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Objective Function Instability

Once good results were found, certain similarity to the work of Davies (see 2002 thesis) was encountered. There was a linearly (almost logarithmic) flat drop in the objective function value. It was decided that such problems need to be resolved at once. For both images and shapes, this was now an important issue to address in a principled fashion.

Figure: Evaluation going below target when initialised at the registration target. The target of registration is indicated by the straight horizontal line.

Twining in particular was one person who could suggest ideas or provide help on the matter. The problem can be overcome by using knowledge on models and comparison between models and their constituent reconstructed instances. This process of comparison allows the corresponding discrepancies to be determined.

Figure shows that when the registration algorithm is initialised at the conceived correct solution, it can still slide below it. In fact, it always does. This suggests that the algorithm is not controlled properly and that the description length term can miss the correct solution.

Figure: A long optimisation with the successful algorithm shows that it surpasses what is questionably the correct solution.

Figure should make it clear that given a large enough number of iterations, no clear convergence is reached . Even more problematically, the value of the objective function slides below the point where it ought to have been optimal, by definition.