Polygonal entropy: A convexity measure

The notion of polygonal entropy is introduced which captures the degree of nonconvexity of a polygon through a measure of polygonal visibility. We show that the entropy of a simple polygon is maximal if and only if it is convex. When 'normalized' the entropy measure is a number between ε (a small positive nonzero number) and 1 providing a convenient index which represents the degree of irregularity (nonconvexity) of a simple polygon. A similar but less computationally burdensome measure is also proffered. Suggested uses of the measure are: the evaluation of computational complexity of vision algorithms, pattern recognition and architectural space planning.