Recursive voids for identifying a nonconvex boundary of a set of points in the plane

We introduce a method that identifies the boundary of a nonconvex shape of a set of points in the plane. The boundary of the shape is explored through finding empty regions recursively within a shell that encapsulates all of the points. Our algorithm is output sensitive and runs in linear O ( ℓ n ) time determined by the output parameter ℓ , which is proportional to the length of the nonconvex boundary measured by a threshold unit distance. The recursive nature of our algorithm allows a tree structure that characterizes the empty regions, and by complementarity, the nonconvex shape itself. We use a distance measure based on lowest common ancestor of a pair of nodes in this tree and define the complexity of a shape as the average of the distances between all pairs. We present computational results on data size, threshold, shape complexity and noise on a set of different nonconvex shapes.