Related papers: Applying Lie Groups Approaches for Rigid Registrat…

Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other.…

In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…

Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie…

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…

Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis…

We propose a systematic approach for registering cross-source point clouds. The compelling need for cross-source point cloud registration is motivated by the rapid development of a variety of 3D sensing techniques, but many existing…

3D point cloud registration is a fundamental problem in computer vision and robotics. There has been extensive research in this area, but existing methods meet great challenges in situations with a large proportion of outliers and time…

In healthcare, accurately classifying medical images is vital, but conventional methods often hinge on medical data with a consistent grid structure, which may restrict their overall performance. Recent medical research has been focused on…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

Critical to the registration of point clouds is the establishment of a set of accurate correspondences between points in 3D space. The correspondence problem is generally addressed by the design of discriminative 3D local descriptors on the…

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven…

Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to…

In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation. First, point clouds sampled from manifolds originally embedded in some Euclidean space $\mathbb{R}^D$ are transformed…

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…

Non-rigid alignment of point clouds is crucial for scene understanding, reconstruction, and various computer vision and robotics tasks. Recent advancements in implicit deformation networks for non-rigid registration have significantly…

We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods have shown great potential through bypassing the detection of repeatable keypoints which is difficult to do especially in…

Accurate registration of 2D imagery with point clouds is a key technology for image-LiDAR point cloud fusion, camera to laser scanner calibration and camera localization. Despite continuous improvements, automatic registration of 2D and 3D…

Seeking consistent point-to-point correspondences between 3D rigid data (point clouds, meshes, or depth maps) is a fundamental problem in 3D computer vision. While a number of correspondence selection methods have been proposed in recent…