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Morphology on umbra Matrices

The umbra transform serves as a connection between gray-scale morphology and the classical two-valued morphology of G. Matheron and H. Hadwiger. From a general set-theoretic perspective, the umbra transform of an image (or signal) results in an infinite set, even in the discrete case. By employing bound matrix image representation it is possible to represent the umbra by a finite data structure, the result being an approach that is both intuitive and computational. Moreover, the method is essentially dimensionally independent and thus applies to both morphological image and signal processing.