Related papers: Applying Lie Groups Approaches for Rigid Registrat…

We present an image representation method which is derived from analyzing Gaussian probability density function (\emph{pdf}) space using Lie group theory. In our proposed method, images are modeled by Gaussian mixture models (GMMs) which…

The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a LieDer pair and study the corresponding cohomologies. We show that a LieDer pair…

Rigid registration of partial observations is a fundamental problem in various applied fields. In computer graphics, special attention has been given to the registration between two partial point clouds generated by scanning devices.…

Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D…

Cross-modal data registration has long been a critical task in computer vision, with extensive applications in autonomous driving and robotics. Accurate and robust registration methods are essential for aligning data from different…

The purpose of this article is to analyze several Lie algebras associated to "orbit configuration spaces" obtained from a group G acting freely, and properly discontinuously on the upper 1/2-plane H^2. The Lie algebra obtained from the…

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…

The Iterative Closest Point (ICP) algorithm is a crucial component of LiDAR-based SLAM algorithms. However, its performance can be negatively affected in unstructured environments that lack features and geometric structures, leading to low…

In this paper, we propose a transformer-based procedure for the efficient registration of non-rigid 3D point clouds. The proposed approach is data-driven and adopts for the first time the transformer architecture in the registration task.…

The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

We suggest a new, alternative algebraic method for computation of geometrical quantities by means of the embedding of local loops into Lie groups.

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration…

Point cloud registration has seen recent success with several learning-based methods that focus on correspondence matching and, as such, optimize only for this objective. Following the learning step of correspondence matching, they evaluate…

In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation…

In this paper, we address the registration of historical WWII images to present-day ortho-photo maps for the purpose of geolocalization. Due to the challenging nature of this problem, we propose to register the images jointly as a group…

Point cloud registration is important in computer-aided interventions (CAI). While learning-based point cloud registration methods have been developed, their clinical application is hampered by issues of generalizability and explainability.…

Point cloud registration is a common step in many 3D computer vision tasks such as object pose estimation, where a 3D model is aligned to an observation. Classical registration methods generalize well to novel domains but fail when given a…

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity…