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Existence and synthesis of minimal-basis morphological solutions for a restoration-based boundary-value problem

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Abstract

The present paper formulates digital binary filter design for the subtractive-noise restoration problem in terms of the classical boundary-value-problem paradigm. The boundary-value problem involves both operator relations and invariant (fixed-point) boundary conditions. Noise-hole restoration is to be achieved while certain shape-based structures remain invariant, and the boundary-value problem incorporates these conditions. A design approach is formulated that derives an increasing, translation-invariant solution via the morphological basis expansion directly from the statement of the boundary-value problem itself without positing any a priori class of structuring elements over which to search. Existence conditions are analyzed and, when they exist, solutions are found that possess both minimal bases and minimal structuring elements. These solutions are extensive. Owing to duality, antiextensive solutions result for the classical union-noise model and these are discussed.

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Authors and Affiliations

  1. Texas Center for Applied Technology and Department of Electrical Engineering, Texas A&M University, 77843-3128, College Station, TX, USA

    Edward R. Dougherty

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  1. Edward R. Dougherty
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Dougherty, E.R. Existence and synthesis of minimal-basis morphological solutions for a restoration-based boundary-value problem. J Math Imaging Vis 6, 315–333 (1996). https://doi.org/10.1007/BF00123350

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