Related papers: Hybrid Riemannian Metrics for Diffeomorphic Shape …

We investigate certain immersions of constant curvature from Riemann surfaces into flag manifolds equipped with invariant metrics, namely primitive lifts associated to pseudoholomorphic maps of surfaces into complex Grassmannians. We prove…

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero…

We study metrics on shape space of immersions that have a particularly simple horizontal bundle. More specifically, we consider reparametrization invariant Sobolev metrics $G$ on the space $\operatorname{Imm}(M,N)$ of immersions of a…

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…

We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional order $q\in [0,\infty)$. We establish the…

These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.

Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…

Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

Image registration is a key technique in medical image analysis to estimate deformations between image pairs. A good deformation model is important for high-quality estimates. However, most existing approaches use ad-hoc deformation models…

We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix…

We introduce a region-specific diffeomorphic metric mapping (RDMM) registration approach. RDMM is non-parametric, estimating spatio-temporal velocity fields which parameterize the sought-for spatial transformation. Regularization of these…

This study proposes an end-to-end unsupervised diffeomorphic deformable registration framework based on moving mesh parameterization. Using this parameterization, a deformation field can be modeled with its transformation Jacobian…

We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…

We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main…

In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems…

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration…

We show that, on an oriented compact surface, two sufficiently $C^2$-close Riemannian metrics with strictly convex boundary, no conjugate points, hyperbolic trapped set for their geodesic flows, and same marked boundary distance, are…

We show, using two different approaches, that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on…