A Quantitative Evaluation Method for Nonstationarity of Training Image Based on Pattern Tiles Distance

An a priori model for multipoint statistics (MPS) modeling approaches is a training image. Before using MPS modeling, it must be determined whether the training images satisfy the spatial statistical stationarity. Modeling can be performed using the regular MPS approach if a training image is stationary. Otherwise, an enhanced method of nonstationary modeling is required. For instance, partition-based nonstationary modeling is an option. This study proposes a nonstationary evaluation metric based on pattern tile distances. It is possible to more accurately quantify the characteristics of the various distributions of spatial structure features in the entire space and achieve the goal of quantitatively evaluating the nonstationary metrics of training images by quantifying the distances of lower-level subpatterns in the pattern. Furthermore, an automatic partitioning approach based on pattern tile discrepancy is proposed for nonstationary training images to avoid the subjective and inefficient issues of manual partitioning when the training images cannot meet the stationary requirement of MPS modeling.