Related papers: Applying Lie Groups Approaches for Rigid Registrat…
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…
We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…
We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded as a result of a quantization procedure.…
This study presents a high-accuracy, efficient, and physically induced method for 3D point cloud registration, which is the core of many important 3D vision problems. In contrast to existing physics-based methods that merely consider…
In robotic inspection of aviation parts, achieving accurate pairwise point cloud registration between scanned and model data is essential. However, noise and outliers generated in robotic scanned data can compromise registration accuracy.…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose…
This paper reports on a novel nonparametric rigid point cloud registration framework that jointly integrates geometric and semantic measurements such as color or semantic labels into the alignment process and does not require explicit data…
Point cloud registration aims to provide estimated transformations to align point clouds, which plays a crucial role in pose estimation of various navigation systems, such as surgical guidance systems and autonomous vehicles. Despite the…
Point-cloud data acquired using a terrestrial laser scanner (TLS) play an important role in digital forestry research. Multiple scans are generally used to overcome occlusion effects and obtain complete tree structural information. However,…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
This paper considers online object-level mapping using partial point-cloud observations obtained online in an unknown environment. We develop and approach for fully Convolutional Object Retrieval and Symmetry-AIded Registration (CORSAIR).…
We use the techniques of integration of Poisson manifolds into symplectic Lie groupoids to build symplectic resolutions (= desingularizations) of the closure of a symplectic leaf. More generally, we show how Lie groupoids can be used to…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
Recent advances in computer vision and deep learning have shown promising performance in estimating rigid/similarity transformation between unregistered point clouds of complex objects and scenes. However, their performances are mostly…
We present a new paradigm for rigid alignment between point clouds based on learnable weighted consensus which is robust to noise as well as the full spectrum of the rotation group. Current models, learnable or axiomatic, work well for…
In this paper, we propose an algorithm for registering sequential bounding boxes with point cloud streams. Unlike popular point cloud registration techniques, the alignment of the point cloud and the bounding box can rely on the properties…