Abstract

Multiple-point statistics (MPS) is a simulation technique allowing to generate images that reproduce the spatial features present in a training image (TI). MPS algorithms consist in sequentially filling a simulation grid such that patterns around the simulated values come from the TI. Following this principle, joint simulations of multiple variables can be handled and complex heterogeneous fields can be generated. However, inconsistent patterns are often found in the results and some spatial features can be difficult to reproduce. In this paper, a new MPS algorithm based on a multi-resolution representation of the TI is proposed to enhance the quality of the realizations. The method consists in first building a pyramid of images from the TI by successive convolution using Gaussian-like kernels. Secondly, a MPS simulation is done at the lowest resolution level. Then, the result is expanded to the next level of resolution (one rank higher) and used as a conditioning variable for a joint MPS simulation at that level. This last step is repeated up to the initial resolution, where the final simulation is retrieved. The method is implemented in the DeeSse code based on the direct sampling algorithm. Most of the features provided by the direct sampling (conditioning to hard data, uni- or multi-variate simulation of categorical and continuous variables, scaling and rotation of the training structures) are compatible with the proposed method and the usability is maintained. Finally, various examples show that in most of the situations, combining Gaussian pyramids with MPS allows to get results of better quality and in less time compared to direct MPS simulations.

中文翻译：

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使用多分辨率图像的多点统计

摘要

多点统计（MPS）是一种模拟技术，允许生成可重现训练图像（TI）中存在的空间特征的图像。MPS算法包括顺序填充仿真网格，以便围绕仿真值的模式来自TI。遵循此原理，可以处理多个变量的联合模拟，并且可以生成复杂的异构场。但是，结果中经常会出现不一致的模式，并且某些空间特征可能难以复制。本文提出了一种新的基于TI多分辨率表示的MPS算法，以提高实现的质量。该方法包括首先使用类高斯核通过连续卷积从TI构建图像金字塔。其次，MPS仿真以最低的分辨率级别完成。然后，将结果扩展到下一个分辨率级别（高一级），并用作该级别的联合MPS仿真的条件变量。重复执行此最后步骤，直到达到初始分辨率，然后在其中检索最终模拟。该方法基于直接采样算法在DeeSse代码中实现。直接采样所提供的大多数功能（对硬数据的条件处理，分类和连续变量的单变量或多变量模拟，训练结构的缩放和旋转）与所提出的方法兼容，并且保持了可用性。最后，各种示例表明，在大多数情况下，