Hybrid human-machine binary morphological operator design. An independent constraint approach

A basic paradigm in mathematical morphology is the construction of set operators by concatenations of dilations and erosions via the operations of composition, union, intersection and complementation. Since its introduction, in the 1960s by Matheron and Serra, this paradigm has been applied on image analysis for designing set operators, that were called morphological operators. Classically, morphological operators are constructed based on the experience and intuition of human beings. Recently, an approach for the automatic design of morphological operators, based on statistical optimization from the observation of collections of image pairs, was proposed. The two approaches have drawbacks: usually, the "rst approach is slow and depends on an expert in mathematical morphology, while the second requires large amounts of observed data. This paper proposes a symbiosis between the human and the statistical design approaches. The idea is that the design procedure be composed of simpli"ed forms of both. Thus, avoiding di$culties that arise when applying each one independently. The strategy adopted to achieve this goal is restricting the space of operators considered with a human-designed envelope. ( 2000 Elsevier Science B.V. All rights reserved.