Multi-scale Heat Kernel Based Volumetric Morphology Signature
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 captur
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Ludong University, School of Information and Electrical Engineering, Yantai, 264025 China 2 Arizona State University, School of Computing, Informatics, and Decision Systems Engineering, Tempe, AZ, 878809 USA
Abstract. 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 LaplaceBeltrami 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. Keywords: Heat kernel, Volumetric Laplace-Beltrami operator, Point distribution model, Support vector machine.
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Introduction
In Alzheimer’s disease (AD) research, several MRI-based measures of atrophy, including cortical thickness, hippocampal atrophy or ventricular enlargement, are closely correlated with changes in cognitive performance, supporting their validity as biomarkers of early AD identification. As we know, the MRI imaging
This work was partially supported by the joint special fund of Shandong province Natural Science Fundation (ZR2013FL008), National Natural Science Foundation of China (61471185), National Health Institutes (R21AG043760,U54EB020403) and National Science Foundation (DMS-1413417,IIS-1421165).
c Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part III, LNCS 9351, pp. 751–759, 2015. DOI: 10.1007/978-3-319-24574-4_90
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G. Wang and Y. Wang
Fig. 1. Pipeline of the volumetric morphology signature computation.
measurement of medial temporal atrophy is not sufficiently accurate on its own to serve as an absolute diagnostic criterion for the clinical diagnosis of AD at the mild cognitive impairment (MCI) stage. A key research question is how to select the features which have a high discriminatory power. For example, the cortical thickness was the popular feature which has been used to capture the difference between different clinical groups. Currently, there are two different computational paradigms on brai
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