ROMMEL BARTOLOME


Enhancement by Histogram Manipulation





Making pictures better by enhancing its contrast through its gray level histogram



For the next activity, we used histogram manipulation for the enhancement of images. Well, why do we need it at all? Of course, not every picture is perfect. When I mean of “perfect” (if in such case it exists), I may say that there may be flaws in the picture such as incorrect lightning or just the plain limitation of one’s camera which makes it “imperfect”.





A picture can be characterized with the number of gray levels it has. In general, an image with good contrast (which is better!) has a uniform distribution of gray levels. Therefore, the image histogram must be “flat” line covering the whole gray level scale. By manipulating the histogram of the image, we may be able to enhance its contrast.


A histogram of a grayscale image is equal to the graylevel probability distribution function (PDF) if normalized by the total number of pixels. [1] Using the PDF, we can calculate for the cumulative distribution function (CDF) of the image. Using back projection of the original CDF to a desired CDF, one may improve the quality of an image. Figure 1 shows how back projection is done:​


Figure 1. Steps in altering the grayscale distribution.( 1) From pixel grayscale, find CDF value (2). Trace this value in the desired CDF (3). Replace pixel value by grayscale value having this CDF value in desired CDF (4). (Image and description taken from [1])


For this experiment, we have used the image in upper left of Figure 2. It is a lighthouse which was already installed in the Windows 7 operating system. It was turned into grayscale (upper left). The PDF was obtained (lower left) and its CDF (lower right). As one may notice, the PDF is not flat and evenly distributed. This will be the image and the CDF that we shall use. Here is some code snippets I used:


Im = imread(“E:AP 186Act 5LH.jpg”);

Im = rgb2gray(Im)

imwrite(Im, “E:AP 186Act 5LH_gray.png”);


Figure 2. (Upper Left) The image of the lighthouse we shall be using. (Upper Right) The lighthouse in grayscale. (Lower Left) The PDF of the image. (Lower Right) The CDF of the image.


Now, what we shall do is we shall back project the original’s CDF to a desired CDF. I had experimented with different kinds of “desired function”. First, I tried using a cube root function. Here is what I got:


Figure 3. Cube root as the desired function. (Upper left) The original image. (Upper right) The manipulated image using the desired function. (Lower left) The PDF of the original image (red) and the PDF of the image after manipulation using the desired function. (Lower right) The CDF of the original image (red) and the CDF of the image after manipulation using the desired function.


Oh! And it failed! As you can see from the PDF, the gray level distribution went to the left, making the image darker. Next is I tried an exponential, squared and a square root function as my CDF:​


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