Simulation of Earth textures by conditional image quilting

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 multiple-point statistics (MPS) methods, indicate an improvement in CPU time by a factor of at least 50.