Wang Gang, Wang Yalin
Ludong University, School of Information and Electrical Engineering, Yantai, China, 264025.
Arizona State University, School of Computing, Informatics, and Decision Systems Engineering, Tempe, AZ, USA, 878809.
Med Image Comput Comput Assist Interv. 2015;9351:751-9. doi: 10.1007/978-3-319-24574-4_90.
Here we introduce a novel multi-scale heat kernel based regional shape statistical approach that may improve statistical power on the structural analysis. The mechanism of this analysis is driven by the graph spectrum and the heat kernel theory, to capture the volumetric geometry information in the constructed tetrahedral mesh. In order to capture profound volumetric changes, we first use the volumetric Laplace-Beltrami operator to determine the point pair correspondence between two boundary surfaces by computing the streamline in the tetrahedral mesh. Secondly, we propose a multi-scale volumetric morphology signature to describe the transition probability by random walk between the point pairs, which reflects the inherent geometric characteristics. Thirdly, a point distribution model is applied to reduce the dimensionality of the volumetric morphology signatures and generate the internal structure features. The multi-scale and physics based internal structure features may bring stronger statistical power than other traditional methods for volumetric morphology analysis. To validate our method, we apply support vector machine to classify synthetic data and brain MR images. In our experiments, the proposed work outperformed FreeSurfer thickness features in Alzheimer's disease patient and normal control subject classification analysis.
在此，我们介绍一种基于新型多尺度热核的区域形状统计方法，该方法可能会提高结构分析的统计效能。这种分析机制由图谱和热核理论驱动，以捕捉构建的四面体网格中的体积几何信息。为了捕捉深刻的体积变化，我们首先使用体积拉普拉斯 - 贝尔特拉米算子，通过计算四面体网格中的流线来确定两个边界表面之间的点对对应关系。其次，我们提出一种多尺度体积形态特征，通过点对之间的随机游走描述转移概率，这反映了内在的几何特征。第三，应用点分布模型来降低体积形态特征的维度并生成内部结构特征。基于多尺度和物理的内部结构特征可能比其他传统的体积形态分析方法具有更强的统计效能。为了验证我们的方法，我们应用支持向量机对合成数据和脑磁共振图像进行分类。在我们的实验中，在阿尔茨海默病患者和正常对照受试者的分类分析中，所提出的方法优于FreeSurfer厚度特征。
