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

TL;DR

This paper introduces a novel quasi-conformal map-based algorithm for diffeomorphic registration of images and surfaces with large deformations, ensuring smooth, bijective mappings even with many landmarks or intensity matching.

Contribution

It presents a new energy minimization approach using Beltrami coefficients to achieve large deformation registration with guaranteed diffeomorphism.

Findings

Effective landmark-based registration with large deformations

Guarantees of diffeomorphic (bijective) mappings

Successful experiments on synthetic and real data

Abstract

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, even with very large deformations. Using the proposed algorithm, landmark-based registration between images or surfaces can be effectively computed. The obtained registration is guaranteed to be diffeomorphic (1-1 and onto), even with a large deformation or large number of landmark constraints. The proposed algorithm can also be combined with matching intensity (such as image intensity or surface curvature) to improve the accuracy of the registration. Experiments have been carried out on both synthetic and real data. Results demonstrate the efficacy of the proposed algorithm to obtain diffeomorphic registration between images or surfaces.