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At this stage, the model-based objective function could only cope well with set sizes that were rather small. It found it difficult to minimise a model by altering just one instance whose overall effect on that model was minute.
This problem was in no sense new. In a model-driven objective function, such as in the work of Kotcheff and Taylor, alteration of one single data instance does not affect the model considerably. The greater the set size becomes, the lower the effect which parameterisation (or in this case, image warps) have. The only exception to this is when a warp is applied uniformly to all data instances. In the case of registration though, it is impractical.
In order to deal with large enough problems, where for instance, dozens of images need be accounted for, resolutions need to be found that make convergence linearly proportional to the size of the set. The problem was also well-acquainted in the work on landmarks selection where sets remained 10 or 20 in size.
This fundamental problem suggests that a model-based approach is limited. It is not yet sufficiently well-behaved to study a population, only a smaller-scale case study.