Optimization of image processing by Boolean function transformation

From the point of view of binary Mathematical Morphology every operator with a finite processing window can be defined by a Boolean function. Such function contains then both the information about the type of operation (dilation, erosion, Hit-or-Miss Transformation, etc.) and a structuring element used. To implement transformations optimally it is then possible to use some elements of the Theory of Switching Circuits such as Boolean function minimisation and decomposition instead of applying the traditional morphological approaches that offer the structuring element decomposition or operator decomposition. The proposed method brings simplification of some tasks and their software and hardware implementations.