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The problem -- Manual fix -- Histogram equalisation -- Source and parameters
On a recent vacation, my camera reached the lower limit of its range of exposure times. Apparently the relative proximity of New Zealand to the equator compared to Europe and the great weather were too much. What is more, the regions in the shadow turned out uniformly dark compared to those in the sun. The upshot was that the photos were not unusable or ugly, but lacked contrast in different image regions while the contrast between sunny and shadowy regions was stark. This problem was especially noticeable in photos on the river on bright days, where the foam and waves cause bright reflections.
The most obvious way to enhance such images — that are partly overexposed and partly underexposed — is to postprocess them manually with an image manipuilation program such as GIMP. Just adjusting brightness and contrast may be sufficient for photos that are either underexposed or overexposed, but for pictures with regions of both, it will not do. For those, you need a more general transformation of pixel's brightness, which is provided by GIMP's curves tool (Colors -> Curves or Tools -> Color Tools -> Curves in the context menu). It allows enhancing (i.e. stretching) those intervals of brightness that are overused at the expense of compressing those that are little used. This results in better contrast for both bright and dark region (with the little-used intermediate brightnesses compressed).
The images above show an example. Here the dark regions are more problematic than the bright ones — the crevice on the left is blacked out and the person standing on the right in the background is almost invisible. Increasing the slope of the brightness curve where the histogram has peaks increases contrast there. (Note that the histogram is logarithmic, so the peaks are more pronounced than they may seem.) As a result, the person standing on the rock is visible in the processed image (right), and the crevice and the rock in the foreground show more structure. The foamy regions of the water have gained a little contrast, too.
To my discredit, it was only after manually correcting hundreds of photos that I remembered the more-or-less automatic method for doing such corrections. (In fact, my father did most of the manual corrections. He is retired and hates bad photos.) To see the principle, let us again go over what we have done when correcting the brightness manually. We applied a transformation function to the brightness of each pixel that had a large slope where many pixels had a similar brightness and a small slope where few pixels were. That stretched the regions of the brightness histgram with a high pixel density and compressed those with a low density. Simply put, we have reduced the variation of the histogram, made it flatter.
The method we have applied manually is well-known in the image processing literature as "histogram equalisation" (HE). In fact the original form of this method may be too extreme, as it makes the histogram completely flat. (Strictly speaking, this is only true when the histogram is averaged out. The method is deterministic and cannot increase the total number of different brightness values, so some values do not occur at all in the result image.) Two improvements have been invented over the years:
So what does the result of histogram equalisation look like for our test image? Here it is:
This looks less enhanced than the manual result above. The cliff face is darker, and the person less visible. In fact, displaying a histogram with GIMP shows that I have been overdoing it a bit with the manual correction. The brightened cliff produces a different peak in the histogram from before, and the peak on the right from the water partly remains. (You can see the histogram of the original image in the curves dialog above.) The histogram of the HE-processed image is indeed completely flat on average. The darker parts of the water have been darkened still more, increasing contrast there and erasing the corresponding peak in the histogram. The cliff has been brightened enough to flatten the left histogram peak, but not enough to make the standing person or the interior of the crevice clearly visible.
This is a bit disappointing for a state-of-the-art image processing method. So can it be fixed? As mentioned above, a variant called CLAHE allows enhancing different regions of the image independently. We apply it to the image, choosing 8 by 8 tiles and an amplification limit of 1.7 (see below about these parameters):
Now the inside of the crevice is better visible, and so is the standing person, if only slightly (click on the images to see larger versions). But the structure of the cliff face is much enhanced. This is a consequence of the adaptivity of this method, which allows treating that image region independently. The water turbulences also have more contrast than in any of the previous result images.
But there are a few drawbacks too: The PFD (life jacket) of the paddler is darker than in the previous attempts, and the darker regions of the water look a bit grey (this was also true in the previous results). This is because these pixels are among relatively few dark ones of their neighbourhood region, and are therefore darkened more still. The human eye perceives darker pixels as less colourful, which makes the result less appealing. But one can apply histogram equalisation to any quantity of a pixel, not just the brightness. By transforming the colour saturation instead, one can intensify the colours. (It seem I invented this application, at least I have not read this anywhere.) Contrast limiting has to be used, or the colours will turn out psychedelic. Adaptiveness helps to concentrate the enhancement on the most colourful spots, so I use 8 by 8 tiles again, and a magnification limit of 1.3. The result is:
The colours are more intense; besides the paddler the water is also greener. Unfortunately the rock face also has a greenish tinge, but that is something for which my camera is mostly to blame.
So what have we learned? Histogram equalisation is a powerful method that can help a lot in improving the quality of images. Its different variants and parameter values have their individual advantages and disadvantages, both compared with each other and compared to a global manual contrast enhancement. There is no fully automatic method that produces what you consider perfection. But experimenting with them a little can help with degraded images.
I have written a C program performing histogram equalisation that is pretty generic. The source code is here. It is designed for versatility rather than performance or comfort and can process only PNM images (but see below for a wrapper script). It can process both greyscale and colour images with up to 16 bits depth.
The program can take a number of parameters, most of which relate to the histogram equalisation method to apply:
The third command line option is -s which enables transforming the colour saturation rather than the brightness. pnmclahe defines the brightness of a colour pixel as the largest colour component and transforms the other components proportionally. The colour saturation is defined as the difference between the largest and smalles colour components, and its transformation is linear so that the interval below the smalles and above the largest colour component keep the same ratio.
Running pnmclahe without arguments or with the -h option makes it output a usage message.
To apply pnmclahe to images in any format, it is advantageous to write a wrapper shell script which also contains appropriate ImageMagick convert commands. This shell script is an example. Besides format conversion, it also saves the original image in a subdirectory and uses that backup as a source image on second and later runs. It also copies EXIF metainformation from the original image to the end result.
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