Modeling the Space of Point Landmark Constrained Diffeomorphisms
Modeling the Space of Point Landmark Constrained Diffeomorphisms
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DOI：
10.1007/978-3-030-58577-8_22
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Chengfeng Wen;Yang Guo;X. Gu
中科院分区：
文献类型：
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作者：
Chengfeng Wen;Yang Guo;X. Gu
曲面配准在形状分析和几何处理中起着重要的作用。通常，评价曲面映射结果的标准有三个：微分同胚性、小变形和特征对齐。为了满足这些要求，本文提出了一种新的点界标约束微分同胚空间模型。基于Teichmüler理论，这个映射空间由Beltrami系数生成，Beltrami系数无穷小等于0。这些Beltrami系数是一个线性方程组的解。利用这一理论模型，可以在微分同胚空间中通过线性约束的迭代优化来实现最优配准，如调和映射和Teichmüler映射，从而最小化不同类型的失真。理论模型严谨，具有实用价值。实验结果证明了该方法的有效性和有效性。
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 Teichmüller theory, this mapping space is generated by the Beltrami coefficients, which are infinitesimally Teichmüller 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 Teichmüller 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.