Related papers: Applying Lie Groups Approaches for Rigid Registrat…

The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the…

We present a novel, effective method for global point cloud registration problems by geometric topology. Based on many point cloud pairwise registration methods (e.g ICP), we focus on the problem of accumulated error for the composition of…

We can use a method called registration to integrate some point clouds that represent the shape of the real world. In this paper, we propose highly accurate and stable registration method. Our method detects keypoints from point clouds and…

This paper presents a framework for rigid point-set registration and merging using a robust continuous data representation. Our point-set representation is constructed by training a one-class support vector machine with a Gaussian radial…

We consider the point cloud registration problem, the task of finding a transformation between two point clouds that represent the same object but are expressed in different coordinate systems. Our approach is not based on a point-to-point…

Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities.…

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…

Registration of point clouds related by rigid transformations is one of the fundamental problems in computer vision. However, a solution to the practical scenario of aligning sparsely and differently sampled observations in the presence of…

Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two point clouds. However, the finding of reliable correspondence relies on establishing a robust and…

This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is modeled by representing the processes in a reproducing kernel…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

In this paper, a shape-constrained iterative algorithm is proposed to register a rigid template point-cloud to a given reference point-cloud. The algorithm embeds a shape-based similarity constraint into the principle of gravitation. The…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We present a novel, data driven approach for solving the problem of registration of two point cloud scans. Our approach is direct in the sense that a single pair of corresponding local patches already provides the necessary transformation…

This paper addresses the task of time separated aerial image registration. The ability to solve this problem accurately and reliably is important for a variety of subsequent image understanding applications. The principal challenge lies in…

Point cloud analysis is a fundamental task in 3D computer vision. Most previous works have conducted experiments on synthetic datasets with well-aligned data; while real-world point clouds are often not pre-aligned. How to achieve rotation…

This paper presents DeepI2P: a novel approach for cross-modality registration between an image and a point cloud. Given an image (e.g. from a rgb-camera) and a general point cloud (e.g. from a 3D Lidar scanner) captured at different…

Point cloud registration is a fundamental problem in 3D computer vision, graphics and robotics. For the last few decades, existing registration algorithms have struggled in situations with large transformations, noise, and time constraints.…

Point cloud registration is a key problem for computer vision applied to robotics, medical imaging, and other applications. This problem involves finding a rigid transformation from one point cloud into another so that they align. Iterative…

In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…