Enhancement by Histogram Manipulation

For this activity, I used an x-ray image whose histogram is not that spread along the grayscale range of values (0-255). Taking the PDF of the histogram, the plot has so may bump and curves.
By back projecting the original array of image to the CDF of its histogram, it enhances both the image and the histogram of the original image.

Below are the histograms , CDF , output image of the original image and the enhanced image:






The source code of this image enhancement is written below:

a = imread("G:\Documents and Settings\Semicon_2\Desktop\X-Ray.jpg");
n = size(a);
row = n(1);
col = n(2);
b = im2gray(a);
c = 255*b;
x = [0:255];
//Loop for Histogram//
for d = 1:256
counter = 0.0; //Initialize count
for i = 1:row // Number of rows
for j = 1:col // Number of columns
if c(i,j) == d
counter = counter + 1.0;
end
x(d) = counter;

end
end
end


x1 = x/max(x);
x2 = cumsum(x1);
x3 = x2/max(x2);
c2 = c;
//Loop for Back - Projection//
for i = 1:row// Number of rows
for j = 1:col// Number of columns
c2(i,j) = x3(c(i,j)+1) ;
end
end

c3 = floor(255*c2);
x4 = [0:255];
//Loop for the final histogram//
for d = 1:256
counter = 0.0; //Initialize count
for i = 1:row // Number of rows
for j = 1:col // Number of columns
if c3(i,j) == d
counter = counter + 1.0;
end
x4(d) = counter;

end
end
end

x5 = x4/max(x4);
x6 = cumsum(x5);
x7 = x6/max(x6);

scf(1)
plot(x7);
scf(2)
imshow(c2);
scf(3);scf(1)
plot(x7);
scf(2)
imshow(c2);
scf(3);
imshow(b);


My modified program which includes a desired function G(z) which is a hyperbolic tangent with a form:
G = tanh(16*(z-128)/255);
The process of back-projection shown in a figure below:The value of the new image will come from the desired CDF. The resulting image is shown below:





I acknowledge the help extended byElizabeth Prieto and Rafael Jaculbia in debugging my program. I give myself a grade of 9 for the reason that I found it hard to understand how back-projection part.

Source:
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