Utilizing spatial association analysis to determine the number of multiple grids for multiple-point statistics

Abstract

Scale selection is a fundamental issue of spatial analysis. Based on spatial association analysis, this paper proposes a quantitative method for estimating the scale, which is represented using the minimal number of multiple grids in a single normal equation simulation. First, the largest scale structural information that a data template can consider for the finest grid is computed using the distance between the central cell and the border of the data template. The maximum distance at which cells are associated with each other in the training image is then analyzed using join count statistics. Finally, the minimal number of multiple grids is estimated based on the criterion that the data template used on the largest grid should account for the maximum distance between associated cells. The proposed method is validated using two- and three-dimensional experiments. The results show that increasing the number of multiple grids does not significantly improve the simulation quality when the number of multiple grids used is larger than that estimated. A sensitivity analysis demonstrates that the proposed method adapts to the configuration of the data template, the geometric structure of the target surface objects, and a re-scaled training image if it adequately represents the large-scale structural information of the target surface objects.