Related papers: Hybrid Riemannian Metrics for Diffeomorphic Shape …

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…

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…

Traditional machine learning (ML) algorithms, such as multiple regression, require human analysts to make decisions on how to treat the data. These decisions can make the model building process subjective and difficult to replicate for…

This paper focuses on the study of open curves in a manifold M, and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [11] to define…

Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the…

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…

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…

In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics,…

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…

We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove…

In this article we study the problem of thoracic image registration, in particular the estimation of complex anatomical deformations associated with the breathing cycle. Using the intimate link between the Riemannian geometry of the space…

We study parameterisation-independent closed planar curve matching as a Bayesian inverse problem. The motion of the curve is modelled via a curve on the diffeomorphism group acting on the ambient space, leading to a large deformation…

In terms of dilatations, it is proved a series of criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between regular domains on the Riemann surfaces

We propose a fluid-based registration framework of medical images based on implicit neural representation. By integrating implicit neural representation and Large Deformable Diffeomorphic Metric Mapping (LDDMM), we employ a Multilayer…

We address the problem of 3D shape registration and we propose a novel technique based on spectral graph theory and probabilistic matching. The task of 3D shape analysis involves tracking, recognition, registration, etc. Analyzing 3D data…

In this paper, we propose a learning-based framework for non-rigid shape registration without correspondence supervision. Traditional shape registration techniques typically rely on correspondences induced by extrinsic proximity, therefore…

We study some properties of $SU_n$ endowed with the Frobenius metric $\phi$, which is, up to a positive constant multiple, the unique bi-invariant Riemannian metric on $SU_n$. In particular we express the distance between $P, Q \in SU_n$ in…

We study some Riemannian metrics on the space of regular smooth curves in the plane, viewed as the orbit space of maps from $S^1$ to the plane modulo the group of diffeomorphisms of $S^1$, acting as reparameterizations. In particular we…

The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves,…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…