Automatic programming of binary morphological machines
Júnior Barrera, Flávio S. Corrêa da Silva, Gerald Jean Francis Banon · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
An important aspect of Mathematical Morphology is the description of set operators by a formal language, the Binary Morphological Language (BML), whose vocabulary are chlations, erosions, antidilations, antierosions, union and intersection.This language is complete (i.e. it can represent any set operator) and expressive (i.e.many useful operators can be represented as phrases with relatively few words).Since the sixties special machines, the Binary Morphological Machines (BMMach's), have been built to implement the BML with increasing efficiency.However, designing useful BMMach programs is not ao elementary task.Recently, much research effort has been addressed to automating the programming of BMMach's.The goal is to find suitable knowledge representation fomialisms to describe operations over geometric structures and to translate them into BMMach programs.We propose an approach for the automated programming of translation invariant operators: operators are describecl either by logical expressions or by sample input-output lists and translated into BMMach prograrns by semantic evaluation, probably approximately correct (PAC) leaming or automated deduction over abstract operations.The generated operators are optimizecl by transformations on their decomposition structure.A priori knowledge is modeled by associating probability distnbutions to occurrences of images.The design of optimal and suboptirnal morphological filters can be seen as particular cases of the proposed approach.Some examples illustrate the main ideas presented.