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A patchwork approach to stochastic simulation: A route towards the analysis of morphology in multiphase systems

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  • El Ouassini, Ayoub
  • Saucier, Antoine
  • Marcotte, Denis
  • Favis, Basil D.

Abstract

We propose a new sequential stochastic simulation approach for black and white images in which we focus on the accurate reproduction of the small scale geometry. Our approach aims at reproducing correctly the connectivity properties and the geometry of clusters which are small with respect to a given length scale called block size. Our method is based on the analysis of statistical relationships between adjacent square pieces of image called blocks. We estimate the transition probabilities between adjacent blocks of pixels in a training image. The simulations are constructed by juxtaposing one by one square blocks of pixels, hence the term patchwork simulations. We compare the performance of patchwork simulations with Strebelle’s multipoint simulation algorithm on several types of images of increasing complexity. For images composed of clusters which are small with respect to the block size (e.g. squares, discs and sticks), our patchwork approach produces better results than Strebelle’s method. The most noticeable improvement is that the cluster geometry is usually reproduced accurately. The accuracy of the patchwork approach is limited primarily by the block size. Clusters which are significantly larger than the block size are usually not reproduced accurately. As an example, we applied this approach to the analysis of a co-continuous polymer blend morphology as derived from an electron microscope micrograph.

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  • El Ouassini, Ayoub & Saucier, Antoine & Marcotte, Denis & Favis, Basil D., 2008. "A patchwork approach to stochastic simulation: A route towards the analysis of morphology in multiphase systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 418-436.
  • Handle: RePEc:eee:chsofr:v:36:y:2008:i:2:p:418-436
    DOI: 10.1016/j.chaos.2006.06.100
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    References listed on IDEAS

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    1. Saucier, Antoine & Muller, Jiri, 1999. "Textural analysis of disordered materials with multifractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(1), pages 221-238.
    2. Saucier, Antoine & Richer, Jacques & Muller, Jiri, 2002. "Assessing the scope of the multifractal approach to textural characterization with statistical reconstructions of images," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(1), pages 231-259.
    3. Saucier, Antoine & Muller, Jiri, 1993. "Remarks on some properties of geometrical multifractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(3), pages 350-362.
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