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

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.