Laplacian eigenfunctions and their application to image data analysis, Journal of Plasma and Fusion Research, vol. 92, no. 12, pp. 904-911, 2016 (in Japanese). Invited paper.

English Abstract

This paper first discusses the basic properties, computations, and applications of the eigenvalues and eigenfunctions of the Laplacians defined on a general shape domain Rd, d ∈ N without imposing any boundary conditions a priori, by analyzing the integral operators commuting with those Laplacians, which was proposed by the author in 2008. We then review the 2013 work of F. Beg and his group on the classification of hippocampus shapes extracted from 3D MRI images using the eigenvalues of such integral operators, and compare our spectral analysis scheme for data measured on a general shape domain using the integral operators with the scheme based on the so-called patient-specific basis functions proposed by Winters et al. in 2009.

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