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

Current learning-based methods predict NeRF or 3D Gaussians from point clouds to achieve photo-realistic rendering but still depend on categorical priors, dense point clouds, or additional refinements. Hence, we introduce a novel point…

Change detection from traditional \added{2D} optical images has limited capability to model the changes in the height or shape of objects. Change detection using 3D point cloud \added{from photogrammetry or LiDAR surveying} can fill this…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

We propose a novel approach to self-supervised learning of point cloud representations by differentiable neural rendering. Motivated by the fact that informative point cloud features should be able to encode rich geometry and appearance…

Representing 3D shape in deep learning frameworks in an accurate, efficient and compact manner still remains an open challenge. Most existing work addresses this issue by employing voxel-based representations. While these approaches benefit…

The development of practical applications, such as autonomous driving and robotics, has brought increasing attention to 3D point cloud understanding. While deep learning has achieved remarkable success on image-based tasks, there are many…

Advancements in sensors, algorithms, and compute hardware have made 3D perception feasible in real time. Current methods to compare and evaluate the quality of a 3D model, such as Chamfer, Hausdorff, and Earth-Mover's distance, are…

Learning and selecting important points on a point cloud is crucial for point cloud understanding in various applications. Most of early methods selected the important points on 3D shapes by analyzing the intrinsic geometric properties of…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

Semantic scene understanding from point clouds is particularly challenging as the points reflect only a sparse set of the underlying 3D geometry. Previous works often convert point cloud into regular grids (e.g. voxels or bird-eye view…

Many neural networks for point clouds are, by design, invariant to the symmetries of this datatype: permutations and rigid motions. The purpose of this paper is to examine whether such networks preserve natural symmetry aware distances on…

In this paper, we address the classification of instances each characterized not by a singular point, but by a distribution on a vector space. We employ the Wasserstein metric to measure distances between distributions, which are then used…

It is an important task to reconstruct surfaces from 3D point clouds. Current methods are able to reconstruct surfaces by learning Signed Distance Functions (SDFs) from single point clouds without ground truth signed distances or point…

The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…

Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in…

Chamfer Distance (CD) is widely used as a metric to quantify difference between two point clouds. In point cloud completion, Chamfer Distance (CD) is typically used as a loss function in deep learning frameworks. However, it is generally…

Self-supervised methods have been proven effective for learning deep representations of 3D point cloud data. Although recent methods in this domain often rely on random masking of inputs, the results of this approach can be improved. We…

Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…

Capturing real-world 3D spaces as point clouds is efficient and descriptive, but it comes with sensor errors and lacks object parametrization. These limitations render point clouds unsuitable for various real-world applications, such as…

The semantic segmentation of point clouds is an important part of the environment perception for robots. However, it is difficult to directly adopt the traditional 3D convolution kernel to extract features from raw 3D point clouds because…