Convexity Measure for Shapes with Partially Extracted Boundaries

Shape descriptors are used in many computer vision tasks. Convexity is one of the most widely used shape descriptors in practical applications 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, but there also other approaches. Independently of whether the convexity descriptors are area based or boundary based, all of them assume that the shape (or shape boundary) is completely known and that the measures apply to the complete data. In this paper we define a convexity measure that can be applied to shapes with partially extracted boundaries. More formally, the new convexity measure deals with planar curves or with disconnected curves consisting of several planar curve segments.