Canonical morphology versus statistical treatment of outlines through Fourier shape analysis: an empirical comparison

The analysis of outlines is considered a powerful tool for morphometric studies, since the absence of assumptions on characters to be selected and measured reduces subjectivity. Fourier shape analysis converts each digitalized outline into a suite of numerical descriptors (the Fourier coefficients) that describe curves. The coefficients are the input to multivariate statistical analyses, that elaborates a numerical comparison of shapes. A friendly, easy accessible and practical method for a statistical approach to shape analysis and the sensitivity of both Elliptic Fourier Analysis and Fast Fourier Transform have been tested here on a set of Goodallia triangularis shells. Shape analysis results to be faster and more reliable than canonical morphometry. In the comparison of the Principal Component Analysis based on the two different Fourier transformations, Fast Fourier Transform produces the sharpest separation of the shell outlines into clusters while Elliptic Fourier Analysis results are comparably less clear. Both techniques separate the two forms of Goodallia triangularis.