A simple algorithm for measuring the concavity/convexity ratio and lobe counting of a closed curve. With a review of the literature on form factors measuring concavity.

The algorithm described here identifies concave and convex segments of a closed contour by vector algebra, thereby defining the shape of a two-dimensional object in multiple ways: (1) as a ratio of total concave vs. total convex periphery length, (2) as the number of convexity changes per unit of perimeter length (or number of lobes per contour), (3) as the mean +/- SD of convex and/or concave segment lengths, and (4) as a measure of the discrete curvature from a finite number of points on the contour. The algorithm can be used, in its capacity to distinguish regularity and amplitude of indentations ("wrinkles" and "lobes"), in studies where the number, regularity and magnitude of surface fluctuations are important differentiating morphologic characteristics of the object. This short algorithm can easily be integrated among other classic algorithms measuring periphery, area, shortest and longest diameter, and form factors derived therefrom. The possibility of automating this method makes it possibly useful for the discrimination of shapes by artificial vision.