# Results

Source | Alignment with 4 bins | Alignment with 8 bins | Alignment with 16 bins
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# Conclusions

Aligning the RGB channels of a photograph to maximize mutual information between two (distinct) pairs of channels usually produces the same result as aligning the channels to make the photograph "look good". When at least 16 bins were used to represent the distributions of brightness values on each channel, maximizing the mutual information between channels also maximized how good the photograph looks for 100% of 8 photographs. Using 8 bins, the alignment was almost always optimal in terms of how good the image looks except for the example shown in the second to last row.

I think that this image was not aligned to look as good as possible because the distribution of brightness values in the blue channel is clumped into three areas. Thus, when the number of bins is reduced, almost all of the blue brightness values separate into three (or less) bins. To get a feel for what the distributions look like with fewer bins, look at this version of the source image where the color depth is dramatically reduced to 16 colors:

When there is only one bin the mutual information is the same regardless of how the channels are positioned. In this case, no alignment is better than any other in terms of mutual information, and the alignment will most likely look terrible. Then it's natural to expect that the alignment will get worse in terms of how good the image looks as the number of bins is decreased since it is worst when the number of bins is smallest. The picture in the second to last row starts to look bad with a larger number of bins than the other examples because there is little variety in the blue channel to begin with.