Optical EngineeringFacilitation of optimal binary morphological filter design via structuring element libraries and design constraints
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For both the binary and gray scales, mean square optimal digital morphological filters have been 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; however, without prior statistical information or an adequate image-noise model, even in the binary setting, filter design is computationally intractable for moderately sized observation windows. The mitigation of the computational burden via design constraints is the focus here. Although the resulting filter will be suboptimal, if the constraints are imposed in a suitable manner, little loss of filter performance occurs in return for design tractability. Three approaches are considered: limiting the number of terms in the Matheron expansion, constraining the observation window, and employing structuring element libraries. In the latter methodology various sublibraries are formed and a suboptimal filter is derived from image-noise statistics in conjunction with a basis search restricted to relevant sublibraries. This study analyzes two techniques for library construction: the expert approach involves prior sublibrary formation based on knowledge of important filter bases and the first-order approach employs single-erosion statistical information to limit the basis search to likely useful candidates.