Brain Surface Parameterization Using Riemann Surface Structure
Brain Surface Parameterization Using Riemann Surface Structure
复制标题
使用黎曼表面结构进行脑表面参数化
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Yau
中科院分区：
文献类型：
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作者：
Yalin Wang;X. Gu;Kiralee M. Hayashi;T. Chan;P. Thompson;S. Yau
我们开发了一种通用的方法，它使用全纯1-形式来参数化具有复杂(可能是分支)拓扑的解剖曲面。我们没有将曲面几何演化为平面或球面，而是利用了所有可定向曲面都是Riemann曲面并允许共形结构的事实，这在曲面上引入了特殊的曲线坐标系。基于黎曼曲面结构，我们可以将曲面规范地划分为多个面片。这些面片中的每一个都可以共形映射到平行四边形。由此产生的曲面细分和零部件的参数化是固有的和稳定的。为了说明这项技术，我们计算了大脑MRI扫描中几种解剖表面的保形结构，包括皮质、海马体和侧脑室。我们发现，由此产生的参数在不同受试者中是一致的，即使是对于分支结构，如脑室，否则很难参数化。与其他基于曲面膨胀的变分方法相比，我们的方法适用于具有任意复杂性的曲面，同时保证了参数化过程中的最小失真。它还提供了一种明确匹配解剖表面(如皮质)中的标志性曲线的方法，提供了一个基于表面的框架，用于统计比较解剖结构并在表面上生成网格，用于基于PDE的信号处理。
We develop a general approach that uses holomorphic 1-forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across subjects, even for branching structures such as the ventricles, which are otherwise difficult to parameterize. Compared with other variational approaches based on surface inflation, our technique works on surfaces with arbitrary complexity while guaranteeing minimal distortion in the parameterization. It also offers a way to explicitly match landmark curves in anatomical surfaces such as the cortex, providing a surface-based framework to compare anatomy statistically and to generate grids on surfaces for PDE-based signal processing.