Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation

Computer vision provides several tools for analyzing and simulating textures. The principles of these techniques are similar to those in multiple-point geostatistics, namely, the reproduction of patterns and consistency in the results from a perceptual point of view, thus, ensuring the reproduction of long range connectivity. The only difference between these techniques and geostatistical simulation accounting for multiple-point statistics is that conditioning is not an issue in computer vision. We present a solution to the problem of conditioning simulated fields while simultaneously honoring multiple-point (pattern) statistics. The proposal is based on a texture synthesis algorithm where a fixed search (causal) pattern is used. Conditioning is achieved by adding a non-causal search neighborhood that modifies the conditional distribution from which the simulated category is drawn, depending on the conditioning information. Results show an excellent reproduction of the features from the training image, while respecting the conditioning information. Some issues related to the data structure and to the computer efficiency are discussed.