A Bayesian Approach to Morphological Models Characterization

Image Analysis and Stereology

François Willot¹  Bruno Figliuzzi¹  Grégoire Naudin²  Pierre Dupuis²  Bernard Querleux²  Antoine Montaux-Lambert²  Etienne Huguet² 

[1] Center for Mathematical Morphology - Mines ParisTech - PSL Research University;L'Oréal R&I;

关键词: bayesian models;    monte carlo markov chains algorithms;    morphological models;   

DOI  :  10.5566/ias.2641

来源: DOAJ

【 摘 要 】

Morphological models are commonly used to describe microstructures observed in heterogeneous materials. Usually, these models depend upon a set of parameters that must be chosen carefully to match experimental observations conducted on the microstructure. A common approach to perform the parameters determination is to try to minimize an objective function, usually taken to be the discrepancy between measurements computed on the simulations and on the experimental observations, respectively. In this article, we present a Bayesian approach for determining the parameters of morphological models, based upon the definition of a posterior distribution for the parameters. A Monte Carlo Markov Chains (MCMC) algorithm is then used to generate samples from the posterior distribution and to identify a set of optimal parameters. We show on several examples that the Bayesian approach allows us to properly identify the optimal parameters of distinct morphological models and to identify potential correlations between the parameters of the models.

【 授权许可】

Unknown