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In contrast to the literature where local patterns in 3D point clouds are captured by customized convolutional operators, in this paper we study the problem of how to effectively and efficiently project such point clouds into a 2D image…

This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…

Point cloud completion aims to infer a complete shape from its partial observation. Many approaches utilize a pure encoderdecoder paradigm in which complete shape can be directly predicted by shape priors learned from partial scans,…

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…

In the area of 3D shape analysis, the geometric properties of a shape have long been studied. Instead of directly extracting representative features using expert-designed descriptors or end-to-end deep neural networks, this paper is…

In this work, we explore the idea that effective generative models for point clouds under the autoencoding framework must acknowledge the relationship between a continuous surface, a discretized mesh, and a set of points sampled from the…

Most existing point cloud completion methods suffer from the discrete nature of point clouds and the unstructured prediction of points in local regions, which makes it difficult to reveal fine local geometric details. To resolve this issue,…

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…

3D point cloud completion, the task of inferring the complete geometric shape from a partial point cloud, has been attracting attention in the community. For acquiring high-fidelity dense point clouds and avoiding uneven distribution,…

Discrete point cloud objects lack sufficient shape descriptors of 3D geometries. In this paper, we present a novel method for aggregating hypothetical curves in point clouds. Sequences of connected points (curves) are initially grouped by…

Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…

Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an abstraction from the usual definition of convex sets in vector spaces, we formalize in Coq an intrinsic…

Point cloud compression plays a crucial role in reducing the huge cost of data storage and transmission. However, distortions can be introduced into the decompressed point clouds due to quantization. In this paper, we propose a novel…

Feature encoding is essential for point cloud analysis. In this paper, we propose a novel point convolution operator named Shell Point Convolution (SPConv) for shape encoding and local context learning. Specifically, SPConv splits 3D…

We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…

We describe a simple pre-training approach for point clouds. It works in three steps: 1. Mask all points occluded in a camera view; 2. Learn an encoder-decoder model to reconstruct the occluded points; 3. Use the encoder weights as…

Reconstructing hand-held objects in 3D from monocular images remains a significant challenge in computer vision. Most existing approaches rely on implicit 3D representations, which produce overly smooth reconstructions and are…

A generative model for high-fidelity point clouds is of great importance in synthesizing 3d environments for applications such as autonomous driving and robotics. Despite the recent success of deep generative models for 2d images, it is…

We present a novel algorithm for point cloud segmentation. Our approach transforms unstructured point clouds into regular voxel grids, and further uses a kernel-based interpolated variational autoencoder (VAE) architecture to encode the…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…