Shi Yonggang, Morra Jonathan H, Thompson Paul M, Toga Arthur W
Lab of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA, USA.
Inf Process Med Imaging. 2009;21:467-78. doi: 10.1007/978-3-642-02498-6_39.
We propose in this work a novel variational method for computing maps between surfaces by combining informative geometric features and regularizing forces including inverse consistency and harmonic energy. To tackle the ambiguity in defining homologous points on smooth surfaces, we design feature functions in the data term based on the Reeb graph of the Laplace-Beltrami eigenfunctions to quantitatively describe the global geometry of elongated anatomical structures. For inverse consistency and robustness, our method computes simultaneously the forward and backward map by iteratively solving partial differential equations (PDEs) on the surfaces. In our experiments, we successfully mapped 890 hippocampal surfaces and report statistically significant maps of atrophy rates between normal controls and patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD).
在这项工作中，我们提出了一种新颖的变分方法，通过结合信息几何特征和正则化力（包括逆一致性和谐波能量）来计算曲面之间的映射。为了解决在光滑曲面上定义同源点时的模糊性问题，我们基于拉普拉斯 - 贝尔特拉米特征函数的里布图在数据项中设计特征函数，以定量描述细长解剖结构的全局几何形状。为了实现逆一致性和鲁棒性，我们的方法通过在曲面上迭代求解偏微分方程（PDE）来同时计算正向和反向映射。在我们的实验中，我们成功地对890个海马体曲面进行了映射，并报告了正常对照组与轻度认知障碍（MCI）和阿尔茨海默病（AD）患者之间具有统计学意义的萎缩率映射。
