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Initial Exploration of the Problem

One of our aims was to benchmark different registration methods and come up with comparative results which highlight the up- and down-sides of each method. We had a particular interest in the underlying behaviour of each method and the quality of registration as evaluated by a model of appearance. Results are shown in Figure 1.

Figure: A comparative analysis of different objective functions. It illustrates that the model complexity decreases only for our newly-proposed objective functions. The Y-Axis value is an indicator of model compactness.

Months later we discovered that the registration method which we had proposed could become ever more successful. Up to a certain point in time, we were simply unable to get decent results. It was revealed that the transformations applied were restricted to remain small in extent. The problem was resolved by changing this restriction term, whereupon larger, more radical transformation were permissibly applied and a good solution was shortly approached. The issue of speed (or efficiency) remained a worrying factor. It had to be addressed in order to make a our registration method more practical in 2-D (and potentially an even greater number of dimensions).