Shiqing Xin

Zixiong Wang, Yunxiao Zhang, Rui Xu et al.

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods.

Junjie Gao, Qiujie Dong, Ruian Wang et al.

In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received substantial attention owing to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. Nonetheless, this paradigm exhibits two notable limitations.Firstly, the utilization of the Dual Softmax operation has the potential to promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. This propensity arises from the fact that a source superpoint typically maintains associations with multiple target superpoints. Secondly, it is imperative to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Based on these considerations, we propose {\em OAAFormer} to enhance correspondence quality. On one hand, we introduce a soft matching mechanism, facilitating the propagation of potentially valuable correspondences from coarse to fine levels. Additionally, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7\% in the inlier ratio, as well as an enhancement of 2-4\% in registration recall. =

Qiujie Dong, Xiaoran Gong, Rui Xu et al.

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.

Qinghao Guo, Pengfei Wang, Chen Zong et al.

Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs. Its iterative Voronoi sweep for interference detection leads to redundant predicate evaluations and scales poorly on rotationally symmetric structures (e.g., spheres, cones or cylinders), where candidate counts grow quadratically. We propose P2M++ to address these limitations through three key contributions. First, we adaptively augment the set of mesh vertices with auxiliary sites in regions of high Voronoi vertex density to localize complex interference within minimal spatial regions. Second, we reformulate interference detection as a series of sphere-triangle collision tests centered at Voronoi cell corners, which are efficiently resolved using the base mesh's BVH. Finally, we enhance runtime performance by replacing the standard kd-tree search with a faster recursive dynamic programming implementation. Experimental results demonstrate that P2M++ is 3x-10x faster than the original P2M during preprocessing and 1.5x faster in queries, with even more pronounced gains on rotationally symmetric geometries.

Pengfei Wang, Qinghao Guo, Haisen Zhao et al.

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k=1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p_i is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P_{1:i-1} = {p_1, \dots, p_{i-1}} or within p_i's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1\times--10\times speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries -- enabling k-NN searches within any subset P_{1:m} (m \leq n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

Zimeng Wang, Zhiyang Dou, Rui Xu et al.

We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input or suffer from substantial computational costs, thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.

Zixiong Wang, Pengfei Wang, Pengshuai Wang et al.

Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns the noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised fashion. We use the IMLS to regularize the distance values reported by the MLP while using the MLP to regularize the normals of the data points for running the IMLS. We also prove that at the convergence, our neural network, benefiting from the mutual learning mechanism between the MLP and the IMLS, produces a faithful SDF whose zero-level set approximates the underlying surface. We conducted extensive experiments on various benchmarks, including synthetic scans and real scans. The experimental results show that {\em Neural-IMLS} can reconstruct faithful shapes on various benchmarks with noise and missing parts. The source code can be found at~\url{https://github.com/bearprin/Neural-IMLS}.

Pengfei Wang, Shuangmin Chen, Dongming Yan et al.

The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features -- for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh. In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses. Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification -- effectively capturing the global structure of complex geometries with only a few hundred vertices.

Rui Xu, Longdu Liu, Ningna Wang et al.

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.

Qiujie Dong, Rui Xu, Pengfei Wang et al.

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

Rui Xu, Wenyue Chen, Jiepeng Wang et al.

Gaussian Splattings demonstrate impressive results in multi-view reconstruction based on Gaussian explicit representations. However, the current Gaussian primitives only have a single view-dependent color and an opacity to represent the appearance and geometry of the scene, resulting in a non-compact representation. In this paper, we introduce a new method called SuperGaussians that utilizes spatially varying colors and opacity in a single Gaussian primitive to improve its representation ability. We have implemented bilinear interpolation, movable kernels, and even tiny neural networks as spatially varying functions. Quantitative and qualitative experimental results demonstrate that all three functions outperform the baseline, with the best movable kernels achieving superior novel view synthesis performance on multiple datasets, highlighting the strong potential of spatially varying functions.

Qiujie Dong, Huibiao Wen, Rui Xu et al.

Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high-quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature directions. Second, singular points should be strategically placed and effectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions. To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions...

Rui Xu, Jiepeng Wang, Hao Pan et al.

In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, there are additional attributes which are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes is insufficiently sampled by existing training scheme of diffusion generative models, causing degraded test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses insynchronized time steps for different dimensions and attributes, thus allowing for varying degrees of control over them.

