Wang Yalin, Gu Xianfeng, Chan Tony F, Thompson Paul M, Yau Shing-Tung
Mathematics Department, UCLA, Los Angeles, CA 90095, USA.
Med Image Comput Comput Assist Interv. 2006;9(Pt 2):946-54. doi: 10.1007/11866763_116.
In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
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具有重要意义。在此，我们介绍一种基于代数函数的参数化方法。通过使用里奇流方法求解 Yamabe 方程，我们可以将脑表面共形映射到多孔圆盘上。所得的参数化没有任何奇点，并且是内在的和稳定的。为了说明该技术，我们在脑部 MRI 扫描中计算了几种类型解剖表面的参数化，包括带有各种标记曲线的海马体和大脑皮层。对于大脑皮层表面，我们表明参数化结果与选定的标记曲线一致，并且可以使用约束调和映射相互匹配。与先前的平面共形参数化方法不同，我们的算法不会引入任何奇点。它还提供了一种方法来明确匹配诸如皮层等解剖表面之间的标记曲线，并计算用于解剖结构统计比较的共形不变量。
