Shape analysis via inconsistent surface registration

• URL: http://arxiv.org/abs/2003.01357v1
• Date: Tue, 3 Mar 2020 06:58:16 GMT
• Title: Shape analysis via inconsistent surface registration
• Authors: Gary P. T. Choi, Di Qiu, Lok Ming Lui
• Abstract summary: We develop a framework for shape analysis using inconsistent surface mapping. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory.
• Score: 4.367664806447789
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between those parts, without assuming any global 1-1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.

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