Seed Silhouettes as Geometric Objects: New Applications of Elliptic Fourier Transform to Seed Morphology

Abstract

Historically, little attention has been paid to the resemblance between seed silhouettes to geometric figures. Cardioid and derivatives, ellipses, heart curves, lemniscates, lenses, lunes, ovals, superellipses, waterdrops, and other figures can be used to describe seed shape, as well as models for quantification. Algebraic expressions representing the average silhouettes for a group of seeds are available, and their shape can be described and quantified by comparison with geometric models. Bidimensional closed-plane figures resulting from the representation of Fourier equations can be used as models for shape analysis. Elliptic Fourier Transform equations reproduce the seed silhouettes for any closed-plane curve corresponding to the contour of the image of a seed. We review the geometric properties of the silhouettes from seed images and discuss them in the context of seed development, plant taxonomy, and environmental adaptation. Silene is proposed as a model for the study of seed morphology. Three groups have been recently defined among Silene species based on the structure of their seed silhouettes, and their geometric properties are discussed. Using models based on Fourier Transform equations is useful in Silene species where the seeds are homogenous in shape but don’t adjust to described figures.