I am disturbed by section 2.1

how can you estimate the homography by simply minimizing the error between the brightness intensities of the original and the transformed image ? Isn't there a mild problem with regularlization here ? in terms of a tradeoff between number of pixels which overlap and the amount of error accumulated ?

what is the error for pixels where the two two images don't overlap ? any choice you make, will introduce a bias one way or the other.

what am I missing ?