Related papers: Flat Delaunay Complexes for Homeomorphic Manifold …

We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to…

Point cloud completion aims to reconstruct complete 3D shapes from partial observations, which is a challenging problem due to severe occlusions and missing geometry. Despite recent advances in multimodal techniques that leverage…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

In this paper we present SA-CNN, a hierarchical and lightweight self-attention based encoding and decoding architecture for representation learning of point cloud data. The proposed SA-CNN introduces convolution and transposed convolution…

Point clouds can be regarded as discrete samples of smooth manifolds and are typically analyzed via the eigenfunctions of the Laplace-Beltrami operator. This paper extends manifold spectral analysis to the fractional domain, enabling…

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use…

Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…

Pre-trained point cloud analysis models have shown promising advancements in various downstream tasks, yet their effectiveness is typically suffering from low-quality point cloud (i.e., noise and incompleteness), which is a common issue in…

We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to…

Point cloud obtained from 3D scanning is often sparse, noisy, and irregular. To cope with these issues, recent studies have been separately conducted to densify, denoise, and complete inaccurate point cloud. In this paper, we advocate that…

Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by…

A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…

Real-world environment-derived point clouds invariably exhibit noise across varying modalities and intensities. Hence, point cloud denoising (PCD) is essential as a preprocessing step to improve downstream task performance. Deep learning…

It is important that a spatial network's construction algorithm reproduces the structural properties of the original physical embedding. Here, we assess the Delaunay triangulation as a spatial network construction algorithm for seven…

A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extended to point clouds equipped with an $\mathbb{R}$-valued…

We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold reconstruction where a smooth $n$-dimensional submanifold…

Point cloud completion aims to recover missing geometric structures from incomplete 3D scans, which often suffer from occlusions or limited sensor viewpoints. Existing methods typically assume fixed input/output densities or rely on…

We propose a method for 3D shape reconstruction from unoriented point clouds. Our method consists of a novel SE(3)-equivariant coordinate-based network (TF-ONet), that parametrizes the occupancy field of the shape and respects the inherent…