Template decomposition plays an important role in image processing algorithm optimization and parallel image processing. In this paper, a template decomposition technique based on the factorization of max-polynomials is presented. A morphological template may be represented by a max-polynomial, a notation used in combinatorial optimization. The problem of decomposition of a morphological template is thus reduced to the problem of factorization of the corresponding max-polynomial. A sufficient condition for decomposing a one-dimensional morphological template into a set of two-point templates is established. Once the condition is satisfied, the construction of the decomposition is straightforward. A general procedure is also given for testing whether such a decomposition exists for an arbitrary one-dimensional morphological template.
Dong Li, Dong Li,
"Max-polynomials and template decomposition", Proc. SPIE 1568, Image Algebra and Morphological Image Processing II, (1 July 1991); doi: 10.1117/12.49891; https://doi.org/10.1117/12.49891