Probabilistic convexity measure

In order to improve the effectiveness of shape-based classification, there is an ongoing interest in creating new shape descriptors or creating new measures for descriptors that are already defined and used in shape classification tasks. Convexity is one of the most widely used shape descriptors and also one of the most studied in the literature. There are already several defined convexity measures. The most standard one comes from the comparison between a given shape and its convex hull. There are also some non-trivial approaches. Here, we define a new measure for shape convexity. It incorporates both area-based and boundary-based information, and in accordance with this it is more sensitive to boundary defects than exclusively area-based convexity measures. The new measure has several desirable properties and it is invariant under similarity transformations. When compared with convexity measures that trivially follow from the comparison between a measured shape and its convex hull then the new convexity measure also shows some advantages, particularly for shapes with holes.