Fundamentals of Digital Image and Video Processing - Week 2 Solutions

Hi coursera people,

I'm thrilled to take the course "Fundamentals of Digital Image and Video Processing". Matlab programming assignments have just started. The question 7 of week 2 involves some coding, which we are expected to write to get the right answers.

Here's the question :

In this problem you will implement spatial-domain low-pass filtering using MATLAB, and evaluate the difference between the filtered image and the original image using two quantitative metrics called Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR). Given two N1×N2 images x(n1,n2) and y(n1,n2), the MSE is computed as MSE=1N1N2∑N1n1=1∑N2n2=1[x(n1,n2)−y(n1,n2)]2. The PSNR is defined as PSNR=10log10(MAX2IMSE), where MAXI is the maximum possible pixel value of the images. For the 8-bit gray-scale images considered in this problem, MAXI=255. Follow the instructions below to finish this problem. (1) Download the original image from here. The original image is a 256×256 8-bit gray-scale image. (2) Convert the original image from type 'uint8' (8-bit integer) to 'double' (real number). (3) Create a 3×3 low-pass filter with all coefficients equal to 1/9, i.e., create a 3×3 MATLAB array with all elements equal to 1/9. (4) Low-pass filter the original image (converted to type 'double') with the filter created in step (3). This can be done using the built-in MATLAB function "imfilter". The function "imfilter" takes three arguments and returns one output. The first argument is the original image (converted to type 'double'); the second argument is the low-pass filter created in step (3); and the third argument is a string specifying the boundary filtering option. For this problem, use 'replicate' (including the single quotes) for the third argument. The output of the function "imfilter" is the filtered image. (5) Compute and record the PSNR value between the original image (converted to type 'double') and the filtered image by using the formulae given above. (6) Repeat steps (3) through (5) using a 5×5 low-pass filter with all coefficients equal to 1/25. Enter the PSNR values you have obtained from your experiments (The PSNR corresponding to 3×3 filter first, followed by the PSNR corresponding to 5×5 filter). Make sure you order the answers correctly and separate them by a space. Enter the numbers to 2 decimal points.

Here's my approach :

I = imread('C:\Users\****\Desktop\digital-images-week2_quizzes-lena.gif'); % read the image

I2 = im2double(I); % convert the uint8 image to double

B = [1/9, 1/9, 1/9; 1/9, 1/9, 1/9; 1/9, 1/9, 1/9]; % create the 3x3 array

C = imfilter(I2, B, 'replicate'); % apply the filter

MSE = mean(mean((I2 - C).^2,2)); % get the MSE

MaxI=1;% the maximum possible pixel value of the images.

PSNR1=10*log10((MaxI^2)/MSE); % get the PSNR

PSNR1 % print the PSNR

B1 = [1/25, 1/25, 1/25, 1/25, 1/25; 1/25, 1/25, 1/25, 1/25, 1/25; 1/25, 1/25, 1/25, 1/25, 1/25; 1/25, 1/25, 1/25, 1/25, 1/25; 1/25, 1/25, 1/25, 1/25, 1/25];

C1 = imfilter(I2, B1, 'replicate');

MSE1 = mean(mean((I2 - C1).^2,2));

PSNR2=10*log10((MaxI^2)/MSE1);

PSNR2