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

Ka Chun Lam The Chinese University of Hong Kong Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09013

SIAM Journal on Imaging Sciences, 7, (4), 2364–2392, 2014.11
Registration, which aims to find an optimal one-to-one correspondence between diff erent data, is an important problem in various fi elds. This problem is especially challenging when large deformations occur. In this paper, we present a novel algorithm to obtain di ffeomorphic 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 eff ectively 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 e ffectively computed. The obtained registration is guaranteed to be diff eomorphic (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 diff eomorphic registration between images or surfaces.
Registration, large deformation, diff eomorphic, quasi-conformal mapping, Beltrami coefficient
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@inproceedings{ka2014landmark,
  title={Landmark and Intensity Based Registration with Large Deformations via Quasi-Conformal Maps},
  author={Ka Chun Lam, and Ronald Lok Ming Lui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905170944912938625},
  booktitle={SIAM Journal on Imaging Sciences},
  volume={7},
  number={4},
  pages={2364–2392},
  year={2014},
}
Ka Chun Lam, and Ronald Lok Ming Lui. Landmark and Intensity Based Registration with Large Deformations via Quasi-Conformal Maps. 2014. Vol. 7. In SIAM Journal on Imaging Sciences. pp.2364–2392. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905170944912938625.
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