Estimation of shape mixture by granulometric methods

Francis M. Sand; Edward R. Dougherty

doi:10.1117/12.179201

30 June 1994 Estimation of shape mixture by granulometric methods

Francis M. Sand, Edward R. Dougherty

Proceedings Volume 2300, Image Algebra and Morphological Image Processing V; (1994) https://doi.org/10.1117/12.179201
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

It is known that if a binary random image is composed of a disjoint union of translates of i.i.d. randomly scaled homothetics of an arbitrary compact set, then, for any convex, compact granulometric generator, the granulometric moments are asymptotically normal and there exist asymptotic representations of the moments of the granulometric moments. The present paper extends the asymptotic theory to a random image composed of a disjoint union of translates of scaled homothetics of a finite collection of compact primitives (shapes) under the condition that the mixture proportions of the shapes are known and fixed. Grain sizing is independent, with the sizings for each primitive being identically distributed. Based on this new granulometric structure theorem for mixed grain images, an estimation method is proposed that estimates the mixture proportions from estimates of the granulometric-moment means derived from running the granulometry on realizations of the mixed process. The granulometric mixture estimation is compared to maximum-likelihood estimation.

Citation Download Citation

Francis M. Sand and Edward R. Dougherty "Estimation of shape mixture by granulometric methods", Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, (30 June 1994); https://doi.org/10.1117/12.179201

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