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Inferring missing regions from severely occluded point clouds is highly challenging. Especially for 3D shapes with rich geometry and structure details, inherent ambiguities of the unknown parts are existing. Existing approaches either learn…

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…

Point clouds are popular 3D representations for real-life objects (such as in LiDAR and Kinect) due to their detailed and compact representation of surface-based geometry. Recent approaches characterise the geometry of point clouds by…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

When classifying point clouds, a large amount of time is devoted to the process of engineering a reliable set of features which are then passed to a classifier of choice. Generally, such features - usually derived from the 3D-covariance…

Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph…

We introduce PC2WF, the first end-to-end trainable deep network architecture to convert a 3D point cloud into a wireframe model. The network takes as input an unordered set of 3D points sampled from the surface of some object, and outputs a…

In real-world scenarios, scanned point clouds are often incomplete due to occlusion issues. The tasks of self-supervised and weakly-supervised point cloud completion involve reconstructing missing regions of these incomplete objects without…

We present a novel graph-neural-network-based system to effectively represent large-scale 3D point clouds with the applications to autonomous driving. Many previous works studied the representations of 3D point clouds based on two…

Rigid registration of partial observations is a fundamental problem in various applied fields. In computer graphics, special attention has been given to the registration between two partial point clouds generated by scanning devices.…

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…

Three dimensional (3D) object recognition is becoming a key desired capability for many computer vision systems such as autonomous vehicles, service robots and surveillance drones to operate more effectively in unstructured environments.…

We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…

In this paper, we propose Neural Points, a novel point cloud representation and apply it to the arbitrary-factored upsampling task. Different from traditional point cloud representation where each point only represents a position or a local…

In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a…

Processing 3D pointclouds with Deep Learning methods is not an easy task. A common choice is to do so with Graph Neural Networks, but this framework involves the creation of edges between points, which are explicitly not related between…

In the field of autonomous driving and robotics, point clouds are showing their excellent real-time performance as raw data from most of the mainstream 3D sensors. Therefore, point cloud neural networks have become a popular research…

Rethink convolution-based graph neural networks (GNN) -- they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a…