Stochastic simulation of patterns using Bayesian pattern modeling

In this paper, a Bayesian framework is introduced for pattern modeling and multiple point statistics simulation. The method presented here is a generalized clustering-based method where the patterns can live on a hyper-plane of very low dimensionality in each cluster. The provided generalizationallows a remarkable increase in variability of the model and a significant reduction in the number of necessary clusters for pattern modeling which leads to more computational efficiency compared with clustering-based methods. The Bayesian model employed here is a nonlinear model which is composed of a mixture of linear models. Therefore, the model is stronger than linear models for data modeling and computationally more effective than nonlinear models. Furthermore, the model allows us to extract features from incomplete patterns and to compare patterns in feature space instead of spatial domain. Due to the lower dimensionality of feature space, comparison in feature space results in more computational efficiency as well. Despite most of the previously employed methods, the feature extraction filters employed here are customized for each training image (TI). This causes the features to be more informative and useful. Using a fully Bayesian model, the method does not require extensive parameter setting and tunes its parameters itself in a principled manner. Extensive experiments on different TIs (either continuous or categorical) show that the proposed method is capable of better reproduction of complex geostatistical patterns compared with other clustering-based methods using a very limited number of clusters.     

CHDS: conflict handling in direct sampling for stochastic simulation of spatial variables

Stochastic Environmental Research and Risk Assessment - In recent years, multiple-point geostatistical (MPS) approaches have gained significant popularity for modeling subsurface heterogeneity in...     

Exploiting transformation-domain sparsity for fast query in multiple-point geostatistics

Multiple-point geostatistics has recently attracted significant attention for characterization of environmental variables. Such methods proceed by searching a large database of patterns obtained from a training image to find a match for a given data-event. The template-matching phase is usually the most time-consuming part of a MPS method. Linear transformations like discrete cosine transform or wavelet transform are capable of representing the image patches with a few nonzero coefficients. This sparsifying capability can be employed to speed up the template-matching problem up to hundreds of times by multiplying only nonzero coefficients. This method is only applicable to rectangular data-events because it is impossible to represent an odd-shaped data-event in a transformation domain. In this paper, the method is applied to speed up the image quilting (IQ) method. The experiments show that the proposed method is capable of accelerating the IQ method tens of times without sensible degradation in simulation results. The method has the potential to be employed for accelerating optimization-based and raster-scan patch-based MPS algorithms.     

Fast direct sampling for multiple-point stochastic simulation

Multiple-point statistics simulation has recently attracted significant attention for the simulation of complex geological structures. In this paper, a fast direct sampling (FDS) algorithm is presented based on a fast gradient descent pattern matching strategy. The match is directly extracted from the training image (TI) and so the method does not require intensive preprocessing and database storage. The initial node of the search path is selected randomly but the following nodes are selected in a principled manner so that the path is conducted to the right match. Each node is selected based on the matching accuracy and the behavior of the TI in the previous node. A simple initialization strategy is presented in this paper which significantly accelerates the matching process at the expense of a very naïve preprocessing stage. The proposed simulation algorithm has several outstanding advantages: it needs no (or very limited) preprocessing, does not need any database storage, searches for the match directly in the TI, is not limited to fixed size patterns (the pattern size can be easily changed during simulation), is capable of handling both continuous and categorical data, is capable of handling multivariate data, and finally and more importantly, is a fast method while maintaining high standards for the matching quality. Experiments on different TIs reveal that the simulation results of FDS and DS are comparable in terms of pattern reproduction and connectivity while FDS is far faster than DS.     

Investigating extreme scenarios with multiple-point geostatistics and variance maximization

Stochastic Environmental Research and Risk Assessment - In many geoscience applications, the data extracted from environmental variables are very limited. Multiple-point geostatistical (MPS)...