Set Operations on Closed Intervals and their Applications to the Automatic Programming of MMach’s

Abstract

Recently much research effort has been addressed to the automatic programming of Binary Morphological Machines (MMach’s). A very promising approach to this problem is the description of the target operator by input-output pairs of images and the translation of these data into efficient MMach programs. This approach can be decomposed in two equally important steps: i — learning of the target operator from pairs of images; ii — search of economical representations for the operators learned. The theory presented in this paper is useful for both steps of this procedure.We will present some set operations on closed intervals and give efficient algorithms to perform them. These operations will be used to parallelize MMach programs and to prove the equivalence between distinct MMach programs.

The authors have received partial financial support of Olivetti do Brasil, CNPq, grant PROTEM-CC-ANIMOMAT, and cooperation USP-COFECUB.