Zhenyu Shu, Junlong Yu, Kai Chao et al.

This paper presents GaussEdit, a framework for adaptive 3D scene editing guided by text and image prompts. GaussEdit leverages 3D Gaussian Splatting as its backbone for scene representation, enabling convenient Region of Interest selection and efficient editing through a three-stage process. The first stage involves initializing the 3D Gaussians to ensure high-quality edits. The second stage employs an Adaptive Global-Local Optimization strategy to balance global scene coherence and detailed local edits and a category-guided regularization technique to alleviate the Janus problem. The final stage enhances the texture of the edited objects using a sophisticated image-to-image synthesis technique, ensuring that the results are visually realistic and align closely with the given prompts. Our experimental results demonstrate that GaussEdit surpasses existing methods in editing accuracy, visual fidelity, and processing speed. By successfully embedding user-specified concepts into 3D scenes, GaussEdit is a powerful tool for detailed and user-driven 3D scene editing, offering significant improvements over traditional methods.

Jiayi Kong, Chen Zong, Junkai Deng et al.

Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Diffusion (VAD), for computing UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.

Zhenyu Shu, Jian Yao, Shiqing Xin

Point cloud completion is a vital task focused on reconstructing complete point clouds and addressing the incompleteness caused by occlusion and limited sensor resolution. Traditional methods relying on fixed local region partitioning, such as k-nearest neighbors, which fail to account for the highly uneven distribution of geometric complexity across different regions of a shape. This limitation leads to inefficient representation and suboptimal reconstruction, especially in areas with fine-grained details or structural discontinuities. This paper proposes a point cloud completion framework called Degree-Flexible Point Graph Completion Network (DFG-PCN). It adaptively assigns node degrees using a detail-aware metric that combines feature variation and curvature, focusing on structurally important regions. We further introduce a geometry-aware graph integration module that uses Manhattan distance for edge aggregation and detail-guided fusion of local and global features to enhance representation. Extensive experiments on multiple benchmark datasets demonstrate that our method consistently outperforms state-of-the-art approaches.

Rui Xu, Tianyang Xue, Qiujie Dong et al.

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to the large number of tokens required and constrained quantization granularity. These issues prevent faithful reproduction of fine geometric details and structured density patterns. We introduce MeshMosaic, a novel local-to-global framework for artist mesh generation that scales to over 100K triangles--substantially surpassing prior methods, which typically handle only around 8K faces. MeshMosaic first segments shapes into patches, generating each patch autoregressively and leveraging shared boundary conditions to promote coherence, symmetry, and seamless connectivity between neighboring regions. This strategy enhances scalability to high-resolution meshes by quantizing patches individually, resulting in more symmetrical and organized mesh density and structure. Extensive experiments across multiple public datasets demonstrate that MeshMosaic significantly outperforms state-of-the-art methods in both geometric fidelity and user preference, supporting superior detail representation and practical mesh generation for real-world applications.

Zhaonan Wang, Manyi Li, ShiQing Xin et al.

Point cloud denoising task aims to recover the clean point cloud from the scanned data coupled with different levels or patterns of noise. The recent state-of-the-art methods often train deep neural networks to update the point locations towards the clean point cloud, and empirically repeat the denoising process several times in order to obtain the denoised results. It is not clear how to efficiently arrange the iterative denoising processes to deal with different levels or patterns of noise. In this paper, we propose an adaptive and iterative point cloud denoising method based on the score-based diffusion model. For a given noisy point cloud, we first estimate the noise variation and determine an adaptive denoising schedule with appropriate step sizes, then invoke the trained network iteratively to update point clouds following the adaptive schedule. To facilitate this adaptive and iterative denoising process, we design the network architecture and a two-stage sampling strategy for the network training to enable feature fusion and gradient fusion for iterative denoising. Compared to the state-of-the-art point cloud denoising methods, our approach obtains clean and smooth denoised point clouds, while preserving the shape boundary and details better. Our results not only outperform the other methods both qualitatively and quantitatively, but also are preferable on the synthetic dataset with different patterns of noises, as well as the real-scanned dataset.

Hongbo Li, Haikuan Zhu, Sikai Zhong et al.

