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.
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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