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7.2.2

Criteria for Parameter Estimation

An exemplary instance is specified by a triple where is the exemplary configuration (recognition solution) telling how the scene () should be labeled or interpreted in terms of the model reference (). The configuration may be a structural mapping from to .   Assume that there are L model objects; then at least L exemplary instances have to be used for learning to recognize the L object. Let the instances be given as

We propose two-level criteria for learning from examples:

  1. Correctness. This defines a parameter estimate which encodes constraints into the energy function in a correct way. A correct estimate, denoted , should embed each into the minimum of the corresponding energy , that is

     

    where the definition of is dependent upon the given scene and the model of a particular exemplary instance as well as . Briefly speaking, a correct is one which makes the minimal configuration defined in (7.1) coincide with the exemplary configuration .

  2. Optimality. This is aimed to maximize the generalizability of the parameter estimate to other situations. A measure of instability is defined for the optimality and is to be minimized.
The correctness criterion is necessary for a vision system to perform correctly and is of fundamental importance. Only when this is met does the MRF model make a correct use of the constraints. The optimality criterion is not necessary in this regard but makes the estimate most generalizable.