Image processing operations and their digital signal analogs

The authors demonstrate several homomorphic relationships between Minkowski´s addition of black and white images and their discrete signal counterparts. In particular, several special relationships involving the Z-transform and discrete convolution of signals are used to demonstrate analagous properties in the image domain. In addition to the work in black and white images, extensions to fuzzy sets and colored images are suggested. The importance of the propositions discussed is twofold; by relating the theories of mathematical morphology in the one area are shown to have analogs in the other. The work contributes to a unified theory of image and signal processing