Related papers: Flat Delaunay Complexes for Homeomorphic Manifold …
We challenge the common assumption that deeper decoder architectures always yield better performance in point cloud reconstruction. Our analysis reveals that, beyond a certain depth, increasing decoder complexity leads to overfitting and…
Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a…
Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one…
We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is…
We prove that any conformally flat submanifold with flat normal bundle in a conformally flat Riemannian manifold is locally holonomic, that is, admits a principal coordinate system. As one of the consequences of this fact, it is shown that…
Point clouds are a fundamental 3D representation in computer vision, enabling a wide range of perception tasks. However, real-world point clouds often suffer from degradations such as incompleteness, noise, outliers, and irregular density,…
A central objective of topological data analysis is to identify topologically significant features in data represented as a finite point cloud. We consider the setting where the ambient space of the point sample is a compact Riemannian…
The Delaunay filtration $\mathcal{D}_{\bullet}(X)$ of a point cloud $X\subset \mathbb{R}^d$ is a central tool of computational topology. Its use is justified by the topological equivalence of $\mathcal{D}_{\bullet}(X)$ and the offset (i.e.,…
The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm, we introduce the core dissimilarity, from which we construct the core…
While three-dimensional (3D) building models play an increasingly pivotal role in many real-world applications, obtaining a compact representation of buildings remains an open problem. In this paper, we present a novel framework for…
Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes…
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay…
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…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Reconstruction-based methods have demonstrated very promising results for 3D anomaly detection. However, these methods face great challenges in handling high-precision point clouds due to the large scale and complex structure. In this…
Three-dimensional urban reconstruction of buildings from single-view images has attracted significant attention over the past two decades. However, recent methods primarily focus on rooftops from aerial images, often overlooking essential…
Point clouds captured by depth sensors are often contaminated by noises, obstructing further analysis and applications. In this paper, we emphasize the importance of point distribution uniformity to downstream tasks. We demonstrate that…
In this paper, we tackle the challenging problem of point cloud completion from the perspective of feature learning. Our key observation is that to recover the underlying structures as well as surface details, given partial input, a…
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…