Estimating the Parameters of a Stochastic Geometrical Model for Multiphase Flow Images Using Local Measures

Leo Theodon, Tatyana Eremina, Kassem Dia, Fabrice Lamadie, Jean-Charles Pinoli, Johan Debayle

Abstract

This paper presents a new method for estimating the parameters of a stochastic geometric model for multiphase flow image processing using local measures. Local measures differ from global measures in that they are only based on a small part of a binary image and consequently provide different information of certain properties such as area and perimeter. Since local measures have been shown to be helpful in estimating the typical grain elongation ratio of a homogeneous Boolean model, the objective of this study was to use these local measures to statistically infer the parameters of a more complex non-Boolean model from a sample of observations. An optimization algorithm is used to minimize a cost function based on the likelihood of a probability density of local measurements. The performance of the model is analysed using numerical experiments and real observations. The errors relative to real images of most of the properties of the model-generated images are less than 2%. The covariance and particle size distribution are also calculated and compared.


Keywords
Local Measures; Maximum Likelihood; Minkowski Functionals; Statistical Inference; Stochastic Geometry

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DOI: 10.5566/ias.2638

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Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)