Supplementary Materials for manuscript: Improving pattern reconstruction using correlation functions computed in directions

These Materials contain the results of all simulations performed for study accepted for publication:
Gerke K.M., Karsanina M.V., Vasilyev R.V., Mallants D., 2014. Improving pattern reconstruction using correlation functions computed in directions. Europhysics Letters (http://iopscience.iop.org/0295-5075).
Short abstract: In this Letter we introduce a new method to calculate correlation functions in four principal directions (i.e. two orthogonal and two diagonal) and separately utilize them for image reconstruction. We show this method is particularly suitable for anisotropic porous media but also improves image reconstruction for isotropic structures. Based on analysis of numerous reconstructions of four binary patterns using different sets of two-point probability and linear (for both phases) correlation functions, we quantify the accuracy of each set. Averaging of correlation functions in all directions almost always results in poorer reconstructions. Addition of separate directions significantly improves the quality of replicas with only a minor increase in computational effort.