Act 5: Too dark? Image enhancement by histogram manipulation

"Don't trust your eyes." - Dr. Soriano

People say that seeing is believing. As humans, we are used to trusting our senses. However, our perception is not perfect; for example, upon exposure to pain, it takes an intensity change of more than 6% before we notice any change. (I have to find a proper source for this; it just stuck in my mind while sleep-listening to RadioLab.) In the ranges of greatest sensitivity, small changes in intensity are noticeable, but when we get far away from that range, large changes go unnoticed. It's like comparing a bite of food when you're famished to a bite in the middle of a long meal.

Most modern electronics have a wider range of sensitivity than we do. They allow us to observe differences that are not registered by our senses. Image enhancement by histogram manipulation simply magnifies the differences so as to be detectable by humans.

What's a histogram again? A histogram is simply a frequency distribution of color intensities in an image. For a grayscale image, the x-axis ranges from black to shades of gray to white (0 to 1 OR 0 to 255), while a truecolor image will have three histograms: intensities of red, green, and blue. On a side note, that's how a digital camera decides the correct exposure: its ideal exposure occurs when the histogram is centrally balanced and not truncated at the sides. I'll add examples here when I have some free time.

Foraging for underexposed images in Flickr, I found a dark picture with only a few discernible details: a tree branch, some shrubs, and a pool ladder.

Nulkku's "The Darkness" (accessible here)

We open it in Scilab by typing:

Img = gray_imread('image3.jpg');
imsize = size(Img); //gets the dimensions of the image

 A histogram with 256 bins can be called by typing histplot(256, Img), but we need the values of the histogram if we're going to fix it manually. To get an array of values and frequency of value occurrence,

[freqs, val] = imhist(Img, 256);

 Displaying the histogram gives us the following picture.

Histogram of original image

From the histogram alone, we can immediately tell that this image is too dark, since the values are crowded at 0. Since it looks truncated, we can assume that the some details would not be recoverable - it "bunched up" blacker details to 0. Increasing the brightness in image editing programs simply shifts the histogram to the right, thus there isn't an increase in detail. Shifting it too much will bunch up the white portions, losing more detail.

First, we were instructed to see what happens if we try to make the histogram approximate a uniform distribution. We take its cumulative distribution function to be able to remap it.

CDF = cumsum(freqs)/sum(freqs);              //normalized CDF of image histogram
CDFline = cumsum(zeros(256,1)+1./256); //linear CDF

The instructions were to get the value of each pixel, (say 0.3 gray) look at where it falls in the corresponding CDF (i.e. 40%), trace the value (40%) to the desired CDF and exchange the original pixel value with the obtained color value in the new CDF. However, that involves a lot of finds and indexing, so I decided to map it instead. I figured out the replacement value for all possible values in the original image and saved the pairs in an array.

trans = [];
for i = 1:256
    new = val(max(find(CDF(i)>=CDFline)))
    if new then
        trans = [trans,new];
    else
        trans = [trans,0];
    end
end

I'm sure there's a more efficient way, but I'm still feeling my way with Scilab. Any advice would be always welcome. :)

Replacing the values only needs one line:

newImg = trans(Img*255+1);

Getting the new histogram is a bit disappointing.

Remapped to a linear CDF

 It's obvious that the new image will be blocky and pixelized. However, that's to be expected as only colour values with frequency greater than 1 can be remapped. We have not added any code that integrates the surrounding colors to smoothen the remapping.

Looking at the new image,

Enhanced image

It doesn't look very nice, but we've successfully brought out more details.

For the second part, we make a Gaussian histogram

 gauss = exp(-0.0005*(128-(1:256))^2);

and set its CDF, shown in the next figure, as the desired CDF.

CDF of a Gaussian distribution

Simply replacing CDFline with CDFgauss in the computation for trans gives us the following histogram and enhanced image.

Histogram of enhanced image #2

Enhanced image using a Gaussian CDF

 It can be seen that the branches at the right are not distractingly white anymore. This type of CDF allows us to highlight more details but looks less synthetic.


I would give myself a grade of 10 for being able to complete the activities detailed in the histogram manipulation manual.