Root signal sets of morphological filters

Abstract

The theory of state description for the binary root signal set of morphological filters is presented. Some properties of root signals are discussed. For a signal of length n and structuring element of size k, the number of binary roots for morphological opening and closing is represented by the difference equation R(n + 1) = 2R(n) − R(n − 1) + R(n − k). For open-closing and clos-opening, the difference equation is R(n + 1) = R(n) + R(n + 1 − k).