This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve curvature-based anisotropic metric by using a dot product loss between high-d edge vectors. This can dramatically reduce the computational time and increase the scalability. Then, we propose a novel feature-sensitive remeshing on the generated high-d embedding to automatically capture sharp geometric features. We define a high-d normal metric, and then derive an automatic differentiation on a high-d centroidal Voronoi tessellation (CVT) optimization with the normal metric to simultaneously preserve geometric features and curvature anisotropy that exhibit in the original 3D shapes. To our knowledge, this is the first time that a deep learning framework and a large dataset are proposed to construct a high-d Euclidean embedding space for 3D anisotropic surface meshing. Experimental results are evaluated and compared with the state-of-the-art in anisotropic surface meshing on a large number of surface models from Thingi10K dataset as well as tested on extensive unseen 3D shapes from Multi-Garment Network dataset and FAUST human dataset.

Jiayi Kong, Chen Zong, Jun Luo et al.

The medial axis, a lower-dimensional shape descriptor, plays an important role in the field of digital geometry processing. Despite its importance, robust computation of the medial axis transform from diverse inputs, especially point clouds with defects, remains a significant challenge. In this paper, we tackle the challenge by proposing a new implicit method that diverges from mainstream explicit medial axis computation techniques. Our key technical insight is the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape is the unsigned distance field (UDF) of the shape's medial axis. This allows for formulating medial axis computation as an implicit reconstruction problem. Utilizing a modified double covering method, we extract the medial axis as the zero level-set of the UDF. Extensive experiments show that our method has enhanced accuracy and robustness in learning compact medial axis transform from thorny meshes and point clouds compared to existing methods.

Zhenyu Shu, Jiawei Wen, Shiyang Li et al.

The task of 3D shape captioning occupies a significant place within the domain of computer graphics and has garnered considerable interest in recent years. Traditional approaches to this challenge frequently depend on the utilization of costly voxel representations or object detection techniques, yet often fail to deliver satisfactory outcomes. To address the above challenges, in this paper, we introduce Diff-3DCap, which employs a sequence of projected views to represent a 3D object and a continuous diffusion model to facilitate the captioning process. More precisely, our approach utilizes the continuous diffusion model to perturb the embedded captions during the forward phase by introducing Gaussian noise and then predicts the reconstructed annotation during the reverse phase. Embedded within the diffusion framework is a commitment to leveraging a visual embedding obtained from a pre-trained visual-language model, which naturally allows the embedding to serve as a guiding signal, eliminating the need for an additional classifier. Extensive results of our experiments indicate that Diff-3DCap can achieve performance comparable to that of the current state-of-the-art methods.

Zhenyu Shu, Jiajun Shen, Zhongui Chen et al.

In the field of 3D point cloud generation, numerous 3D generative models have demonstrated the ability to generate diverse and realistic 3D shapes. However, the majority of these approaches struggle to generate controllable 3D point cloud shapes that meet user-specific requirements, hindering the large-scale application of 3D point cloud generation. To address the challenge of lacking control in 3D point cloud generation, we are the first to propose controlling the generation of point clouds by shape structures that comprise part existences and part adjacency relationships. We manually annotate the adjacency relationships between the segmented parts of point cloud shapes, thereby constructing a StructureGraph representation. Based on this StructureGraph representation, we introduce StrucADT, a novel structure-controllable point cloud generation model, which consists of StructureGraphNet module to extract structure-aware latent features, cCNF Prior module to learn the distribution of the latent features controlled by the part adjacency, and Diffusion Transformer module conditioned on the latent features and part adjacency to generate structure-consistent point cloud shapes. Experimental results demonstrate that our structure-controllable 3D point cloud generation method produces high-quality and diverse point cloud shapes, enabling the generation of controllable point clouds based on user-specified shape structures and achieving state-of-the-art performance in controllable point cloud generation on the ShapeNet dataset.

Pengfei Wang, Qiujie Dong, Fangtian Liang et al.

Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be connected to form a curve network, and therefore more difficult to deal with. While 3D curve networks or curve sketches provide intuitive shape control, their sparsity and varied topology pose challenges in generating high-quality surfaces to meet such curve constraints. In this paper, we propose NeuVAS, a variational approach to shape modeling using neural implicit surfaces constrained under sparse input shape control, including unstructured 3D curve sketches as well as connected 3D curve networks. Specifically, we introduce a smoothness term based on a functional of surface curvatures to minimize shape variation of the zero-level set surface of a neural SDF. We also develop a new technique to faithfully model G0 sharp feature curves as specified in the input curve sketches. Comprehensive comparisons with the state-of-the-art methods demonstrate the significant advantages of our method.

