Computer vision cross correlation with spacially constant increase in brightness

Question

If I'm taking the correlation between two images as described in the attached formula:

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Which is taken from the following online computer vision textbook: Szelski page 386.

This function does not seem like it would ever be reliable, since if one of your images is brighter than the other, the correlation would be higher than if the images are identical. For instance, take a look at these examples printed on a white board:

As you can see the brighter image has a better correlation with the first image than an identical copy of the first image. What am I doing wrong?

Answer 1

I guess what you're looking for is the normalized cross-correlation, where the values are subtracted by the mean intensity and then divided by the standard deviation of the intensity.