Wang Yalin, Lui Lok Ming, Gu Xianfeng, Hayashi Kiralee M, Chan Tony F, Toga Arthur W, Thompson Paul M, Yau Shing-Tung
Laboratory of Neuro Imaging, Department of Neurology, University of California-Los Angeles School of Medicine, Los Angeles, CA 90095, USA.
IEEE Trans Med Imaging. 2007 Jun;26(6):853-65. doi: 10.1109/TMI.2007.895464.
In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks.
在医学成像中，参数化三维表面模型对于解剖建模与可视化、解剖结构的统计比较以及基于表面的配准和信号处理很有用。在此，我们介绍一种基于黎曼曲面结构的参数化方法，该方法使用一种特殊的曲线网结构（共形网）将表面分割成一组面片，每个面片都可以共形映射到一个平行四边形。由此产生的表面细分以及各组成部分的参数化是内在且稳定的（其解倾向于是光滑函数，并且可以施加狄利克雷问题的边界条件）。共形参数化还有助于将可能在三维脑表面流形上定义的偏微分方程（PDE）转换为二维参数域上的修正PDE。由于共形参数化的雅可比矩阵是对角的，因此参数域上的修正PDE很容易求解。为了说明我们的技术，我们在脑部的三维磁共振成像扫描中计算了几种类型解剖表面的参数化，包括大脑皮层、海马体和侧脑室。对于拓扑同胚且具有相似几何结构的表面，我们表明参数化结果是一致的，并且细分后的表面可以相互匹配。最后，我们通过求解皮层表面上的PDE提出了一种自动脑沟地标定位算法。地标检测结果被用作在表面之间构建共形映射的约束条件，这些表面也明确匹配定义的地标。
