Metric learning in diffeomorphic registration and a new fidelity measure based on unbalanced optimal transport.
Francois-Xavier Vialard
University Paris-Dauphine, France
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2017-04-24 16:00:00
2017-04-24 17:00:00
America/New_York
Metric learning in diffeomorphic registration and a new fidelity measure based on unbalanced optimal transport.
Diffeomorphic registration is an ill-posed inverse problem which isoften solved via the minimization of an energy functional whichinvolves a control on the deformation and a fidelity measure.Motivated by the design of these two terms which is crucial forpractical applications, my talk will be divided into two parts: thefirst one will focus on the design of the regularization of thedeformation in the LDDMM (large deformation by diffeomorphisms)setting. Starting from the simple sum of kernels, we show how toextend it to spatially varying metrics using left-invariantmetrics. We then present a method to estimate this metric in atemplate/population context. The second part of the talk willintroduce the use of optimal transport as a fidelity measure. Afterrecalling standard optimal transport, we present an extension ofoptimal transport to the case of unbalanced measures. Building onrecent numerical advances, we discuss the use of fast scalingalgorithms to approximate the problem via entropicregularization. Preliminary results on synthetic data are shown.
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