Related papers: Tangent Space Backpropagation for 3D Transformatio…

Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…

This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…

Modeling group actions on latent representations enables controllable transformations of high-dimensional image data. Prior works applying group-theoretic priors or modeling transformations typically operate in the high-dimensional data…

Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.

M3d-CAM is an easy to use library for generating attention maps of CNN-based PyTorch models improving the interpretability of model predictions for humans. The attention maps can be generated with multiple methods like Guided…

We present Kaolin, a PyTorch library aiming to accelerate 3D deep learning research. Kaolin provides efficient implementations of differentiable 3D modules for use in deep learning systems. With functionality to load and preprocess several…

In this article, we derive a topological obstruction to the removal of a isolated degenerate complex tangent to an embedding of a 3-manifold into $\mathbb{C}^3$ (without affecting the structure of the remaining complex tangents). We…

Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…

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…

Neural networks that incorporate geometric relationships respecting SE(3) group transformations (e.g. rotations and translations) are increasingly important in molecular applications, such as molecular property prediction, protein structure…

Tiered latent representations and latent spaces for molecular graphs provide a simple but effective way to explicitly represent and utilize groups (e.g., functional groups), which consist of the atom (node) tier, the group tier and the…

We consider the problem of reorienting a rigid object with arbitrary known shape on a table using a two-finger pinch gripper. Reorienting problem is challenging because of its non-smoothness and high dimensionality. In this work, we focus…

The computation of the geometric transformation between a reference and a target image, known as registration or alignment, corresponds to the projection of the target image onto the transformation manifold of the reference image (the set…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…

Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…

Ground robot navigation in complex 3D environments is often hindered by geometric ambiguity, where non-traversable structures such as furniture share local geometric properties with navigable ground. Furthermore, the computational cost of…

Image processing problems in general, and in particular in the field of single-particle cryo-electron microscopy, often require considering images up to their rotations and translations. Such problems were tackled successfully when…

Point set registration is a powerful method that enables robots to manipulate deformable objects. By mapping the point cloud of the current object to the pre-trained point cloud, a transformation function can be constructed. The…