Related papers: Differentiable Topology Estimating from Curvatures…

Semantic pattern of an object point cloud is determined by its topological configuration of local geometries. Learning discriminative representations can be challenging due to large shape variations of point sets in local regions and…

Geometry and topology of decision regions are closely related with classification performance and robustness against adversarial attacks. In this paper, we use differential geometry to theoretically explore the geometrical and topological…

The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…

Point cloud is a principal data structure adopted for 3D geometric information encoding. Unlike other conventional visual data, such as images and videos, these irregular points describe the complex shape features of 3D objects, which makes…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…

Existing normal estimation methods for point clouds are often less robust to severe noise and complex geometric structures. Also, they usually ignore the contributions of different neighbouring points during normal estimation, which leads…

3D point cloud segmentation aims to assign semantic labels to individual points in a scene for fine-grained spatial understanding. Existing methods typically adopt data augmentation to alleviate the burden of large-scale annotation.…

In this paper, we propose a novel fitting method that uses local image features to fit a 3D Morphable Model to 2D images. To overcome the obstacle of optimising a cost function that contains a non-differentiable feature extraction operator,…

The convenience of 3D sensors has led to an increase in the use of 3D point clouds in various applications. However, the differences in acquisition devices or scenarios lead to divergence in the data distribution of point clouds, which…

A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both…

Deep neural networks have revolutionized 3D point cloud processing, yet efficiently handling large and irregular point clouds remains challenging. To tackle this problem, we introduce FastPoint, a novel software-based acceleration technique…

The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze non-diffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of…

In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist of a dense sampling of the object's surface, containing many…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients…

Three-dimensional point clouds provide highly accurate digital representations of objects, essential for applications in computer graphics, photogrammetry, computer vision, and robotics. However, comparing point clouds faces significant…

This paper addresses the problem of generating uniform dense point clouds to describe the underlying geometric structures from given sparse point clouds. Due to the irregular and unordered nature, point cloud densification as a generative…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic…