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Title: Modeling the Space of Point Landmark Constrained Diffeomorphisms
Surface registration plays a fundamental role in shape analysis and geometric processing. Generally, there are three criteria in evaluating a surface mapping result: diffeomorphism, small distortion, and feature alignment. To fulfill these requirements, this work proposes a novel model of the space of point landmark constrained diffeomorphisms. Based on Teichm¨uller theory, this mapping space is generated by the Beltrami coefficients, which are infinitesimally Teichm¨uller equivalent to 0. These Beltrami coefficients are the solutions to a linear equation group. By using this theoretic model, optimal registrations can be achieved by iterative optimization with linear constraints in the diffeomorphism space, such as harmonic maps and Teichm¨uller maps, which minimize different types of distortion. The theoretical model is rigorous and has practical value. Our experimental results demonstrate the efficiency and efficacy of the proposed method.
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Award ID(s):
1762287 1737812
Publication Date:
Journal Name:
European Conference on Computer Vision (ECCV2020)
Sponsoring Org:
National Science Foundation
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