Filters, Random Elds and Maximum Entropy (frame) |towards a Uniied Theory for Texture Modeling

This article presents a statistical theory for texture modeling. This theory combines ltering theory and Markov random eld modeling through the maximum entropy principle , and interprets and clariies many previous concepts and methods for texture analysis and synthesis from a uniied point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f(I) on a random eld, and the objective of texture modeling is to make inference about f(I), given a set of observed texture examples. In our theory, texture modeling consists of two steps. (1) A set of lters is selected from a general lter bank to capture features of the texture, these lters are applied to observed texture images, and the histograms of the ltered images are extracted. These histograms are estimates of the marginal distributions of f(I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f(I). This step is called feature fusion. A stepwise algorithm is proposed to choose lters from a general lter bank. The resulting model, called FRAME (Filters, Random elds And Maximum Entropy), is a Markov random eld (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture model-ing. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is veriied by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled. Experiments on a variety of 1D and 2D textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures which are previously considered as from diierent categories can be modeled and synthesized in a common framework.