Granulometric estimation of sizing parameters and proportions for gamma-distributed grain sizes
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Granulometric method-of-moment estimation is based on the asymptotic representation of expectations of granulometric moments in terms of grain-sizing model parameters, mixture proportions, and geometric constants. Method-of-moment estimation for sizing parameters and mixture proportions is accomplished by replacing granulometric-moment expectations with moment estimations from image realizations and then solving the resulting system of equations for the model parameters. The present paper considers the special case in which all sizing parameters for the various shapes generating the random image possess a common gamma sizing distribution. In particular, the usually difficult system of nonlinear equations reduces to a more computationally tractable form, which is important when there is more than a single image generator.
