Fourier Descriptors for Plane Closed Curves
IEEE Transactions on Computers
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The Fourier Descriptors (FD's) of Zahn and Roskies provide a computationally convenient numerical summary of the shape of closed plane curves whose utility in classification and pattern recognition has been well documented. We investigate the use of FD's as summary statistics for describing variability in shape across a population. As higher harmonics can be considerably affected by the process of digitizing the curve, extracting information about variability in shape across the population from FD vectors will require more care than was required in previous applications. There are difficulties in using the Zahn and Roskies FD's in standard multivariate descriptive statistical procedures. We suggest a modified version of the FD's which are more amenable to such analyses and which are more easily interperable with our biometric data. These modified FD's can be used to produce ''average'' shapes for the population under study, and also to produce shapes on the boundary of, say, 95% tolerance regions of ''typical'' shapes for this population.