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We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is to smoothly match, at a very fast rate, finite sequences of observed 3D-snapshots extracted from movies recording the smooth dynamic deformations of soft surfaces. We have implemented our algorithms in a proprietary software installed at The Methodist Hospital (Cardiology) to monitor mitral valve strain through computer analysis of noninvasive patients echocardiographies.
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of proba
We propose a variational model with diffeomorphic optimal transportation for joint image reconstruction and motion estimation. The proposed model is a production of assembling the Wasserstein distance with the Benamou--Brenier formula in optimal tran
Monotone operator splitting is a powerful paradigm that facilitates parallel processing for optimization problems where the cost function can be split into two convex functions. We propose a generalized form of monotone operator splitting based on Br
In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms one to the o
In this paper, we consider a generalized forward-backward splitting (G-FBS) operator for solving the monotone inclusions, and analyze its nonexpansive properties in a context of arbitrary variable metric. Then, for the associated fixed-point iteratio