Project Description:
Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel algorithm to obtain diffeomorphic image or surface registrations with large deformations 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. Using the proposed algorithm, landmark-matching diffeomorphic (1-1 and onto) registrations between images or surfaces can be effectively obtained, even with a large deformation or large number of feature landmark constraints. The proposed algorithm can also be extended to a hybrid registration model, called Q-Fibra, which combines landmark and intensity (such as image intensity or surface curvature) information to obtain a more accurate registration. Experiments have been carried out on both synthetic and real data. Results demonstrate the efficacy of the proposed algorithm to obtain diffeomorphic registrations between images or surfaces.

Publication:

• K.C. Lam, L.M. Lui, Q-Fibra: Feature and intensity based registration with large deformations via quasi-conformal maps, submitted