ANALYSIS OF FINITE ELEMENT DISCRETIZATIONS OF AN OPTIMAL CONTROL FORMULATION OF THE IMAGE REGISTRATION PROBLEM ∗

Abstract. The goal of image registration is to determine a transformation of an image so that the resulting image is close to another image. We use an optimal control approach to determining the transformation. We precisely define the optimal control problem that solves the image registration problem, and state the optimality system corresponding to that control problem. We then define finite element discretizations of the optimality system and derive error estimates for the approximate solutions. We also define and prove the convergence of a gradient iterative method for the solution of the discrete optimality system. Key words. Image registration, finite element methods, optimal control, gradient methods. AMS subject classifications. 65D18, 94A08, 49M05, 35Q93, 65N30 1. Introduction. Imag