGT, an Implicit Visual Geometry Transformer that implicitly models continuous and coherent geometry from pose-free multi-view images. This formulation learns a continuous neural scene representation in a canonical coordinate system and supports continuous spatial queries at any 3D positions, retrieving local features to predict signed distance (SDF) values and colors using lightweight decoders. It allows direct extraction of continuous and coherent surface geometry, enabling rendering of RGB images, depth maps, and surface normal maps from arbitrary viewpoints. We train IVGT via multi-dataset joint optimization with 2D supervision and 3D geometric regularization. IVGT demonstrates generalization across scenes and achieves strong performance on various tasks, including mesh and point cloud reconstruction, novel view synthesis, depth and surface normal estimation, and camera pose estimation.

Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

We present a unified framework for 3D geometric abstraction using a single continuous 4D wire, parameterized as a B-spline with spatial coordinates and variable width $(x,y,z,w)$. Existing approaches typically represent shapes as collections of many independent curve segments, which often leads to fragmented structures and limited physical realizability. In contrast, we show that a single continuous spline is sufficiently expressive to capture complex volumetric forms while enforcing global topological coherence. By imposing continuity, our method transforms 3D sketching from a local density-accumulation process into a global routing problem, providing a strong inductive bias toward cleaner aesthetics and improved structural coherence. To enable gradient-based optimization, we introduce a differentiable rendering pipeline that efficiently rasterizes variable-width curves with bounded projection error. This formulation supports robust optimization using modern guidance signals such as Score Distillation Sampling (SDS) or CLIP. We demonstrate applications including image-to-3D abstraction, multi-view wire art generation, and differentiable stylized surface filling. Experiments show that our unified representation produces structures with higher semantic fidelity and improved structural coherence compared to approaches based on collections of discrete curves.

We consider the problem of regenerating 3D objects from 2D images and initial 3D shapes. Most 3D generators operate in a one-shot fashion, converting text or images to a 3D object with limited controllability. We introduce instead MeshReGen, a 3D regenerator that is conditioned on an initial 3D shape. This conceptually simple formulation allows us to support numerous useful tasks, including 3D enhancement, reconstruction, and editing. MeshReGen uses a new conditioning mechanism based on VecSet, which allows the regenerator to update or improve the input geometry with consistent fine-grained details. MeshReGen learns a widely applicable regeneration prior from off-the-shelf 3D datasets via self-supervised pretext tasks and augmentations, without additional annotations. We evaluate both the geometric consistency and fine-grained quality of MeshReGen, achieving state-of-the-art performance in controllable 3D generation across several tasks.

Monocular depth estimation (MDE) is a fundamental yet inherently ill-posed task. Recent vision foundation models (VFMs), particularly DINO-based transformers, have significantly improved accuracy and generalization for dense prediction. Prior works generally follow a unified paradigm: sampling a fixed set of intermediate transformer layers at uniform intervals to build multi-scale features. This common practice implicitly assumes that geometric information is uniformly distributed across layers, which may underutilize the structural 3D cues encoded in VFMs. In this study, we present a systematic layer-wise analysis of DINOv3, revealing that 3D information is distributed non-uniformly: deeper layers exhibit stronger depth predictability and better capture inter-sample geometric variation. Motivated by this, we introduce a Last-Layer-Centric Feature Recombination (LFR) module to enhance geometric expressiveness. LFR treats the final layer as a geometric anchor and adaptively selects complementary intermediate layers according to a minimal-similarity criterion. Selected features are fused with the last-layer representation via compact linear adapters.Extensive experiments show that LFR module consistently improves MDE accuracy and achieves state-of-the-art performance. Our analysis sheds light on how geometric knowledge is organized within VFMs and offers an efficient strategy for unlocking their potential in dense 3D tasks.

Recent unified image generation models have achieved remarkable success by employing MLLMs for semantic understanding and diffusion backbones for image generation. However, these models remain fundamentally limited in spatially-aware tasks due to a lack of intrinsic spatial understanding and the absence of explicit geometric guidance during generation. In this paper, we propose SpatialFusion, a novel framework that internalizes 3D geometric awareness into unified image generation models. Specifically, we first employ a Mixture-of-Transformers (MoT) architecture to augment the MLLM with a parallel spatial transformer to enhance 3D geometric modeling capability. By sharing self-attention with the MLLM, the spatial transformer learns to derive metric-depth maps of target images from rich semantic contexts. These explicit geometric scaffolds are then injected into the diffusion backbone through a specialized depth adapter, providing precise spatial constraints for spatially-coherent image generation. Through a progressive two-stage training strategy, SpatialFusion significantly enhances performance on spatially-aware benchmarks, notably outperforming leading models such as GPT-4o. Additionally, it achieves generalized performance gains across both text-to-image generation and image editing scenarios, all while maintaining negligible inference overhead.

We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in low-overlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, a novel two-stage method that combines geometric, color, and Gaussian information for robust registration. Our approach incorporates a dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the \textbf{Ge}ometric-3D\textbf{GS} module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometric-color context. Leveraging LORA optimization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process, leading to improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap. We validate our method by colorizing the Kitti dataset as ColorKitti and testing on both Color3DMatch and Color3DLoMatch datasets. Our method achieves state-of-the-art performance with \textit{Registration Recall} at 99.9%, \textit{Relative Rotation Error} as low as 0.013, and \textit{Relative Translation Error} as low as 0.024, improving precision by at least a factor of 2.

