Geometric Registration of High-genus Surfaces
Chengfeng Wen, Lok Ming Lui

TL;DR
This paper introduces a novel method for registering high-genus surfaces by conformally mapping them to their universal covering space and minimizing geometric dissimilarity, avoiding complex cut-based approaches.
Contribution
The work proposes a cutting-free, conformal parameterization approach for high-genus surface registration using universal covering spaces, enhancing accuracy and robustness.
Findings
Effective registration of high-genus surfaces demonstrated.
Method applicable to medical imaging data.
Produces smooth, bijective mappings.
Abstract
This paper presents a method to obtain geometric registrations between high-genus () 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 great challenge for surface registration. A possible approach is to partition surfaces into simply-connected patches and registration is done patch by patch. 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…
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