arXiv subjects

Shuangmin Chen

Publications and source records attributed to Shuangmin Chen.

24 records · Page 2Linked to original sources

arXiv2023

Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction

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}.

cs.CV↗

arXiv2023

P2M: A Fast Solver for Querying Distance from Point to Mesh Surface

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables one to eliminate the vast majority of triangles that do not help find the closest point. In this paper, we develop a totally different algorithmic paradigm, named P2M, to speed up point-to-mesh distance queries. Our original intention is to precompute a KD tree (KDT) of mesh vertices to approximately encode the geometry of a mesh surface containing vertices, edges and faces. However, it is very likely that the closest primitive to the query point is an edge e (resp., a face f), but the KDT reports a mesh vertex \u{psion} instead. We call \u{psion} an interceptor of e (resp., f). The main contribution of this paper is to invent a simple yet effective interception inspection rule and an efficient flooding interception inspection algorithm for quickly finding out all the interception pairs. Once the KDT and the interception table are precomputed, the query stage proceeds by first searching the KDT and then looking up the interception table to retrieve the closest geometric primitive. Statistics show that our query algorithm runs many times faster than the state-of-the-art solvers.

cs.GR↗

arXiv2023

Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point cloud with various imperfections, particularly in the presence of data sparsity coupled with nearby gaps or thin-walled structures. In this paper, we propose a smooth objective function to characterize the requirements of an acceptable winding-number field, which allows one to find the globally consistent normal orientations starting from a set of completely random normals. By taking the vertices of the Voronoi diagram of the point cloud as examination points, we consider the following three requirements: (1) the winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences of 0 are balanced around the point cloud, and (3) the normals align with the outside Voronoi poles as much as possible. Extensive experimental results show that our method outperforms the existing approaches, especially in handling sparse and noisy point clouds, as well as shapes with complex geometry/topology.

cs.GR↗

arXiv2023

Laplacian2Mesh: Laplacian-Based Mesh Understanding

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.

cs.CV↗

arXiv2022

SurfaceVoronoi: Efficiently Computing Voronoi Diagrams over Mesh Surfaces with Arbitrary Distance Solvers

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the $m$ distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh. Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs faster than the traditional restricted Voronoi diagram~(RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including (1)surface-based power diagram, (2)constrained Voronoi diagram with curve-type breaklines, and (3)curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.

cs.CG↗

arXiv2020

Top-Down Shape Abstraction Based on Greedy Pole Selection

Motivated by the fact that the medial axis transform is able to encode nearly the complete shape, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select new medial balls, in a top-down style, to enlarge the region spanned by the existing medial balls. The key spirit of the selection strategy is to encourage large medial balls while imposing given geometric constraints. We further propose a speedup technique based on a provable observation that the intersection of medial balls implies the adjacency of power cells (in the sense of the power crust). We further elaborate the selection rules in combination with two closely related applications. One application is to develop an easy-to-use ball-stick modeling system that helps non-professional users to quickly build a shape with only balls and wires, but any penetration between two medial balls must be suppressed. The other application is to generate porous structures with convex, compact (with a high isoperimetric quotient) and shape-aware pores where two adjacent spherical pores may have penetration as long as the mechanical rigidity can be well preserved.

cs.GR↗