How may I calculate fractional derivative of image over rotation and scale for mutual information registration?

So far I managed to deal with translation over x and y axis. Whole registration algorithm is described here (Viola&Wells): https://cs.uwaterloo.ca/~mannr/cs886-w10/ViolaWells_IJCV.pdf

The main function loop reads both fixed and moving image, applies translation, calculates Mutual Information part described in article (17) and directional gradient using Sobel mask (matlab function imgradientxy) for derivative over translation. That works quite fine, until I have to scale and rotate the image.

Can anyone give me advice of how can I deal with this problem? Or perhaps I have made a wrong assumption that directional gradient is what I needed so far? would be really grateful for any response and help.