Shi Yonggang, Lai Rongjie, Gill Raja, Pelletier Daniel, Mohr David, Sicotte Nancy, Toga Arthur W
Lab of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA, USA.
Med Image Comput Comput Assist Interv. 2011;14(Pt 2):327-34. doi: 10.1007/978-3-642-23629-7_40.
In this paper we develop a novel technique for surface deformation and mapping in the high-dimensional Laplace-Beltrami embedding space. The key idea of our work is to realize surface deformation in the embedding space via optimization of a conformal metric on the surface. Numerical techniques are developed for computing derivatives of the eigenvalues and eigenfunctions with respect to the conformal metric, which is then applied to compute surface maps in the embedding space by minimizing an energy function. In our experiments, we demonstrate the robustness of our method by applying it to map hippocampal atrophy of multiple sclerosis patients with depression on a data set of 109 subjects. Statistically significant results have been obtained that show excellent correlation with clinical variables. A comparison with the popular SPHARM tool has also been performed to demonstrate that our method achieves more significant results.
在本文中，我们开发了一种用于高维拉普拉斯 - 贝尔特拉米嵌入空间中的表面变形和映射的新技术。我们工作的关键思想是通过优化表面上的共形度量来实现在嵌入空间中的表面变形。我们开发了数值技术来计算特征值和特征函数相对于共形度量的导数，然后通过最小化能量函数将其应用于计算嵌入空间中的表面映射。在我们的实验中，我们将该方法应用于对109名受试者的数据集中患有抑郁症的多发性硬化症患者的海马萎缩进行映射，以此证明了我们方法的稳健性。我们获得了具有统计学意义的结果，这些结果与临床变量显示出极好的相关性。我们还与流行的SPHARM工具进行了比较，以证明我们的方法取得了更显著的结果。
