Abstract
Mathematical Morphology (MM) is a general framework for studying mappings between complete lattices. In particular, mappings between binary images that are translation invariant and locally defined within a window are of special interest in MM. They are called W-operators. A key aspect of MM is the representation of W-operators in terms of dilations, erosions, intersection, union, complementation and composition. When W-operators are expressed in this form, they are called morphological operators. An implementation of this decomposition structure is called morphological machine (MMach). A remarkable property of this decomposition structure is that it can be represented efficiently by graphs called Binary Decision Diagrams (BDDs). In this paper, we propose a new architecture for MMachs that is based on BDDs. We also show that reduced and ordered BDDs (ROBDDs) are non-ambiguous schemes for representing W- operators and we present a method to compute them. This procedure can be applied for the automatic proof of equivalence between morphological operators, since the W-operator they represent are equal if and only if they have the same ROBDD.
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Barrera, J., Hashimoto, R.F. (2005). Binary Decision Diagrams as a New Paradigm for Morphological Machines. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_1
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DOI: https://doi.org/10.1007/1-4020-3443-1_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3442-8
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