Why is human vision relevant? Texture modeling is not merely a mathamatical problem. The reason that we treat a set of images as an equivalence class for a texture pattern is not just for image coding, but serves certain purpose. Consider an iid white noise image, such image contains a huge amount of information, but we "believe" that such information has no indication to the structures of our environment, and thus call it "noise" pattern as a "summary". In other words, we are not interested in the details or instance of the individual pixel values in the iid noise images. Unfortunately it is nearly impossible to quantify our purpose of visual perception, especially in generic vision. Therefore it is important to look at human visual perception which is assumed to be adapted to our environment and serve the purpose of human activities.
In human vision, the most influential work was contributed by Julesz and his colleagues over 1960-80s. In psychophysics, many insightful observations are made in terms of experiments or demos, like Julesz's texture discrimination experiment. Indeed sometimes it is hard to evaluate what exactly their conclusions are, for the lack of rigoreous math. I believe his study pointed two important directions.
The first is his observation that early vision is sensitive to some features and not others. This indicates the sufficient statistics and further the equivalence class in our study.
The second insight is the existence of atomic elements or textons in perception. This leads to our study of generatve models of texture.
But his work was limited to artificial images. Other important contributions include (Karni and Sagi, 1991) who observed the plasticity of textons over training, and (Chubb, Landy, Bergen et al 1991) who observe that the marginal histogram of Gabor filtered images seemed to provide sufficient statistics in human texture perception.
By now, we understand that it is inappropriate to treat neurons as filters, because they are bases with lateral inhibitation. This leads to the generative models. Our thought was particularly influenced by (Olshausen and Field, 97).
1. B. Julesz, Dialogues on Perception, 1995.
2. .A. Olshausen and D.J. Field, "Sparse coding with over-complete basis set: A strategy employed by V1?", Vision Research, 37:3311-3325, 1997.