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11 August 1995 Generalized method of moments for shape distribution in random images
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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.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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);


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