Perceptual convexity

Often objects which are not convex in the mathematical sense are treated as 'perceptually convex'. We present an algorithm for recognition of the perceptual convexity of a 2-d contour. We start by reducing the notion of 'a contour is perceptually convex' to the notion of 'a contour is Y-convex'. The latter reflects an absence of large concavities in the OY direction of an XOY frame. Then we represent a contour by a G-graph and modify the slowest descent-the small leaf trimming procedure recently introduced for the estimation of shape similarity. We prove that executing the slowest descent down to a G-graph consisting of 3 vertices allows us to detect large concavities in the QY direction. This allows us to recognize the perceptual convexity of an input contour.