Landmark- and Intensity-Based Registration with Large Deformations via Quasi-conformal Maps

We present a new approach to obtain diffeomorphic registrations with large deformations using landmark and intensity information via quasi-conformal maps. The basic idea is to minimize an energy functional involving a Beltrami coefficient term, which measures the distortion of the quasi-conformal map. The Beltrami coefficient effectively controls the bijectivity and smoothness of the registration. In this paper, we first propose the quasi-conformal landmark registration (QCLR) algorithm to obtain diffeomorphic (1-1 and onto) registrations between images or surfaces. Using QCLR, landmark-aligned diffeomorphisms between images or surfaces can be obtained, even with a large geometric difference or a large number of landmark constraints. This algorithm is then extended to the quasi-conformal hybrid registration (QCHR) algorithm, which combines landmark and intensity (such as image intensity or surface curvature) information to achieve a more accurate registration result. Experiments have been carried out on both synthetic and real data. Results demonstrate the stability and efficacy of the proposed algorithm to obtain diffeomorphic registrations between images or surfaces.