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

We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…

Reshaping accurate and realistic 3D human bodies from anthropometric parameters (e.g., height, chest size, etc.) poses a fundamental challenge for person identification, online shopping and virtual reality. Existing approaches for creating…

Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…

Let $M$ be a topological spherical space form, i.e. a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature…

Constant rescaling of a Riemannian metric appears in many computational settings, often through a global scale parameter that is introduced either explicitly or implicitly. Although this operation is elementary, its consequences are not…

For the shape control of deformable free-form surfaces, simulation plays a crucial role in establishing the mapping between the actuation parameters and the deformed shapes. The differentiation of this forward kinematic mapping is usually…

Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…

We address the problem of shaping deformable plastic materials using non-prehensile actions. Shaping plastic objects is challenging, since they are difficult to model and to track visually. We study this problem, by using kinetic sand, a…

We prove that every Riemann surface not isomorphic to the Riemann sphere admits an infinitesimal deformation of the complex structure. The proof is based in an investigation of the length of geodesics for the Kobayashi/Poincare metric.

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature…

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the…

In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…

We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…

This paper proposes the application of some well known two-dimensional geometrical shape descriptors for the visualisation of the structure of architectural open spaces. The paper demonstrates the use of visibility measures such as distance…

In this paper, it is presented a methodology to estimate the deformation involved between two objects attending to its physical properties. This methodology can be used, for example, in Computational Vision or Computer Graphics…

Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…

The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…