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Comparative Analysis of Objective Functions

In late 2003 and in early 2004, a comparative analysis of different registration methods was conducted. Some results are shown in Figure .

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

One of the primary aims was to benchmark different registration methods and come up with comparative results which highlight the up- and down-sides of each method. There had been a particular interest in the underlying behaviour of each method and the quality of registration as evaluated by a model of appearance.

Months later it was discovered that the registration method which had later been proposed had the potential of becoming much more successful. Up to a certain point in time, functions used for registration 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 the registration method more practical in 2-D (and potentially an even greater number of dimensions).