Fast algorithms to compute the elementary operators of mathematical morphology

Mathematical Morphology (MM) studies the representation of image operators in terms of some families of simple operators, called the elementary operators of MM. A drawback of this approach is that the representation of some operators is not efficient, since it uses a large number of elementary operators. Fast algorithms are the solution found by some authors to implement image operators that have complex representations. Two drawbacks of this solution are: i-they change the architecture of the software that implement the operators by the morphological representation. ii-these implementations are very specific and can not be used to implement other operators. Here, we study some of these fast algorithms and show that they can be transformed into morphological representations with equivalent performance, if proper data structures and algorithms are used to implement the elementary operators. Finally, some experimental results that illustrate these ideas are given.