Object Descriptors Based on a List of Rectangles: Method and Algorithm

Most morphological operators use a unique structuring element, possibly at different scales, to describe an object. In addition, morphological algorithms are often restricted to 1D structuring elements, combinations of 1D elements, or isotropic structuring elements (like circles), because of the lack of methods directly applicable to arbitrary shaped 2D structuring elements. While these descriptors have proved useful in the past, we propose an alternative that uses the list of maximal rectangles contained in a set X. In particular, we focus on an opening that preserves large rectangles contained in a set X and on its companion 2D algorithm that builds a list of all the maximal rectangles that fit inside an arbitrary set X. This list is the base of new descriptors that have been used successfully for machine learning tasks related to the analysis of human silhouettes. For convenience, we provide the C source code and a program of our algorithm at http://www.ulg.ac.be/telecom/rectangles.