Related papers: $E(3) \times SO(3)$-Equivariant Networks for Spher…

Each voxel in a diffusion MRI (dMRI) image contains a spherical signal corresponding to the direction and strength of water diffusion in the brain. This paper advances the analysis of such spatio-spherical data by developing convolutional…

We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where…

Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each…

Representation learning has become increasingly important, especially as powerful models have shifted towards learning latent representations before fine-tuning for downstream tasks. This approach is particularly valuable in leveraging the…

Diffusion-weighted magnetic resonance imaging (DW-MRI) is the only non-invasive approach for estimation of intra-voxel tissue microarchitecture and reconstruction of in vivo neural pathways for the human brain. With improvement in…

This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\mathbb{S}^2$ onto the SO(3) group, which…

Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter…

We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in…

Magnetic resonance imaging (MRI) super-resolution (SR) methods that computationally enhance low-resolution acquisitions to approximate high-resolution quality offer a compelling alternative to expensive high-field scanners. In this work we…

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group…

Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance,…

6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry…

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We…

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for…

Diffusion-weighted Magnetic Resonance Imaging (dMRI) is an essential tool in neuroimaging. It is arguably the sole noninvasive technique for examining the microstructural properties and structural connectivity of the brain. Recent years…

Constrained Spherical Deconvolution (CSD) is widely used to estimate the white matter fiber orientation distribution (FOD) from diffusion MRI data. Its angular resolution depends on the maximum spherical harmonic order ($l_{max}$): low…

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a critical imaging method for capturing and modeling tissue microarchitecture at a millimeter scale. A common practice to model the measured DW-MRI signal is via fiber orientation…

Analyzing volumetric data with rotational invariance or equivariance is an active topic in current research. Existing deep-learning approaches utilize either group convolutional networks limited to discrete rotations or steerable…

Modern diffusion MRI sequences commonly acquire a large number of volumes with diffusion sensitization gradients of differing strengths or directions. Such sequences rely on echo-planar imaging (EPI) to achieve reasonable scan duration.…