Related papers: A general framework for rotation invariant point c…

In this paper, we are concerned with rotation equivariance on 2D point cloud data. We describe a particular set of functions able to approximate any continuous rotation equivariant and permutation invariant function. Based on this result,…

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames,…

Rotation estimation of known rigid objects is important for robotic applications such as dexterous manipulation. Most existing methods for rotation estimation use intermediate representations such as templates, global or local feature…

PointNet has recently emerged as a popular representation for unstructured point cloud data, allowing application of deep learning to tasks such as object detection, segmentation and shape completion. However, recent works in literature…

Point cloud registration involves determining a rigid transformation to align a source point cloud with a target point cloud. This alignment is fundamental in applications such as autonomous driving, robotics, and medical imaging, where…

3D anomaly detection (AD) is a crucial task in computer vision, aiming to identify anomalous points or regions from point cloud data. However, existing methods may encounter challenges when handling point clouds with changes in orientation…

Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the…

Point cloud-based large scale place recognition is an important but challenging task for many applications such as Simultaneous Localization and Mapping (SLAM). Taking the task as a point cloud retrieval problem, previous methods have made…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

Implicit Neural Point Cloud (INPC) is a recent hybrid representation that combines the expressiveness of neural fields with the efficiency of point-based rendering, achieving state-of-the-art image quality in novel view synthesis. However,…

Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any…

Reinforcement Learning (RL) from raw visual input has achieved impressive successes in recent years, yet it remains fragile to out-of-distribution variations such as changes in lighting, color, and viewpoint. Point Cloud Reinforcement…

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…

Global point cloud registration is an essential module for localization, of which the main difficulty exists in estimating the rotation globally without initial value. With the aid of gravity alignment, the degree of freedom in point cloud…

In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are…

Recent advances in rotation-invariant (RI) learning for 3D point clouds typically replace raw coordinates with handcrafted RI features to ensure robustness under arbitrary rotations. However, these approaches often suffer from the loss of…

The goal of this paper is to present invariants of planar point clouds, that is functions which take the same value before and after a linear transformation of a planar point cloud via a $2 \times 2$ invertible matrix. In the approach we…

Traditional algorithms of point set registration minimizing point-to-plane distances often achieve a better estimation of rigid transformation than those minimizing point-to-point distances. Nevertheless, recent deep-learning-based methods…