Geometric Registration of High-Genus Surfaces

Ronald Lok Ming Lui The Chinese University of Hong Kong Chengfeng Wen The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09018

SIAM Journal on Imaging Sciences, 7, (1), 337-365, 2014
This paper presents a method of obtaining geometric registrations between high-genus (g≥1) surfaces. Surface registration between simple surfaces, such as simply connected open surfaces, has been well studied. However, very few works have been carried out for the registration of high-genus surfaces. The high-genus topology of the surface poses a great challenge for surface registration. A possible approach is to partition surfaces into simply connected patches and registration can be done in a patch-by-patch manner. Consistent cuts are required, which are usually difficult to obtain and prone to error. In this work, we propose an effective way to obtain geometric registration between high-genus surfaces without introducing consistent cuts. The key idea is to conformally parameterize the surface into its universal covering space, which is either the Euclidean plane or the hyperbolic disk embedded in R2. Registration can then be done on the universal covering space by iteratively minimizing a shape mismatching energy measuring the geometric dissimilarity between the two surfaces. The Beltrami coefficient of the mapping is considered and adjusted in order to control the bijectivity of the mappings in each iteration. Our proposed algorithm effectively computes a smooth registration between high-genus surfaces that matches geometric information as much as possible. The algorithm can also be applied to find a smooth registration minimizing any general energy functionals. Numerical experiments on high-genus surface data show that our proposed method is effective for registering high-genus surfaces with geometric matching. We also applied the method to register anatomical structures for medical imaging, which demonstrates the usefulness of the proposed algorithm.
surface registration, high-genus surface, universal covering space, conformal parameterization, shape mismatching energy
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  title={Geometric Registration of High-Genus Surfaces},
  author={Ronald Lok Ming Lui, and Chengfeng Wen},
  booktitle={SIAM Journal on Imaging Sciences},
Ronald Lok Ming Lui, and Chengfeng Wen. Geometric Registration of High-Genus Surfaces. 2014. Vol. 7. In SIAM Journal on Imaging Sciences. pp.337-365.
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