Simulation of Earth textures by conditional image quilting

Abstract

Training image-based approaches for stochastic simulations have recently gained attention in surface and subsurface hydrology. This family of methods allows the creation of multiple realizations of a study domain, with a spatial continuity based on a training image (TI) that contains the variability, connectivity, and structural properties deemed realistic. A major drawback of these methods is their computational and/or memory cost, making certain applications challenging. It was found that similar methods, also based on training images or exemplars, have been proposed in computer graphics. One such method, image quilting (IQ), is introduced in this paper and adapted for hydrogeological applications. The main difficulty is that Image Quilting was originally not designed to produce conditional simulations and was restricted to 2-D images. In this paper, the original method developed in computer graphics has been modified to accommodate conditioning data and 3-D problems. This new conditional image quilting method (CIQ) is patch based, does not require constructing a pattern databases, and can be used with both categorical and continuous training images. The main concept is to optimally cut the patches such that they overlap with minimum discontinuity. The optimal cut is determined using a dynamic programming algorithm. Conditioning is accomplished by prior selection of patches that are compatible with the conditioning data. The performance of CIQ is tested for a variety of hydrogeological test cases. The results, when compared with previous multiplepoint statistics (MPS) methods, indicate an improvement in CPU time by a factor of at least 50.

Hydrostratigraphic modeling using multiple-point statistics and airborne transient electromagnetic methods

“…The algorithm is originally designed to synthesize and/or replicate patterns from 2-D images but has since been modified to accommodate conditioning data and 3-D geoscience problems (Mahmud et al, 2014). The concept of the iqsim method is straightforward.…”

“…This guarantees a controlled modeling environment in which the TI contains highly relevant hydrostratigraphic architecture. The main contributions of this study are (1) a practical real-world example of stochastic reconstruction of incomplete geophysical datasets; (2) comparison of three MPS methods for integrating geophysical data -snesim (Liu, 2006;Strébelle and Journel, 2000), direct sampling (DS) and image quilting (iqsim) (Hoffimann et al, 2017;Mahmud et al, 2014); (3) validation of the comparison results by (a) visual inspection, (b) a mathematical comparison method called the analysis of distance (ANODI) (Tan et al, 2014) and (c) comparison of the simulation results against the borehole lithology logs; and (4) to show the strengths and weaknesses of a stochastic hydrostratigraphic modeling framework, and (5) an example using the direct sampling method and showing how to use the cognitive hydrostratigraphic interpretation of one area to directly generate hydrostratigraphic models of new areas, using only the soft data from the new area.…”

Hydrostratigraphic modelling using multiple-point statistics and airborne transient electromagnetic methods

“…The algorithm is originally designed to synthesize and/or replicate patterns from 2D images, but has since been 265 modified to accommodate conditioning data and 3D geoscience problems (Mahmud et al 2014). The concept of the iqsim method is straightforward.…”

“…By applying several measures to assess and compare the modeling results, the selected MPS tools are tried, tested and compared on real-world data. The main contributions of this study are: 1) a practical real-world example 120 of stochastic reconstruction of incomplete geophysical datasets, 2) Comparison of three MPS methods for integrating geophysical data: snesim (Liu 2006, Strébelle andJournel 2000), direct sampling (DS) ) and image quilting (iqsim) (Hoffimann et al 2017, Mahmud et al 2014, 3) validation of the comparison results by: a) visual inspection, b) a mathematical comparison method called the "analysis of distance" (ANODI) (Tan et al 2014), c) comparison of the simulation results against the borehole lithology logs, 4) to show the strengths/weaknesses of a stochastic 125 hydrostratigraphic modelling framework, and 5) a practical example showing how to use the cognitive hydrostratigraphic interpretation of one area to directly generate hydrostratigraphic models of new areas, using only the soft data from the new area.…”

Conditioning multiple-point statistics simulations to block data

“…These latter methods use patterns database built from the training image and are also based on multiple grid approaches. Other patchbased MPS algorithms not using multiple grids nor databases consist in pasting overlapping boxes of pixels along a raster path, by minimizing a cross-correlation function over the overlapping region in the algorithm ccsim (Tahmasebi et al, 2012), or by minimizing an error between the common area followed by an optimal cut through this area in the algorithm conditional image quilting (CIQ) (Mahmud et al, 2014). Theses methods allow to better model the connectivity of the structures, but make the conditioning difficult.…”