Related papers: Applying Lie Groups Approaches for Rigid Registrat…
Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian…
We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…
Classical pairwise image registration methods search for a spatial transformation that optimises a numerical measure that indicates how well a pair of moving and fixed images are aligned. Current learning-based registration methods have…
In the realm of large-scale point cloud registration, designing a compact symbolic representation is crucial for efficiently processing vast amounts of data, ensuring registration robustness against significant viewpoint variations and…
The goal of rigid registration is to align a source surface $ X $ to a target surface $ Y $. The alignment process involves iteratively transforming $ X $ closer and closer to $ Y $, such that $ X=Z^0 \rightarrow Z^1 \rightarrow Z^2…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then…
LiDAR registration is a fundamental task in robotic mapping and localization. A critical component of aligning two point clouds is identifying robust point correspondences using point descriptors. This step becomes particularly challenging…
There exist elegant methods of aligning point clouds in $\mathbb R^3$. Unfortunately, these methods fail to generalize to the case of Minkowski space, as we will show. Instead, we propose two solutions to the following problem: given…
Point clouds have become increasingly vital across various applications thanks to their ability to realistically depict 3D objects and scenes. Nevertheless, effectively compressing unstructured, high-precision point cloud data remains a…
Deep neural networks are increasingly used for pair-wise image registration. We propose to extend current learning-based image registration to allow simultaneous registration of multiple images. To achieve this, we build upon the pair-wise…
Point Cloud Sampling and Recovery (PCSR) is critical for massive real-time point cloud collection and processing since raw data usually requires large storage and computation. In this paper, we address a fundamental problem in PCSR: How to…
A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space,…
Similar to humans perceiving visual scenes as objects, Object-Centric Learning (OCL) can abstract dense images or videos into sparse object-level features. Transformer-based OCL handles complex textures well due to the decoding guidance of…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
Registration is a transformation estimation problem between two point clouds, which has a unique and critical role in numerous computer vision applications. The developments of optimization-based methods and deep learning methods have…
Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…
Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…
Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…
In this paper, we consider Lie algebroids over commutative ringed spaces. Lie algebroids over ringed spaces unify the existing notion of Lie algebroids over smooth manifolds, complex manifolds, analytic spaces, algebraic varieties, and…