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Proceedings Paper

Estimation of shape mixture by granulometric methods
Author(s): Francis M. Sand; Edward R. Dougherty
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Paper 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.

Paper Details

Date Published: 30 June 1994
PDF: 6 pages
Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, (30 June 1994); doi: 10.1117/12.179201
Show Author Affiliations
Francis M. Sand, Fairleigh Dickinson Univ. (United States)
Edward R. Dougherty, Rochester Institute of Technology (United States)

Published in SPIE Proceedings Vol. 2300:
Image Algebra and Morphological Image Processing V
Edward R. Dougherty; Paul D. Gader; Michel Schmitt, Editor(s)

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