Optimal granulometric-induced filters

Edward R. Dougherty

doi:10.1117/12.179209

30 June 1994 Optimal granulometric-induced filters

Edward R. Dougherty

Proceedings Volume 2300, Image Algebra and Morphological Image Processing V; (1994) https://doi.org/10.1117/12.179209
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Euclidean granulometries are used to decompose a binary image into a disjoint union based on interaction between image shape and the structuring elements generating the granulometry. Each subset of the resulting granulometric spectral bands composing the union defines a filter by passing precisely the bands in the subset. Given an observed image and an ideal image to be estimated, an optimal filter must minimize the expected symmetric-difference error between the ideal image and filtered observed image. For the signal-union-noise model, and for both discrete and Euclidean images, given a granulometry, a procedure is developed for finding a filter that optimally passes bands of the observed noisy image.

Citation Download Citation

Edward R. Dougherty "Optimal granulometric-induced filters", Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, (30 June 1994); https://doi.org/10.1117/12.179209

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