9.7
What if we run a program which correctly implements an optimization-based system but find that the result is not what we expect? First of all, we may want to identify whether the fault is due to the local minimum problem caused by the minimization algorithm or due to the incorrectness of the energy function formulation. The local minimum problem is identified if a better solution can be obtained with a different initialization. Otherwise if the algorithm is good enough to find the global minimum but such a solution is still far from our subjective judgment, we may check the formulation, i.e. , that form of the energy function and the involved parameters.
We may try different combinations of parameters to see if we can get the desired results -- though this is not a clever way. Assume that we have exhausted all possible combination and none of the computed solutions are close enough to the desired solution. Then there must be something fundamentally wrong. We have to have a critical look at the problem formulation.
One possible reason may be that some constraints which may be important for solving the problem have not been embedded into the energy function -- current vision models are often formulated based on over-simplified assumptions [Pavlidis 1992,Rosenfeld 1993] for tractability reasons. Another possibility is that some assumptions about the prior knowledge and the observed data are incorrectly made. An example is the oversmoothing problem in the MAP restoration and reconstruction. The MAP formulation was blamed for the problem; however, it is really the improper use of the quadratic smoothness prior which causes problem.