The relative success of some methods for measuring and describing the shape of complex objects

Abstract

We examined and compared several morphometric methods for describing complex shapes. We chose the leaves of maples (Acer) and other tree species because they can all be visually discriminated from each other solely by leaf shape. We digitized the leaf outlines with a video camera and then examined the outlines with several morphometric methods to determine the extent to which margin details could be quantified and compared. Elliptic Fourier analysis provides complete and accurate descriptions of complex outlines and can be used to reconstruct images accurately. We compared several metrics that summarize overall shape complexity. A new measure of margin roughness is useful for quantifying and comparing margin detail independently of overall shape. Fractal dimension is highly correlated with the ratio of perimeter to area (dissection index) and reveals little additional information about shape. In combination, the summaries of shape complexity provide good discrimination of groups. We used canonical discriminant analysis to compare methods for outlines to traditional morphometric analysis of measurements taken between landmark points. Groups were discriminated from each other more clearly with outline methods than with landmark-based analyses.