Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation

Parra, Álvaro; Ortíz, Julián M.

doi:10.1007/s00477-011-0489-1

Cited by 36 publications

(16 citation statements)

References 20 publications

(14 reference statements)

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“…In that case, the boundary cut procedure removes such inconsistencies by setting the boundary at a location that minimizes the overlap errors. Note that until step 2d, IQ shares similarities with previous patch‐based methods [ El Ouassini et al ., ; Parra and Ortiz , ; Tahmasebi et al ., ], notably the use of an overlap region. However, optimally cutting the patches produces significantly improved pattern continuity, as shown in Figure .…”

Section: Methodsmentioning

confidence: 99%

Simulation of Earth textures by conditional image quilting

Mahmud

Mariethoz

Caers

et al. 2014

Water Resources Research

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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.

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Section: Methodsmentioning

confidence: 99%

Simulation of Earth textures by conditional image quilting

Mahmud

Mariethoz

Caers

et al. 2014

Water Resources Research

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“…However, adapting these methods for random paths does not seem to present major difficulties. Even in cases where this may prove difficult, it has been showed that conditioning is possible with unilateral paths (Parra and Ortiz, 2011). In addition, soft conditioning is often present in texture applications, from the user-constrained textures of Ashikhmin (2001) to the image analogies of Hertzmann et al (2001).…”

Section: Resultsmentioning

confidence: 99%

“…The fact that patches can be updated locally means that it is possible to adapt the method to all types of conditioning constraints found in earth science applications. Although approximate because only locally accommodating conditioning data, the idea to change the shape of patches for conditioning is promising and goes in the direction of some recent developments in patch-based MPS methods (Parra and Ortiz, 2011;Tahmasebi et al, 2012a). Several patch-based texture synthesis approaches further deform the content of the patches to improve the alignment of structures crossing their boundaries, e.g.…”

Section: Patch-based Methodsmentioning

confidence: 99%

“…Unilateral paths offer the possibility of a rigorous dependence with successively simulated values, but with many algorithms it can lead to difficulties in conditioning. Conditioning under unilateral path can be achieved an alteration of the unilateral scheme in order to look ahead for conditioning data (Daly, 2004;Parra and Ortiz, 2011) or by using iterative methods (Kjønsberg and Kolbjørnsen, 2008). Despite this, the random simulation path is still widely used in geostatistics, which is justified by its flexibility to assimilate conditioning data (Fig.…”

Section: Simulation Pathmentioning

confidence: 99%

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Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research

Mariethoz

Lefèbvre

2014

Computers & Geosciences

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a b s t r a c tMultiple-Point Simulations (MPS) is a family of geostatistical tools that has received a lot of attention in recent years for the characterization of spatial phenomena in geosciences. It relies on the definition of training images to represent a given type of spatial variability, or texture. We show that the algorithmic tools used are similar in many ways to techniques developed in computer graphics, where there is a need to generate large amounts of realistic textures for applications such as video games and animated movies. Similarly to MPS, these texture synthesis methods use training images, or exemplars, to generate realistic-looking graphical textures.Both domains of multiple-point geostatistics and example-based texture synthesis present similarities in their historic development and share similar concepts. These disciplines have however remained separated, and as a result significant algorithmic innovations in each discipline have not been universally adopted. Texture synthesis algorithms present drastically increased computational efficiency, patterns reproduction and user control. At the same time, MPS developed ways to condition models to spatial data and to produce 3D stochastic realizations, which have not been thoroughly investigated in the field of texture synthesis.In this paper we review the possible links between these disciplines and show the potential and limitations of using concepts and approaches from texture synthesis in MPS. We also provide guidelines on how recent developments could benefit both fields of research, and what challenges remain open.

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“…The initial realizations are still generated by using raster paths, but, then, random paths are used in order to improve their quality and conditioning; see below. Furthermore, another issue with the current pattern-based stochastic methods is their reliance on a sole Euclidean distance, which has been proven to identify patterns in the TI that are visually not similar to those in the realization [Lowe, 1999]. Therefore, in this study, the idea of using multiple distance functions that try to identify higher-order differential elements will be discussed.…”

Section: Raster Versus Random Pathsmentioning

confidence: 99%

Enhancing multiple‐point geostatistical modeling: 2. Iterative simulation and multiple distance function

Tahmasebi

Sahimi

2016

Water Resources Research

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This series addresses a fundamental issue in multiple‐point statistical (MPS) simulation for generation of realizations of large‐scale porous media. Past methods suffer from the fact that they generate discontinuities and patchiness in the realizations that, in turn, affect their flow and transport properties. Part I of this series addressed certain aspects of this fundamental issue, and proposed two ways of improving of one such MPS method, namely, the cross correlation‐based simulation (CCSIM) method that was proposed by the authors. In the present paper, a new algorithm is proposed to further improve the quality of the realizations. The method utilizes the realizations generated by the algorithm introduced in Part I, iteratively removes any possible remaining discontinuities in them, and addresses the problem with honoring hard (quantitative) data, using an error map. The map represents the differences between the patterns in the training image (TI) and the current iteration of a realization. The resulting iterative CCSIM—the iCCSIM algorithm—utilizes a random path and the error map to identify the locations in the current realization in the iteration process that need further “repairing;” that is, those locations at which discontinuities may still exist. The computational time of the new iterative algorithm is considerably lower than one in which every cell of the simulation grid is visited in order to repair the discontinuities. Furthermore, several efficient distance functions are introduced by which one extracts effectively key information from the TIs. To increase the quality of the realizations and extracting the maximum amount of information from the TIs, the distance functions can be used simultaneously. The performance of the iCCSIM algorithm is studied using very complex 2‐D and 3‐D examples, including those that are process‐based. Comparison is made between the quality and accuracy of the results with those generated by the original CCSIM algorithm, which demonstrates the superior performance of the iCCSIM.

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Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation

Cited by 36 publications

References 20 publications

Simulation of Earth textures by conditional image quilting

Simulation of Earth textures by conditional image quilting

Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research

Enhancing multiple‐point geostatistical modeling: 2. Iterative simulation and multiple distance function

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