Automatic image Enhancement - Scanned Document

Dropbox have make a blog post about there automatic enhancement method for scanned document image - Fast Document Rectification and Enhancement

I followed the post and they mention a formula to make the enhancement:

J(x,y) = gain(x,y)*I(x,y) + offset(x,y)

where J is the output image and I is the Input image, the problem is i don't understand how they calculate gain and offset for each pixel

Here is a simple input and output image that can illustrate the result: Input image:

Output image :

Thank you for your reply