A diffuse-interface approach to morphological image registration
Benedikt Wirth, CIMS

Abstract: In many applications, one is interested in simultaneously detecting the edges of two images and registering these via a matching deformation. The edge detection can be performed using the Ambrosio-Tortorelli approximation of the Mumford--Shah functional, which for each of the two images yields a phase-field function encoding the image edges. The matching deformation can be found by additionally minimizing a mismatch penalty (in the simplest case the squared $L²$-difference between the phase field of one image and the deformed phase field of the other) plus a regularization of the deformation (for example its nonlinear elastic deformation energy). We investigate the performance of this joint image segmentation and image registration method, and study its sharp-interface limit.