Finding Optimal Sequential Decompositions Of Erosions And Dilations

. A fundamental problem in the eld of automatic design of morphological operators is the transformation of standard morphological representations, that are adequate for operator learning, into other equivalent representations, that permit eÆcient implementations of the operators learned. In this paper, we study this problem restricted to the families of set translation invariant erosions and dilations. We present a general method for the decomposition of erosions (respec., dilations) by arbitrarily shaped structuring elements into a minimum number of compositions of erosions (respec. dilations) by subsets of the elementary square (i.e.,the 3 3 square centered at the origin). The fundamental idea of the method proposed is the application of Combinatorial Optimization techniques, supported by generic algebraic and geometrical properties of erosions and dilations. Key words: erosion, dilation, Minkowski addition, decomposition, structuring element. 1. Introduction The problem of desi..