Related papers: Point-set Distances for Learning Representations o…

Point clouds-based Networks have achieved great attention in 3D object classification, segmentation and indoor scene semantic parsing. In terms of face recognition, 3D face recognition method which directly consume point clouds as input is…

We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

3D point clouds enhanced the robot's ability to perceive the geometrical information of the environments, making it possible for many downstream tasks such as grasp pose detection and scene understanding. The performance of these tasks,…

Scene flow represents the 3D motion of each point in the scene, which explicitly describes the distance and the direction of each point's movement. Scene flow estimation is used in various applications such as autonomous driving fields,…

In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…

Point cloud segmentation is a fundamental task in 3D scene understanding. Its progress is constrained by the high cost and time required for dense 3D annotations, making labeled samples difficult to obtain. Beyond annotation scarcity,…

The Earth Mover's Distance (EMD) is the measure of choice between point clouds. However the computational cost to compute it makes it prohibitive as a training loss, and the standard approach is to use a surrogate such as the Chamfer…

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and…

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…

Remarkable performance from Transformer networks in Natural Language Processing promote the development of these models in dealing with computer vision tasks such as image recognition and segmentation. In this paper, we introduce a novel…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

As a popular representation of 3D data, point cloud may contain noise and need to be filtered before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distribution in the filtered…

In this paper, we propose a novel learning-based pipeline for partially overlapping 3D point cloud registration. The proposed model includes an iterative distance-aware similarity matrix convolution module to incorporate information from…

In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation. First, point clouds sampled from manifolds originally embedded in some Euclidean space $\mathbb{R}^D$ are transformed…

Point cloud is a critical 3D representation with many emerging applications. Because of the point sparsity and irregularity, high-quality rendering of point clouds is challenging and often requires complex computations to recover the…

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point…