Texture Modeling by Multiple Pairwise Pixel Interactions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
A Compact Model for Viewpoint Dependent Texture Synthesis
SMILE '00 Revised Papers from Second European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
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Two MLEs of Gibbs potentials in Gibbs random field image models with translation invariant pixel interactions are discussed. The unconditional MLE presents the potentials in an implicit form of a system of stochastic equations to be solved by analytic and stochastic approximation. The conditional MLE, provided a training sample holds the least upper bound (top rank) in the Gibbs energy within the parent population, results in the explicit, to scaling factors, potentials. Then only these factors have to be found using analytic and stochastic approximation. Both MLEs are consistent, in a statistical sense, but may need large training samples for determining the potentials with a tolerable accuracy. For typical in practice small samples the conditional MLE suggests how to interpolate the potentials using the available training data.