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Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…

Point cloud completion referring to completing 3D shapes from partial 3D point clouds is a fundamental problem for 3D point cloud analysis tasks. Benefiting from the development of deep neural networks, researches on point cloud completion…

We address the problem of learning accurate 3D shape and camera pose from a collection of unlabeled category-specific images. We train a convolutional network to predict both the shape and the pose from a single image by minimizing the…

Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize…

We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or…

Real-scanned point clouds are often incomplete due to viewpoint, occlusion, and noise. Existing point cloud completion methods tend to generate global shape skeletons and hence lack fine local details. Furthermore, they mostly learn a…

Point cloud patterns are hard to learn because of the implicit local geometry features among the orderless points. In recent years, point cloud representation in 2D space has attracted increasing research interest since it exposes the local…

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…

3D point cloud completion is very challenging because it heavily relies on the accurate understanding of the complex 3D shapes (e.g., high-curvature, concave/convex, and hollowed-out 3D shapes) and the unknown & diverse patterns of the…

Among 2D convolutional networks on point clouds, point-based approaches consume point clouds of fixed size directly. By analysis of PointNet, a pioneer in introducing deep learning into point sets, we reveal that current point-based methods…

In this article we describe a new convolutional neural network (CNN) to classify 3D point clouds of urban or indoor scenes. Solutions are given to the problems encountered working on scene point clouds, and a network is described that…

This paper focuses on the recently popular task of point cloud completion guided by multimodal information. Although existing methods have achieved excellent performance by fusing auxiliary images, there are still some deficiencies,…

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…

Point clouds are widely used representations of 3D data, but determining the visibility of points from a given viewpoint remains a challenging problem due to their sparse nature and lack of explicit connectivity. Traditional methods, such…

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…

In this paper, we explore point-cloud based deep learning models to analyze numerical simulations arising from finite element analysis. The objective is to classify automatically the results of the simulations without tedious human…

3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry…

Point cloud analysis has a wide range of applications in many areas such as computer vision, robotic manipulation, and autonomous driving. While deep learning has achieved remarkable success on image-based tasks, there are many unique…

Normal estimation on 3D point clouds is a fundamental problem in 3D vision and graphics. Current methods often show limited accuracy in predicting normals at sharp features (e.g., edges and corners) and less robustness to noise. In this…