Domain-variant gray-scale morphology

Eugene J. Kraus

doi:10.1117/12.44324

1 April 1991 Domain-variant gray-scale morphology

Eugene J. Kraus

Proceedings Volume 1451, Nonlinear Image Processing II; (1991) https://doi.org/10.1117/12.44324
Event: Electronic Imaging '91, 1991, San Jose, CA, United States

Abstract

Spatially variant versions of classic morphological operations are introduced. The probes used are locally variant on their domains. Range invariant morphological filters are introduced. A generalized Matheron Representation Theorem for these filters in terms of spatially variant erosions is proved. Locally variant openings and locally variant algebraic openings are introduced, and a generalized Matheron Representation Theorem for locally variant algebraic openings is proved. The theory presented is quite general and is valid for functions defined on subsets of any space X and with values in any ordered commutative group G for which the concept of least upper bound and greatest lower bound are meaningful. When G equals R, the real numbers, and X equals Rn the theory encompasses real signal processing (n equals 1), real image processing (n equals 2), and real multivariable signal processing (n > 2). When G equals Z, the integers, and X equals Zn the theory encompasses the digitized versions of each form of processing.

Citation Download Citation

Eugene J. Kraus "Domain-variant gray-scale morphology", Proc. SPIE 1451, Nonlinear Image Processing II, (1 April 1991); https://doi.org/10.1117/12.44324

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