Sun Hui, Yushkevich Paul A, Zhang Hui, Cook Philip A, Duda Jeffrey T, Simon Tony J, Gee James C
Penn Image Computing and Science Laboratory, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA .
IEEE Trans Med Imaging. 2007 Sep;26(9):1166-78. doi: 10.1109/TMI.2007.900322.
The continuous medial representation (cm-rep) is an approach that makes it possible to model, normalize, and analyze anatomical structures on the basis of medial geometry. Having recently presented a partial differential equation (PDE)-based approach for 3-D cm-rep modeling [1], here we present an equivalent 2-D approach that involves solving an ordinary differential equation. This paper derives a closed form solution of this equation and shows how Pythagorean hodograph curves can be used to express the solution as a piecewise polynomial function, allowing efficient and robust medial modeling. The utility of the approach in medical image analysis is demonstrated by applying it to the problem of shape-based normalization of the midsagittal section of the corpus callosum. Using diffusion tensor tractography, we show that shape-based normalization aligns subregions of the corpus callosum, defined by connectivity, more accurately than normalization based on volumetric registration. Furthermore, shape-based normalization helps increase the statistical power of group analysis in an experiment where features derived from diffusion tensor tractography are compared between two cohorts. These results suggest that cm-rep is an appropriate tool for normalizing the corpus callosum in white matter studies.
连续中线表示（cm-rep）是一种基于中线几何对解剖结构进行建模、归一化和分析的方法。最近我们提出了一种基于偏微分方程（PDE）的三维cm-rep建模方法[1]，在此我们提出一种等效的二维方法，该方法涉及求解常微分方程。本文推导了该方程的闭式解，并展示了如何使用毕达哥拉斯 hodograph 曲线将解表示为分段多项式函数，从而实现高效且稳健的中线建模。通过将该方法应用于胼胝体矢状中截面基于形状的归一化问题，证明了其在医学图像分析中的实用性。使用扩散张量纤维束成像，我们表明基于形状的归一化比基于体积配准的归一化更准确地对齐了由连通性定义的胼胝体子区域。此外，在一项比较两个队列中从扩散张量纤维束成像得出的特征的实验中，基于形状的归一化有助于提高组分析的统计功效。这些结果表明，cm-rep 是白质研究中胼胝体归一化的合适工具。
