Related papers: 3 methods to put a Riemannian metric on Shape Spac…

We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.

Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…

Controlling the shape of deformable linear objects using robots and constraints provided by environmental fixtures has diverse industrial applications. In order to establish robust contacts with these fixtures, accurate estimation of the…

We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape…

Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dimensional shapes represented by triangular meshes of a given…

An information-geometric approach to sensor management is introduced that is based on following geodesic curves in a manifold of possible sensor configurations. This perspective arises by observing that, given a parameter estimation problem…

We show that a Riemannian foliation on a topological $n$-sphere has leaf dimension 1 or 3 unless n=15 and the Riemannian foliation is given by the fibers of a Riemannian submersion to an 8-dimensional sphere. This allows us to classify…

In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…

We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of…

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…

This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…

The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still…

In order to manipulate a deformable object, such as rope or cloth, in unstructured environments, robots need a way to estimate its current shape. However, tracking the shape of a deformable object can be challenging because of the object's…

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…

In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…

We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…

Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…

Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…

Using (casual) images to texture 3D models is a common way to create realistic 3D models, which is a very important task in computer graphics. However, if the shape of the casual image does not look like the target model or the target…