Fundamentals of Digital Image and Video Processing - Week 8 Solutions

Hi Coursera people,

I never knew this week would be so much interesting! I could understand almost every bit of information spoken in the class! :)

Here is the question number 7 of week 8.

In this problem, you will write a MATLAB program to compute the entropy of a given gray-scale image. Follow the instructions below to finish this problem. (1) Download the input image from here. The input is a gray-scale image with pixel values in the range [0,255]. Treat the pixel intensities in this image as symbols emitted from a DMS. (2) Build a probability model (i.e., an alphabet with associated probabilities) corresponding to this input image. Specifically, this alphabet consists of symbols {0,1,2,⋯,255}. In order to find the probabilities associated with each symbol, you will need to scan over all the pixels in this image, and for each pixel, adjust the probability associated with that pixel's intensity value accordingly, or in other words find the histogram of the image. Make sure you normalize the probability model correctly such that each probability is a real-valued number in [0,1]. (3) Compute the entropy using the formula that you have learned in class. Enter the result below to at least 2 decimal points.

Here is my attempt at the code.

A = imread('C:\~Coursera courses\Image and Video processing\Week 8\Cameraman256.bmp');
for i = 1:256
DMS(i,1) = i-1;
DMS(i,2) = 0;
end
for i = 1:256
for j = 1:256
for k = 1:256
if A(i,j) == DMS(k,1)
DMS(k,2) = DMS(k,2)+1;
end
end
end
end
sum = 0;
for i = 1:256
sum = sum + DMS(i,2);
end
for i = 1:256
prob(i) = DMS(i,2)/sum;
end
ans=0;
for i = 1:256
entropy(i) = -1 * prob(i) * log2(prob(i));
ans = ans + entropy(i);
end
ans

-Cheers,
Vijay.