I got the main idea from a paper: ``A Modified Histogram Equalization for Contrast Enhancement Preserving the Small Parts in Images''. Bit of a mouthful for what is just a bounded histogram.
I also made made another small modification which makes it tunable. Allowing for a fairly smooth range from what should be the same as 'normalise' in paint programs, up to the fully sun-seared over-exposed normal result from histogram equalisation.
Here's an example of the range of output.
One has to look closely with this particular image because they are already fairly balanced but a smooth range of 'enhancement' should be apparent.
I also played with a colour version which applies the histogram to the Y channel of a YUV image.
As of now it does tend to upset the colour balance a little bit and tends toward a metallic effect; but it's arguable better than what the gimp's equalise does to colour images.
Yikes. Although the image on the right is arguably more agreeable - the colour is very different from the source. Histogram equalising each component separately is effectively applying a white-balance correction where the colour temperature is some sort of flat grey: this sometimes works ok but it messes with the colour balance by definition.
I have some thoughts on applying the algorithm to floating point values using polynomial curve fitting, but I haven't tried them out yet. This would be to prevent binning from quantising the output.
For such a simple adjustment to the algorithm it's quite a good result - histogram equalisation is usually too harsh to use for much on it's own.