Polynomial Registration

Hi all,

I want to register to brain images to each other with a registration that is fit to a quadratic function. The attachment below demonstrates what I want in two dimensions. I want to be able to do something similar to the second order registration. I am hesitant to try to write my own function to do it because of the complications of finding the optimal cost and search function.


I don’t want to do a non-linear registration because I want my registration to be constrained by a global quadratic function so that is why I haven’t done ANTS or FNIRT. The reason for this is that I think there are some global geometric distortions that are quadratic in nature on my brain images and I want to correct for it!