Related papers: Rotation-Invariant Spherical Watermarking via Thir…

Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a $\mathcal{C}^2$-continuous spline for the trajectory naturally…

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional…

Defining and reliably finding a canonical orientation for 3D surfaces is key to many Computer Vision and Robotics applications. This task is commonly addressed by handcrafted algorithms exploiting geometric cues deemed as distinctive and…

Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…

Recent years have witnessed the emergence and increasing popularity of 3D medical imaging techniques with the development of 3D sensors and technology. However, achieving geometric invariance in the processing of 3D medical images is…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

We present Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), an $E(3)\times SO(3)$ equivariant framework for sparse deconvolution of volumes where each voxel contains a spherical signal. Such 6D data naturally arises in…

We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…

Efficiency and robustness are increasingly needed for applications on 3D point clouds, with the ubiquitous use of edge devices in scenarios like autonomous driving and robotics, which often demand real-time and reliable responses. The paper…

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks…

In this paper, we use known camera motion associated to a video sequence of a static scene in order to estimate and incrementally refine the surrounding depth field. We exploit the SO(3)-invariance of brightness and depth fields dynamics to…

The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection…

We develop a new process of image plane self-calibration for interferometric imaging data. The process is based on Shape-Orientation-Size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a…

It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This…

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…