Using structuring-element libraries to design suboptimal morphological filters
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For both the binary and gray scales, mean-square optimal digital morphological filters have been fully characterized previously in terms of the Matheron erosion representation for increasing, translation-invariant mappings. Included in the characterization is the minimal search strategy for the optimal filter basis; nonetheless, in the absence of prior statistical information or an adequate image-noise model, even in the binary setting design is computationally intractable for moderately sized observation windows.The computational burden can be mitigated by imposing constraints on the filter. The present paper is mainly concerned with the development of structuring-element libraries to which the basis search can be confined. More specifically, the authors focus on the expert-library approach: various sublibraries are formed, each of which corresponds to certain key filters, the overall library is formed as the union of the sublibraries, and a suboptimal filter is derived from image-noise statistics in conjunction with a basis search restricted to relevant sublibraries.
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Image Algebra and Morphological Image Processing II
