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"Texture" provides the perceptual information about the surface, nature etc. about the visual objects. Study in texture learning and synthesis with a mathematical model will hopefully provide us the mathematical nature of visual perceptiveness.
On the other hand, Markov Random Field, nonparametric density estimation and their applications in the real world problems, are becoming popular in both research and industrial fields. The reason for this popularity is because of the mathematical models have more robustness, flexibility and simplicity.
The research problems (given this background) are order estimation and large computational complexity. In my PhD thesis I have tried to solve these issues for the application in homogeneous texture synthesis.