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 both shape coverage and uniformity 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++. The code will be publicly available once the paper is published.
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.
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. =
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.
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.
Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation on three-dimensional (3D) geometric surfaces. Previous works explored the significant direction by defining the operations of convolution and pooling on triangle meshes, but most methods explicitly utilized the graph connection structure of the mesh. Motivated by the geometric spectral surface reconstruction theory, we introduce a novel and flexible convolutional neural network (CNN) model, called Laplacian2Mesh, for 3D triangle mesh, which maps the features of mesh in the Euclidean space to the multi-dimensional Laplacian-Beltrami space, which is similar to the multi-resolution input in 2D CNN. Mesh pooling is applied to expand the receptive field of the network by the multi-space transformation of Laplacian which retains the surface topology, and channel self-attention convolutions are applied in the new space. Since implicitly using the intrinsic geodesic connections of the mesh through the adjacency matrix, we do not consider the number of the neighbors of the vertices, thereby mesh data with different numbers of vertices can be input. Experiments on various learning tasks applied to 3D meshes demonstrate the effectiveness and efficiency of Laplacian2Mesh.
Surface reconstruction from noisy, non-uniformly, and unoriented point clouds is a fascinating yet difficult problem in computer vision and computer graphics. In this paper, we propose Neural-IMLS, a novel approach that learning noise-resistant signed distance function (SDF) for reconstruction. Instead of explicitly learning priors with the ground-truth signed distance values, our method learns the SDF from raw point clouds directly in a self-supervised fashion by minimizing the loss between the couple of SDFs, one obtained by the implicit moving least-square function (IMLS) and the other by our network. Finally, a watertight and smooth 2-manifold triangle mesh is yielded by running Marching Cubes. We conduct extensive experiments on various benchmarks to demonstrate the performance of Neural-IMLS, especially for point clouds with noise.
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.
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.