Texture

Texture is an important characteristic of the appearance of objects in natural scenes and is ubiquitous cue in visual perception. Like gravity in physics, texture plays an important role in computer vision, graphics, and image encoding. For example, textural patterns were the central topics in Gestalt psychology, early vision theory, and Marr's primal sketch. So, understanding texture is an essential part of understanding human vision. The past several years witnessed exciting development on texture analysis and synthesis in both fundamental theories and practical application, with a large number of methods being proposed. Research ideas are merging from computer vision, graphics, modern statistical physics, psychology and neurosciences to form a coherent theme in texture study.

     Much work on texture mainly focuses on the two well-established areas: One is filtering theory, which was inspired by the multi-channel filtering mechanism discovered and generally accepted in neurophysiology. This mechanism suggests that visual system decomposes the retinal image into a set of sub-bands, which are computed by convolving the image with a bank of linear filters followed by some nonlinear procedures. The filtering theory developed along this direction includes the Gabor filters and wavelet pyramids. The filtering methods show excellent performance in classification and segmentation. The second area is statistical modeling, which characterizes texture images as arising from probability distributions on random fields. These include time series models, Markov chain models, and Markov random field (MRF) models. These modeling approaches involve only a small number of parameters, thus provide concise representation for textures. More importantly, they pose texture analysis as a well-defined statistical inference problem.

     We presents a statistical theory for texture modeling, by combining filtering theory and Markov random field modeling through the maximum entropy principle. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f ( I )on a random field, 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 filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture 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 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. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling.

Figure 1 is some examples of texture analysis and synthesis by FRAME model. The upper image is observed and the lower one is sampled.