Asymptotic distributions for morphological granulometric moments

Francis M. Sand; Edward R. Dougherty

doi:10.1117/12.60629

1 June 1992 Asymptotic distributions for morphological granulometric moments

Francis M. Sand, Edward R. Dougherty

Proceedings Volume 1769, Image Algebra and Morphological Image Processing III; (1992) https://doi.org/10.1117/12.60629
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

Treating a binary image as a random process results in the granulometric pattern spectrum being a random function and its moments being random variables. Because these moments are used as image signatures and as local texture descriptors, their statistical distributions, and in particular their moments, are of importance. The present paper employs a theorem of Cramer to show for a certain class of image models that the pattern-spectrum-moment distributions are asymptotically normal, and it provides asymptotic expressions for moments of the spectrum moments. To facilitate application of Cramer's theory the paper introduces the class of orthogonal granulometric generators.

Citation Download Citation

Francis M. Sand and Edward R. Dougherty "Asymptotic distributions for morphological granulometric moments", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); https://doi.org/10.1117/12.60629

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