相关论文: On Procrustes Analysis in Hyperbolic Space

We consider the problem of estimating a cloud of points from numerous noisy observations of that cloud after unknown rotations, and possibly reflections. This is an instance of the general problem of estimation under group action,…

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…

In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of…

Statistical shape models are a useful tool in image processing and computer vision. A Procrustres registration of the contours of the same shape is typically perform to align the training samples to learn the statistical shape model. A…

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…

The Procrustes-Wasserstein problem consists in matching two high-dimensional point clouds in an unsupervised setting, and has many applications in natural language processing and computer vision. We consider a planted model with two…

The Procrustes-based perturbation model (Goodall, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed…

Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…

Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully.…

The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is…

We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…

Today's typical application of geometric morphometrics to a quantitative comparison of organismal anatomies begins by standardizing samples of homologously labelled point configurations for location, orientation, and scale, and then renders…

The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow's…

This paper introduces a novel approach to the fine alignment of images in a burst captured by a handheld camera. In contrast to traditional techniques that estimate two-dimensional transformations between frame pairs or rely on discrete…

3D perception in point clouds is transforming the perception ability of future intelligent machines. Point cloud algorithms, however, are plagued by irregular memory accesses, leading to massive inefficiencies in the memory sub-system,…

Human image animation aims to generate a human motion video from the inputs of a reference human image and a target motion video. Current diffusion-based image animation systems exhibit high precision in transferring human identity into…

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

In this work we investigate the following isoperimetric problem: to find the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the area of the part of the boundary contained in…

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…