Genus zero surface conformal mapping and its application to brain surface mapping
Genus zero surface conformal mapping and its application to brain surface mapping
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DOI：
10.1109/tmi.2004.831226
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发表时间：
2004-08-01
影响因子：
10.6
通讯作者：
Yau, ST
中科院分区：
文献类型：
--
作者：
Gu, XF;Wang, YL;Yau, ST
我们基于有边界或无边界曲面的全纯单形上同调群的结构(Gu和Yau，2002)，(Gu和Yau，2003)，发展了一种通用的全局保角参数化方法。对于亏格为零的曲面，我们的算法可以通过最小化映射的调和能量来找到任意两个亏格零流形之间的唯一映射。本文将该算法应用于大脑皮层表面匹配问题。我们使用网格结构来表示大脑表面。添加进一步的约束以确保保形映射是唯一的。对磁共振成像(MRI)数据的经验测试表明，该映射保持了角度关系，在不同时间采集的磁共振成像中是稳定的，并且对数据三角剖分和分辨率的差异具有鲁棒性。与其他脑表面保角映射算法相比，我们的算法更加稳定，具有良好的可扩展性。
We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.