Indirect Image Registration with Large Diffeomorphic Deformations
This addresses image registration challenges in medical imaging or tomography where direct target images are unavailable, though it appears incremental as it adapts an existing framework to the indirect setting.
The paper tackles indirect image registration where a template is aligned with a target from noisy observations, proving existence, stability, and convergence as data error decreases. It demonstrates applications in 2D tomography with sparse or highly noisy data.
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.