A fast two part direct sampling method based on interpolation

Multiple-point simulation methods are effective in reproducing complex spatial structures, however intensive computations are needed in the pattern matching process. We propose a new method to alleviate the computation burden of direct sampling. This method first constructs a mixed sparse part using a regular sub grid and random cells from the target image. Next, direct sampling is only performed on this part and all other cells are estimated from neighboring conditioning cells rather than simulated. Two estimation methods are proposed for categorical and continuous variables based on the Bayes' theorem and regression under the assumption that different conditioning cells contribute individually to the estimation of the central cell. Comparisons are made between the proposed method and direct sampling. Experiments show that the proposed method can save at most 90% and 40% computation time for the simulation of categorical and continuous variables, which is faster than not only the direct sampling but also the previously proposed two stage direct sampling method, which saves only at most 50% and 13% simulation time to generate results with similar simulation quality.