What sort of NN would be used to warp two compositionally similar images to match each other in structure? In the example the copy painting had almost all of the same general components, laid out with fairly significant differences, and they warped it to match quite precisely.
The basic idea is:
1. Find features in images A and B (SURF / SIFT are common). However, maybe a NN could find interesting features here?
2. Match features so you know what feature from A is where in B. Again, a NN could potentially do this "better".
3. Compute a homography (translation between planes of features) or procrustes transform (or other types of transformations)
4. For each pixel (p) in the target frame (B), take the inverse of the transformation to find the pixel of the original frame (A) (which is usually a fractional pixel because it won't line up)
5. interpolate between nearby pixels in (A) to get the "true" pixel value at (p) in (B). Perhaps a NN could improve this interpolation? We've seen this in super resolution, for example.
You can easily reproduce these steps with just a few function calls in OpenCV. Try it out. https://opencv.org/
Up to step 3 is very helpful to answer questions like: "How much did the camera move between captures of image A and B. So now you can solve structure from motion, visual odometry, etc. This is typically how quadrotors navigate with cameras.