Recent Developments of an Optimal Control approach to Nonrigid Image Registration

Zicong Zhou, Guojun Liao

Keywords: Diffeomorphic Image Registration, Computational Diffeomorphism, Jacobian Determinant, Curl, Green's identities

TL;DR: Image Registration by Optimal Control

Abstract: The Variational Principle (VP) forms diffeomorphisms (non-folding grids) with prescribed Jacobian determinant (JD) and curl under an optimal control set-up, which satisfies the properties of a Lie group. To take advantage of that, it is meaningful to regularize the resulting deformations of the image registration problem into the solution pool of VP. In this research note, (1) we provide an optimal control formulation of the image registration problem under a similar optimal control set-up as is VP; (2) numerical examples demonstrate the confirmation of diffeomorphic solutions as expected.