Algorithms for Mathematical Morphology
Thierry Géraud, Hugues Talbot, Marc Van Droogenbroeck · 2013
This chapter deals with the very important problem of implementing the various image analysis operators, filters and methods. The chapter is organized as follows. It first discusses the translation process of data structures and mathematical morphology definitions in computational terms. It deals with different aspects related to algorithms in the scope of mathematical morphology, proposes a taxonomy, discusses possible tradeoffs, and presents algorithmic classes. The different classes of algorithms presented in the chapter did not appear at the same time in the literature. To illustrate these classes, it presents different algorithms that map the same morphological operator: the geodesic reconstruction by dilation of a function. These aspects are put into perspective for the particular case of the morphological reconstruction operator. From a simple but representative example, the chapter shows that in general there does not exist a single best way to express the implementation of an operator but several. Controlled Vocabulary Terms differential geometry; image reconstruction; mathematical morphology