Discrete black and white object recognition via morphological functions

Two morphological algorithms that attempt to recognize a black and white object directly in its discrete domain are presented. The first algorithm is based on covariance functions, while the second is based on a variant of size distribution functions. In both these algorithms, the scale correction has been automated. Also presented is a complete geometric and algebraic characterization of objects that are identical with respect to the proposed methodologies, and it is shown that the induced equivalent classes over binary images contain objects that are structurally very similar. This has been accomplished by introducing the notions of a strongly attached pixel, discrete structure of an image, and a structure preserving operation. An outcome of the analysis is the insight into the relationship between the discrete structure of an image and the induced equivalence classes