相关论文: Tangent Space Backpropagation for 3D Transformatio…

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

TorchOptics is an open-source Python library for differentiable Fourier optics simulations, developed using PyTorch to enable GPU-accelerated tensor computations and automatic differentiation. It provides a comprehensive framework for…

A space curve in a Euclidean 3-space $\mathbb E^3$ is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf…

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by…

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…

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…

A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…

Automatic differentiation frameworks are optimized for exactly one thing: computing the average mini-batch gradient. Yet, other quantities such as the variance of the mini-batch gradients or many approximations to the Hessian can, in…

Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous…

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This…

This paper proposes a convolution structure for learning SE(3)-equivariant features from 3D point clouds. It can be viewed as an equivariant version of kernel point convolutions (KPConv), a widely used convolution form to process point…

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…

Current popular backbones in computer vision, such as Vision Transformers (ViT) and ResNets are trained to perceive the world from 2D images. However, to more effectively understand 3D structural priors in 2D backbones, we propose Mask3D to…

Humans are remarkably flexible in understanding viewpoint changes due to visual cortex supporting the perception of 3D structure. In contrast, most of the computer vision models that learn visual representation from a pool of 2D images…

We investigate the group contraction method for various space-time groups, including SO(3)->E_2, SO(3,1)->G_3, SO(5-h,h)->P(3,1) (h=1 or 2), and its consequences for representations of these groups. Following strictly quantum mechanical…

Self-supervised learning by predicting transformations has demonstrated outstanding performances in both unsupervised and (semi-)supervised tasks. Among the state-of-the-art methods is the AutoEncoding Transformations (AET) by decoding…

The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real $n$-dimensional manifolds into $\mathbb{C}^n$. The generic topological structure of…

When interacting in a three dimensional world, humans must estimate 3D structure from visual inputs projected down to two dimensional retinal images. It has been shown that humans use the persistence of object shape over motion-induced…

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…

Single-image 3D reconstruction is a research challenge focused on predicting 3D object shapes from single-view images. This task requires significant data acquisition to predict both visible and occluded portions of the shape. Furthermore,…