Robust descriptors of binary shapes with applications

The subject of this paper is to propose and test a set of numerical descriptors of 2D binary planar shapes. Given a shape, A, the transformations of A with a given mathematical morphological operation and different structuring elements are considered. The measures of this family of transformed sets provide a numerical description of the original set A. These descriptors are very robust against noise and maintain a reasonable discriminatory power. The robustness against different levels of contour degradation is tested by simulation. Starting with a clean (without noise) set, Lambda, it is assumed that the observed set, A, is a noisy version (with contour degradation) of Lambda. The performance of the descriptors, when they are used to compare different shapes or shapes from a scene with models, is studied and compared with related descriptors based on the granulometric analysis of the original set, which are the closest previous alternative to our approach in the literature.