A symmetric convexity measure

A new area-based convexity measure for polygons is described. It has the desirable properties that it is not sensitive to small boundary defects, and it is more symmetric with respect to intrusions and protrusions than other published convexity measures. The measure requires a maximally overlapping convex polygon, and this is efficiently estimated using a genetic algorithm (GA1). A second genetic algorithm (GA2) is then used to fine tune the result. In addition, the convex polygon is used to generate other values, measuring the amount of protrusions and intrusions that a polygon contains. Furthermore, the scheme can be modified to find the convex skull, which yields another new convexity measure. Examples of the measures’ application to medical image analysis are shown.