Related papers: Applying Lie Groups Approaches for Rigid Registrat…

This paper presents a robust probabilistic point registration method for estimating the rigid transformation (i.e. rotation matrix and translation vector) between two pointcloud dataset. The method improves the robustness of point…

Many types of 3D acquisition sensors have emerged in recent years and point cloud has been widely used in many areas. Accurate and fast registration of cross-source 3D point clouds from different sensors is an emerged research problem in…

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…

In this paper we propose a framework to leverage Lie group symmetries on arbitrary spaces exploiting \textit{algebraic signal processing} (ASP). We show that traditional group convolutions are one particular instantiation of a more general…

Point Cloud Registration (PCR) is a fundamental and significant issue in photogrammetry and remote sensing, aiming to seek the optimal rigid transformation between sets of points. Achieving efficient and precise PCR poses a considerable…

Rigid registration of point clouds is a fundamental problem in computer vision with many applications from 3D scene reconstruction to geometry capture and robotics. If a suitable initial registration is available, conventional methods like…

In this paper, we unify popular non-rigid registration methods for point sets and surfaces under our general framework, GiNGR. GiNGR builds upon Gaussian Process Morphable Models (GPMM) and hence separates modeling the deformation prior…

Probabilistic 3D point cloud registration methods have shown competitive performance in overcoming noise, outliers, and density variations. However, registering point cloud pairs in the case of partial overlap is still a challenge. This…

A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…

Point cloud registration is a prerequisite for many applications in computer vision and robotics. Most existing methods focus on pairwise registration of two point clouds with high overlap. Although there have been some methods for low…

Using heterogeneous depth cameras and 3D scanners in 3D face verification causes variations in the resolution of the 3D point clouds. To solve this issue, previous studies use 3D registration techniques. Out of these proposed techniques,…

Registration algorithms, such as Iterative Closest Point (ICP), have proven effective in mobile robot localization algorithms over the last decades. However, they are susceptible to failure when a robot sustains extreme velocities and…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

This work investigates the use of robust optimal transport (OT) for shape matching. Specifically, we show that recent OT solvers improve both optimization-based and deep learning methods for point cloud registration, boosting accuracy at an…

Probabilistic methods for point set registration have demonstrated competitive results in recent years. These techniques estimate a probability distribution model of the point clouds. While such a representation has shown promise, it is…

Oriented object detection predicts orientation in addition to object location and bounding box. Precisely predicting orientation remains challenging due to angular periodicity, which introduces boundary discontinuity issues and symmetry…

Shape registration is the process of aligning one 3D model to another. Most previous methods to align shapes with no known correspondences attempt to solve for both the transformation and correspondences iteratively. We present a shape…

Octree-based context learning has recently become a leading method in point cloud compression. However, its potential on lossy compression remains undiscovered. The traditional lossy compression paradigm using lossless octree representation…