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings. Shape combines a structured 3D latent grid, a multi-scale geometry-aware tokenizer (MAGNO) with cross-attention, and a transformer processor using grouped-query attention and RMSNorm. A learned reconstruction prior enables per-region attribution for explainable predictions. Pretraining uses masked-token reconstruction of normalized geometry statistics and multi-resolution contrastive consistency. The 10.9M-parameter backbone is pretrained on 61,052 CAD meshes from Thingi10K, MFCAD, and Fusion360. On a held-out split of 2,983 meshes, Shape achieves reconstruction R2 = 0.729 and 98.1% top-1 retrieval under the Wang-Isola protocol, with near-zero reconstruction train/val gap (contrastive scores use a larger evaluation pool). A 2x2 ablation on loss type and target-space normalization shows per-dimension normalization is critical: without it, performance collapses (R2 < 0.14, top-1 < 88%); with it, both losses succeed (R2 > 0.70, top-1 > 96%). Smooth-L1 offers secondary stability. Code, embeddings, and an interactive demo are released at https://github.com/simd-ai/shape.

High-resolution geometric prediction is essential for robust perception in autonomous driving, robotics, and AR/MR, but current foundation models are fundamentally limited by their scalability to real-world, high-resolution scenarios. Direct inference on 2K images with these models incurs prohibitive computational and memory demands, making practical deployment challenging. To tackle the issue, we present 2K Retrofit, a novel framework that enables efficient 2K-resolution inference for any geometric foundation model, without modifying or retraining the backbone. Our approach leverages fast coarse predictions and an entropy-based sparse refinement to selectively enhance high-uncertainty regions, achieving precise and high-fidelity 2K outputs with minimal overhead. Extensive experiments on widely used benchmark demonstrate that 2K Retrofit consistently achieves state-of-the-art accuracy and speed, bridging the gap between research advances and scalable deployment in high-resolution 3D vision applications. Code will be released upon acceptance.

Recent generative models can produce high-fidelity videos, yet they often exhibit 3D spatial geometric inconsistencies. Existing evaluation methods fail to accurately characterize these inconsistencies: fidelity-centric metrics like FVD are insensitive to geometric distortions, while consistency-focused benchmarks often penalize valid foreground dynamics. To address this gap, we introduce SGC, a metric for evaluating 3D \textbf{S}patial \textbf{G}eometric \textbf{C}onsistency in dynamically generated videos. We quantify geometric consistency by measuring the divergence among multiple camera poses estimated from distinct local regions. Our approach first separates static from dynamic regions, then partitions the static background into spatially coherent sub-regions. We predict depth for each pixel, estimate a local camera pose for each subregion, and compute the divergence among these poses to quantify geometric consistency. Experiments on real and generative videos demonstrate that SGC robustly quantifies geometric inconsistencies, effectively identifying critical failures missed by existing metrics.

Accurate 3D reconstruction of vertebral anatomy from ultrasound is important for guiding minimally invasive spine interventions, but it remains challenging due to acoustic shadowing and view-dependent signal variations. We propose an occupancy-based shape completion method that reconstructs complete 3D anatomical geometry from partial ultrasound observations. Crucially for intra-operative applications, our approach extracts the anatomical surface directly from the image, avoiding the need for anatomical labels during inference. This label-free completion relies on a coupled latent space representing both the image appearance and the underlying anatomical shape. By leveraging a Neural Implicit Representation (NIR) that jointly models both spatial occupancy and acoustic interactions, the method uses acoustic parameters to become implicitly aware of the unseen regions without explicit shadowing labels through tracking acoustic signal transmission. We show that this method outperforms state-of-the-art shape completion for B-mode ultrasound by 80% in HD95 score. We validate our approach both in-silico and on phantom US images with registered mesh models from CT labels, demonstrating accurate reconstruction of occluded anatomy and robust generalization across diverse imaging conditions. Code and data will be released on publication.

We introduce MolMiner, a fragment-based, geometry-aware, and order-agnostic autoregressive model for molecular design. MolMiner supports high-dimensional conditional control over twelve physicochemical and structural properties from partial specifications, constructs molecules via symmetry-aware fragment attachments, and conditions each generation step on force-field-relaxed three-dimensional geometry of the partial structure. Conditional control emerges without auxiliary property losses. On targeted property windows, conditioning lifts hit rates by up to 5.25x over unconditional generation and 3.5x over the training distribution itself -- overriding the model's intrinsic biases -- at the cost of a small reduction in unconditional distributional fidelity. MolMiner unifies dynamic geometry, symmetry handling, order-agnostic generation, and scalable multi-property conditioning within a single framework.

Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation. Classical transformation-space voting methods rely on pairwise matching, scaling as O(n^2) and struggling to resolve coherent multi-instance groups. Recent learning approaches advance global symmetry detection but restrict the solution space to reflection planes, failing to capture rotational or translational repetitions such as the legs of a chair or the steps of a staircase. We propose SymCL, a self-supervised contrastive learning framework that detects partial symmetries across rotation, translation, and reflection (with scale-invariant features) and requires no ground truth annotations. By mapping local geodesic patches to a latent space invariant to the Euclidean group, we reformulate symmetry detection as a density-based clustering problem, enabling the simultaneous discovery of multi-instance symmetric relationships in a single forward pass. We evaluate quantitatively on SymPartNet, a new benchmark annotating all PartNet categories with partial symmetry relations, and demonstrate class-agnostic generalization qualitatively on everyday objects outside the training distribution.