Gu Xianfeng, Wang Yalin, Chan Tony F, Thompson Paul M, Yau Shing-Tung
Division of Engineering and Applied Science, Harvard University, USA.
Inf Process Med Imaging. 2003 Jul;18:172-84. doi: 10.1007/978-3-540-45087-0_15.
It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which finds a conformal mapping between two general genus zero surfaces. We propose a new variational method which can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. We demonstrate the feasibility of our algorithm by applying it 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 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.
众所周知，任何零亏格曲面都可以共形映射到球面上，并且其任何局部部分都可以映射到圆盘上。然而，找到一种在两个一般的零亏格曲面之间找到共形映射的通用方法并非易事。我们提出了一种新的变分方法，该方法可以通过最小化映射的调和能量来找到任意两个零亏格流形之间的唯一映射。我们通过将其应用于皮质表面匹配问题来证明我们算法的可行性。我们使用网格结构来表示脑表面。添加了进一步的约束以确保共形映射是唯一的。对MRI数据的实证测试表明，这些映射保留了角度关系，在不同时间获取的MRI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。与其他脑表面共形映射算法相比，我们的算法更稳定且具有良好的可扩展性。
