You want to determine the histogram equalization function not from the entire images, but on the zone where they will touch or overlap. You obviously want to have identical histograms in the overlap area, so this is where you calculate the functions. You then apply the equalization functions that accomplish this on the entire images. If you have more than two stitches, you still want to have global equalization beforehand, and then use a weighted application of the overlap-equalizing functions that decreases the impact as you move away from the stitched edge.
Apologies if this is all obvious to you already, but your general question leads me to a general answer.