Introduction

The irascible Robin Whatley is my close friend, and an avid English gardener of some appreciable skill. He once commented disparagingly on my tendency to mercilessly prune shrubs into small spheres, irrespective of their natural shapes or the season in which they are likely to bloom. “The trouble with you, Kaesler,” he said, “is that you are not a horticulturist. You're a … geometrician.” Whatley was absolutely right, and the reason that Fourier descriptors of shape appeal to me, and to so many others who measure shapes, is precisely because we are geometricians and are inclined to favor a quantitative method that has a strong geometrical component. In spite of ourselves, we remain somewhat baffled by matrix algebra, while accepting that it is probably a good thing. But to the geometrically inclined, principal component analysis is not so much about matrix algebra as about football-shaped clouds of points suspended in hyperspace, and discriminant function analysis is about, somehow, algorithmically turning those footballs into basketballs. Moreover, those of us who teach have discovered that most of our students are more comfortable, at least initially, with geometrical models of multivariate morphometrics than with purely algebraic ones. Fourier analysis resolves shapes into a set of geometrically comprehensible, additive, sine and cosine curves that can be readily visualized.