How detect book page?

Assume that we have smartphone photo of book page, where one page is about 60% of image size and on this image is part of adjacent page.
If page has 90% image size and no adjacent page, good solution (although a bit slow) is python repository mzucker/page_dewarp (I prefer C++ in this thread but it is not necessary)
How clip by tetragonal (not rectangle) part of image contained one page?
(and maybe also remove fingers from image?)