Syntactic Image Modeling Using Stochastic Tree Grammars

Abstract

This chapter presents some results on stochastic tree languages and their application to image modeling, in particular to texture modeling. An image is described as a composition of its components, called sub-images and primitives. In recent years, stochastic languages have been used in the modeling of image structures. For one-dimensional signal and line patterns, the one-dimensional string representation appears to be quite natural and efficient. However, for two-dimensional images and three-dimensional scenes, an extension from the one-dimensional string language approach to higher dimensions will often result in a more efficient representation. One natural extension of one-dimensional string languages to high-dimensional languages is tree languages. A string could be regarded as a single-branch tree. The capability of having more than one branch often gives trees a more efficient image representation. The probability distribution of the trees representing images can be used to model the noisy situations.