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Some of the more interesting issues are to do with feasibility. The mathematics behind diffeomorphism is said to be ``not fully understood'' and its application to computer vision is unprecedented9. Ensuring that any existing techniques and experiments remain valid in a space of high number of dimensions is another area that is hard to reason about and usually involves some trade-offs and simplifications. Several techniques that work perfectly well in 2-D can be completely useless in 3-D.
What makes this work slightly less worrisome is the proposition of new and better ways of achieving good models of appearance and low error rates, as described in previous papers with similar aims. These proposed steps are usually meaningless, however, if they cannot be backed-up by some ground-truth or a mathematical proof. Fiddling about with parameters and using a-prior knowledge of the problem is a logically good approach, but it contributes very little towards genuine research and exceptional insights.