Supervised MLE-Based Parameter Learning
This chapter shows that the Gibbs models with multiple pairwise pixel interaction proposed in Chapter 2 have almost the same schemes of supervised parameter learning. The learning scheme was proposed first for homogeneous textures in (Gimel’farb, 1996a) and then generalized to piecewise‐homogeneous ones in (Gimel’farb, 1996b, 1996c). It recovers both the interaction structure and potentials from a given training sample (grayscale image or/and region map) by starting from an analytic first approximation of the MLE of the potentials. The approximation, computed from signal histograms that are the sufficient statistics of a particular Gibbs model, enables to compare relative strengths of a great many possible pairwise interactions and recover most characteristic clique families for representing a given texture type. Then, the desired MLE of the potentials for the chosen characteristic clique families [C a : a ∈ A] is obtained by stochastic approximation similar to introduced by Younes (1988).
KeywordsTraining Sample Gray Level Stochastic Approximation Marginal Probability Marginal Probability Distribution
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