I am trying to understand the paper "Visual Correspondence Using Energy Minimization and Mutual Information".
Considering two discrete variables X an Y, e.g. intensities of two grayscale images, Mutual Information (MI) can be easily used as a correspondence measure between the two. Quite clear, also working on tested code.
But, for efficiency and to use weighted approaches in stereo vision algorithms, it would be really good to have MI as a data term, i.e. $$ MI = \sum_p D(p) $$ where p is a pixel position and $D$ represent a data term (to be found, as in the paper).
The paper I linked, should do exactly this. But many passages (Parzen estimation, Taylor expansion..) are quite cryptic.
Anyway, my final goal is to understand how to represent MI as a sum over pixel positions. Anyone that could understand or address me on this stuff?