In section 7, the authors point out that the methods that are based on geometry are correct but there is no guarantee in noisy data. It seems ridiculous to think that this guided search over a very large space of transformations than a method that decomposes the scene into points related by geometric constraints.

Also, it seems that any illumination change or specularity would make it difficult to get a small result for their minimization term. Also they criticize feature-based approaches for inaccuracy of matches but it seems that regions that are difficult to match (like periodic patterns or regions with illumination changes) would also be very difficult in this approach.

One other question that I have is what is the contribution of this paper? They say that they are real-time homography capable, but these applications don't seem like areas that really need real-time