What is described above is something I’ve seen in a documentary. They have a very fancy camera and the person holding the book can just slowly flipping through the pages, and it can reconstruct the flat pages.
I guess the problem is not technology or mathematical model behind it, but how to make it cheap. It is analogous to Google’s self driving car, that you want to solve the same problem with much cheaper technology.
I've seen the poor performance of current phone apps. My point is that one could do better for less coding effort with access to a 3D model. Either a pair of photos, or a 3D camera.
Something that could map the 3D surface onto a sheet would be awesome.