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Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due to their capability to learn short and long-term dependencies between the basic elements of a sequence. Nonetheless, popular tasks such as speech or…

This article introduces yet another representation of rotations in 3-space. The rotations form a 3-dimensional projective space, which fact has not been exploited in Computer Science. We use the four affine patches of this projective space…

We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…

Instance segmentation in point clouds is one of the most fine-grained ways to understand the 3D scene. Due to its close relationship to semantic segmentation, many works approach these two tasks simultaneously and leverage the benefits of…

Learning discriminative shape representation directly on point clouds is still challenging in 3D shape analysis and understanding. Recent studies usually involve three steps: first splitting a point cloud into some local regions, then…

Point cloud normal estimation is a fundamental task in 3D geometry processing. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This results in…

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…

We demonstrate an object tracking method for 3D images with fixed computational cost and state-of-the-art performance. Previous methods predicted transformation parameters from convolutional layers. We instead propose an architecture that…

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel…

This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard…

Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…

We present CpT: Convolutional point Transformer - a novel deep learning architecture for dealing with the unstructured nature of 3D point cloud data. CpT is an improvement over existing attention-based Convolutions Neural Networks as well…

Building on recent work on capsule networks, we propose a new, general-purpose form of "routing by agreement" that activates output capsules in a layer as a function of their net benefit to use and net cost to ignore input capsules from…

This study develops an unsupervised learning algorithm for products of expert capsules with dynamic routing. Analogous to binary-valued neurons in Restricted Boltzmann Machines, the magnitude of a squashed capsule firing takes values…

Convolutional Neural Networks (CNNs) have achieved promising results in medical image segmentation. However, CNNs require lots of training data and are incapable of handling pose and deformation of objects. Furthermore, their pooling layers…

In recent years, the CNNs have achieved great successes in the image processing tasks, e.g., image recognition and object detection. Unfortunately, traditional CNN's classification is found to be easily misled by increasingly complex image…

Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…

Learning-based 3D reconstruction using implicit neural representations has shown promising progress not only at the object level but also in more complicated scenes. In this paper, we propose Dynamic Plane Convolutional Occupancy Networks,…

Object reconstruction from 3D point clouds has been a long-standing research problem in computer vision and computer graphics, and achieved impressive progress. However, reconstruction from time-varying point clouds (a.k.a. 4D point clouds)…

Data organization via forming local regions is an integral part of deep learning networks that process 3D point clouds in a hierarchical manner. At each level, the point cloud is sampled to extract representative points and these points are…