Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling

• Authors: Song Chun Zhu;Yingnian Wu;David Mumford
• Venue: International Journal of Computer Vision
• Year: 1998

This article presents a statistical theory for texture modeling.This theory combines filtering theory and Markov random field modelingthrough the maximum entropy principle, and interprets and clarifies manyprevious concepts and methods for texture analysis and synthesis from aunified point of view. Our theory characterizes the ensemble of imagesI with the same texture appearance by a probabilitydistribution f(I) on a random field, and the objective oftexture modeling is to make inference about f(I), given aset of observed texture examples.In our theory, texture modeling consistsof two steps. (1) A set of filters is selected from a general filter bank tocapture features of the texture, these filters are applied to observedtexture images, and the histograms of the filtered images are extracted.These histograms are estimates of the marginal distributions of f(I). This step is called feature extraction. (2) The maximum entropyprinciple 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 isproposed to choose filters from a general filter bank. The resulting model,called FRAME (Filters, Random fields And Maximum Entropy), is a Markovrandom field (MRF) model, but with a much enriched vocabulary and hence muchstronger descriptive ability than the previous MRF models used for texturemodeling. Gibbs sampler is adopted to synthesize texture images by drawingtypical samples from p(I), thus the model is verified byseeing whether the synthesized texture images have similar visualappearances to the texture images being modeled. Experiments on a variety of1D and 2D textures are described to illustrate our theory and to show theperformance of our algorithms. These experiments demonstrate that manytextures which are previously considered as from different categories can bemodeled and synthesized in a common framework.