Optimal 3 × 3 decomposable disks for morphological transformations

Morphological operations can be efficiently computed on parallel architectures using the decomposition of the structuring elements. In some cases, decomposition is guided to optimize computation for a given underlying hardware, but in other cases it is the shape of the structuring elements which directs the decomposition. In this paper we present a method to decompose disks. Morphological operations with isotropic structuring elements present interesting properties as shape and size descriptors. The method developed is based on a constraint-satisfaction algorithm that gives an optimal decomposable disk. Optimality is given by the shape of the disk since it is the best discrete approximation of a circle that allows a 3 × 3 decomposition. © 1997 Elsevier Science B.V.