Generalized method of moments for shape distribution in random images

Francis M. Sand

doi:10.1117/12.216357

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11 August 1995 Generalized method of moments for shape distribution in random images

Francis M. Sand

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Proceedings Volume 2568, Neural, Morphological, and Stochastic Methods in Image and Signal Processing; (1995) https://doi.org/10.1117/12.216357
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

The pattern spectrum method of moments has been used by the author to estimate the shape distribution in random binary images with unknown grain size. Simultaneous estimation of the parameters of the grain size distribution and the mixture proportions of the specified shapes required solution of simultaneous nonlinear equations and was demonstrated only for a small dimensionality. The generalization of the method permits a larger dimensionality by simplifying the estimation equations. Using an iterative approach to normal grain size distribution, the estimation equations are shown to be : 1) linear in the proportions, 2) cubic in micrometers , 3) quadradic in O² at each stage. An example demonstrates that the iterative process converges rapidly to an accurate estimate of the parameters.

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Francis M. Sand "Generalized method of moments for shape distribution in random images", Proc. SPIE 2568, Neural, Morphological, and Stochastic Methods in Image and Signal Processing, (11 August 1995); https://doi.org/10.1117/12.216357

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