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:\nGerke 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).\nShort 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.\nLineage: These include 10 reconstructions using 12 different sets of correlation functions for four original images of isotropic and anisotropic crosses. We report original and replica images, as well as correlation functions sets for all four originals.

本数据集包含已接收待发表研究的全部仿真结果：
Gerke K.M.、Karsanina M.V.、Vasilyev R.V.、Mallants D.，2014年。《利用沿特定方向计算的相关函数优化图案重构》，《欧洲物理快报》（Europhysics Letters，http://iopscience.iop.org/0295-5075）。

简短摘要：本研究提出一种全新方法，可沿四个主方向（即两个正交方向与两个对角方向）计算相关函数，并将其分别应用于图像重构任务。研究表明，该方法尤其适用于各向异性多孔介质，同时也能优化各向同性结构的图像重构效果。本研究针对四类二元图案，采用不同组合的两点概率相关函数与线性（针对两相）相关函数，开展了大量重构实验，通过分析量化了每组相关函数的重构精度。沿所有方向平均化相关函数的常规做法，几乎总会导致重构效果劣化；而单独使用各方向相关函数的方案，仅需小幅增加计算量，即可显著提升重构副本的质量。

数据集溯源：本数据集包含针对四类各向同性与各向异性十字形原始图像，采用12组不同相关函数开展的10次重构实验结果。本数据集提供了全部四类原始图像、重构副本图像，以及所有四组原始图像对应的相关函数组合。