Issue No. 06 - June (1989 vol. 11)

ISSN: 0162-8828

pp: 586-599

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.24793

ABSTRACT

<p>A unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented. The unification requires a set-theoretic methodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translational-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-invariant, increasing, upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations. The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic filters, linear filters, and shape recognition transforms. Although the developed theory is algebraic, its prototype operations are well suited for shape analysis; hence, the results also apply to systems that extract information about the geometrical structure of signals.</p>

INDEX TERMS

set theory; picture processing; representation theory; morphological image; signal processing; signal transformations; set mappings; semicontinuous system; minimal nonlinear superposition; morphological filters; order-statistic filters; linear filters; shape recognition transforms; shape analysis; geometrical structure; pattern recognition; picture processing; set theory; signal processing

CITATION

P. Maragos, "A Representation Theory for Morphological Image and Signal Processing," in

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 11, no. , pp. 586-599, 1989.

doi:10.1109/34.24793

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