, Volume 18, Issue 8, pp 845-854

Relationships among eigenshape analysis, Fourier analysis, and analysis of coordinates

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Abstract

Eigenshape analysis (a singular value decomposition of a matrix of the tangent angle function φ*(t)) has recently been proposed as an alternative to Fourier analysis for description of outline shapes of organisms. Whenall eigenvectors andall harmonics are retained both approaches represent orthogonal rotations of the same points. Thus distances between pairs of shapes (and any multivariate analyses based on distances) must be the same for both analyses. When true shapes are known to be smooth, dropping higher-order Fourier harmonics results in a desirable smoothing of the digitized outline and a large reduction in computational cost.

An alternative method of eigenshape analysis is presented and related to elliptical Fourier analysis and analysis of raw coordinates.