Rank-based decompositions of morphological templates

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the line ar domain, we consider it timely to investigate matrix decomposition techni ques in the nonlinear domain with applications in image processing. The mat hematical basis for these investigations is the new theory of rank within m inimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing co mmunity. In this paper we derive a heuristic algorithm for the decompositio n of matrices having arbitrary rank.