Perceptual similarity of shapes generated from Fourier descriptors

A metric representation of shape is preserved by a Fourier analysis of the cumulative angular bend of a shape's contour. Three experiments examined the relationship between variation in Fourier descriptors and judgments of perceptual shape similarity. Multidimensional scaling of similarity judgments resulted in highly ordered solutions for matrices of shapes generated by a Fourier synthesis of a few frequencies. Multiple regression analyses indicated that particular Fourier components best accounted for the recovered dimensions. In addition, variations in the amplitude and the phase of a given frequency, as well as the amplitudes of 2 different frequencies, produced independent effects on perceptual similarity. These results suggest that a Fourier representation is consistent with the perceptual similarity of shapes, at least for the relatively low-dimensional Fourier shapes considered.