AP 186 Activity 5: Enhancement by Histogram Manipulation

In this activity we will be modifying the histogram of the image in order to enhance its quality and improve certain image features. This can be done by mapping the graylevel values of the image such that the new image will have the desired cumulative distribution function (CDF).

I've chosen this picture:


and I ran the following code in Scilab:

stacksize(10000000);
A = gray_imread("C:\test1.jpg");
B = tabul(A, "i");
B1 = B(:,1);
B2 = B(:,2);
size(A);
s = 540*720;
B2norm = B2/s;
B2cumsum = cumsum(B2norm);
A1d = A(:);
yCDF = interp1(B1, B2cumsum, A1d);
xdesired = interp1(B1, B1, yCDF);
Aedited = matrix(xdesired, [540, 720]);
imwrite(Aedited, "C:\test1modified.png");

Basically what this code does is it loads the image into scilab, then it gets the image's normalized histogram and CDF. Then, it interpolates in order to get the y values in the image's CDF. After that it interpolates once again in order to get the grayscale value having this CDF value in the desired CDF. All the pixels in the image are backprojected and replaced by the x-values of the desired CDF.

In this case, the desired CDF is a line with slope = 1, that is, its PDF is just a uniform distribution. Executing the code above, I get:

histogram of the image (not normalized)

normalized histogram of the image

Histogram equalized image


Original grayscaled image

and comparing the CDF's before and after:

CDF before enhancement

CDF after enhancement


PDF after enhancement

It is noticeable that the modified image has a higher contrast than the original. The light colored pixels seem to become lighter and the dark pixels seem to become darker. It also looks like that the "gray fog" over the original picture has been removed. The image is called histogram equalized image because we have modified its histogram such that every gray level the original image possess now have equal probability. Thanks to this, the picture is now brightened up a bit. :)

Also, the CDF of the enhanced image is a straight line and that was our desired CDF. Note that there's a small horizontal segment. This is because in the histogram of the original image, there's a range of grayscale values where no or very little pixels possess. This can also be seen in the modified PDF.

Next, I tried the technique on different CDF's. The first one is normal distribution: (mean = 0.5, std = 0.1)

histogram of normal distribution


CDF of normal distribution

The code was slightly changed:

A = gray_imread("C:\test1.jpg");
B = tabul(A, "i");
B1 = B(:,1);
B2 = B(:,2);
size(A);
s = 540*720;
B2norm = B2/s;
B2cumsum = cumsum(B2norm);
A1d = A(:);

y = grand(1, s, 'nor', 0.5, 0.1);
C = tabul(y, "i");
C1 = C(:,1);
C2 = C(:,2);
C2norm = C2/s;
C2cumsum = cumsum(C2norm);

yCDF = interp1(B1, B2cumsum, A1d);
xdesired = interp1(C2cumsum, C1, yCDF);
Aedited = matrix(xdesired, [540, 720]);
imwrite(Aedited, "C:\test1modified.png");

And the resulting image is:

Histogram manipulated image

Original image

Personally, I don't think using the histogram manipulated image is of better quality than the original image; it looks more hazy and less contrasted than the original. This is because for the normal distribution, most of its elements are concentrated near the mean and the standard deviation used here is quite small, meaning the pixels are concentrated around a range of graylevel values, which explains image's low contrast.

Like our first case, the histogram and CDF of the modified image resembles the desired one:

histogram of modified image


CDF of modified image

Next, I tried the exponential distribution:

Histogram of exponential distribution


CDF of exponential distribution

And the result is:

histogram manipulated image

original image

The manipulated image appears a lot darker than the original image because due to the exponential distribution, the pixels are concentrated at the left of the histogram, meaning there are now more pixels having darker values.

And the histogram and CDF of the modified image are:

histogram of manipulated image

CDF of manipulated image

Lastly, I used Photoshop to manipulate the histogram of the image:

Using Photoshop to manipulate the CDF

histogram manipulated image


original image

The image now is of higher contrast and it looks better! For me, its quality is better than the other histogram manipulated images. :D

For the score, I give myself 10/10 for understanding the lesson and being able to produce the requirements.

Score: 10/10

Finally, I would like to thank Dr. Soriano, Joseph Bunao, Arvin Mabilangan, BA Racoma, and Andy Polinar for the insightful and helpful discussions.

References:
1. M. Soriano, "A5 - Enhancement by Histogram Manipulation"