Stochastic Modelling of Patterns Using Graph Cuts

Abstract

Multiple-point geostatistics (MPS) algorithms are very computationally demanding, which can limit their application in certain applications. Texture synthesis methods used in computer graphics involve concepts of training images which are similar as in MPS. Some very computationally efficient texture synthesis algorithms are able to produce geostatistical models that are comparable in quality with state-of-the-art MPS methods, while presenting computational advantages. In this paper we introduce a patch-based method based on graph cuts. It is a general tool which allowing to optimally cut patches incorporating information from previous parches using a max-flow algorithm. The cutting algorithm is based on the representation of a patch as a graph, and guarantees that the cut is optimal between more than two patches. By recording the errors of previous cuts and iteratively replacing patches areas of high error, the simulation is continuously improved and the training image texture is reproduced without noise or artifacts.