Indirect Image Registration with Large Diffeomorphic Deformations

Abstract

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 uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.

43 pages, 4 figures, 1 table; revised

References in corpus (2)

• Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport
• An Interpolating Distance between Optimal Transport and Fisher-Rao

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