Texture synthesis has been under intensive study for decades. Most of recent synthesis approaches are based on MGRF models of textures. Assuming that visual similarity follows the proximity of signal statistics [35], these methods replicates observed sufficient statistics from a training into a synthetic image in order to approximate the perceived visual similarity between images.
An MGRF model is generative, because a new texture could be generated by simulating the underlying stochastic process of a texture that the model describes. Such a synthesis process is coincident with the statistical identification of an MGRF model via MCMC algorithms. Since each state of the Markov chain is related to an image randomly sampled from the current joint distribution, in line with the above assumption, the image at the equilibrium state should be visually similar to a sample of the stationary distribution, i.e. the training sampling. This approach to texture synthesis is so-called model-based. Due to the exponential time complexity of the MCMC algorithms, however, model-based synthesis is rather slow for practical applications.
Non-parametric sampling methods were developed recently for fast texture synthesis. These methods are related to non-parametric analysis in statistics which allows to analyse data without knowing an underlying distribution. In texture synthesis, non-parametric sampling methods avoid building an explicit, parametric probability model (e.g., a Gibbs probability density function) for texture description. Instead, they exploit some local methods, e.g., local neighbourhood matching, for reproducing statistics of the training texture. The main advantage of a method based on non-parametric sampling is that it involves less calculation and provides faster synthesis compared with conventional model-based approaches.
Since MGRF model-based texture synthesis has the same procedure as model identification introduced in the previous section and the synthesis based on a generic MGRF model will be given in Chapter 7, this section only focuses on methods based on non-parametric sampling.