Ling Gao, Zhenyu Shu, Shiqing Xin

3D models are widely used in various industries, and mesh data has become an indispensable part of 3D modeling because of its unique advantages. Mesh data can provide an intuitive and practical expression of rich 3D information. However, its disordered, irregular data structure and complex surface information make it challenging to apply with deep learning models directly. Traditional mesh data processing methods often rely on mesh models with many limitations, such as manifold, which restrict their application scopes in reality and do not fully utilize the advantages of mesh models. This paper proposes a novel end-to-end framework for addressing the challenges associated with deep learning in mesh models centered around graph neural networks (GNN) and is titled InfoGNN. InfoGNN treats the mesh model as a graph, which enables it to handle irregular mesh data efficiently. Moreover, we propose InfoConv and InfoMP modules, which utilize the position information of the points and fully use the static information such as face normals, dihedral angles, and dynamic global feature information to fully use all kinds of data. In addition, InfoGNN is an end-to-end framework, and we simplify the network design to make it more efficient, paving the way for efficient deep learning of complex 3D models. We conducted experiments on several publicly available datasets, and the results show that InfoGNN achieves excellent performance in mesh classification and segmentation tasks.

Mingyang Zhao, Jingen Jiang, Lei Ma et al.

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an $\ell_1$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nyström method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration.

Junjie Gao, Pengfei Wang, Qiujie Dong et al.

Establishing accurate and representative matches is a crucial step in addressing the point cloud registration problem. A commonly employed approach involves detecting keypoints with salient geometric features and subsequently mapping these keypoints from one frame of the point cloud to another. However, methods within this category are hampered by the repeatability of the sampled keypoints. In this paper, we introduce a saliency-guided trans\textbf{former}, referred to as \textit{D3Former}, which entails the joint learning of repeatable \textbf{D}ense \textbf{D}etectors and feature-enhanced \textbf{D}escriptors. The model comprises a Feature Enhancement Descriptor Learning (FEDL) module and a Repetitive Keypoints Detector Learning (RKDL) module. The FEDL module utilizes a region attention mechanism to enhance feature distinctiveness, while the RKDL module focuses on detecting repeatable keypoints to enhance matching capabilities. Extensive experimental results on challenging indoor and outdoor benchmarks demonstrate that our proposed method consistently outperforms state-of-the-art point cloud matching methods. Notably, tests on 3DLoMatch, even with a low overlap ratio, show that our method consistently outperforms recently published approaches such as RoReg and RoITr. For instance, with the number of extracted keypoints reduced to 250, the registration recall scores for RoReg, RoITr, and our method are 64.3\%, 73.6\%, and 76.5\%, respectively.

Qiujie Dong, Zixiong Wang, Manyi Li et al.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

Cheng Lin, Lingjie Liu, Changjian Li et al.

Segmenting arbitrary 3D objects into constituent parts that are structurally meaningful is a fundamental problem encountered in a wide range of computer graphics applications. Existing methods for 3D shape segmentation suffer from complex geometry processing and heavy computation caused by using low-level features and fragmented segmentation results due to the lack of global consideration. We present an efficient method, called SEG-MAT, based on the medial axis transform (MAT) of the input shape. Specifically, with the rich geometrical and structural information encoded in the MAT, we are able to develop a simple and principled approach to effectively identify the various types of junctions between different parts of a 3D shape. Extensive evaluations and comparisons show that our method outperforms the state-of-the-art methods in terms of segmentation quality and is also one order of magnitude faster.

Jian Liu, Shiqing Xin, Zengfu Gao et al.

We propose to synthesize feasible caging grasps for a target object through computing Caging Loops, a closed curve defined in the shape embedding space of the object. Different from the traditional methods, our approach decouples caging loops from the surface geometry of target objects through working in the embedding space. This enables us to synthesize caging loops encompassing multiple topological holes, instead of always tied with one specific handle which could be too small to be graspable by the robot gripper. Our method extracts caging loops through a topological analysis of the distance field defined for the target surface in the embedding space, based on a rigorous theoretical study on the relation between caging loops and the field topology. Due to the decoupling, our method can tolerate incomplete and noisy surface geometry of an unknown target object captured on-the-fly. We implemented our method with a robotic gripper and demonstrate through extensive experiments that our method can synthesize reliable grasps for objects with complex surface geometry and topology and in various scales.