Supervised Conditional MLE-Based Learning
The learning scheme introduced in Chapter 3 involves a sizable number of the unknown potential values for the Gibbs models to be refined by stochastic approximation (see Table 2.4). This number can be considerably reduced by exploiting, instead of the unconditional MLE of Eq. (3.3), the conditional MLE of potentials described in this chapter. In particular, only |A| + 1 unknown parameters have to be refined by stochastic approximation for the models of homogeneous textures in Eqs. (2.3) and (2.10). The conditional MLE gives, to within a scaling factor, an analytical form of a Gibbs potential to be learnt. Such a form permits, in particular, to choose the most appropriate parametric functions approximating the potentials for a given natural texture1.
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- 1.Recall that one such function, the Laplacian-of-Gaussian, has already been mentioned in Chapter 3 with respect to the potentials shown in Figures 3.4–3.9.Google Scholar