problem1.1-assignmentI

%clearing command window, workspace and image windows
clc;
clear all;
close all;
% we are only here working with grayscale image
original_image = imread('grayscale_cat.jpg');
%
%adding noise, using gaussian noise equation
%of mean 10 and variance 20
mean = 10;
sigma = sqrt(20);
original_image= double(original_image);
noisy_image = original_image + mean +(randn(size(original_image))*sigma);

% making a gaussian kernel
sigma = 1;
% we will normalize this mask and hence only exponential part will play a
% role, here mask_matrix is our kernel of 5-by-5 size
mask_matrix = zeros(5,5);
W = 0;                    % used this sum for normalization
for i = 1:5
    for j=1:5
        sq_dist = (i-3)^2+ (j-3)^2;
        mask_matrix(i,j) = exp(-1*(sq_dist)/(2*sigma*sigma));
        W = W + mask_matrix(i,j);
    end
end
mask_matrix = mask_matrix/W;

% we can use the above kernel to filter the noise added
[m,n] = size(noisy_image);
gausian_filtered_image = zeros(m,n);
%adding zeros around the noisy matrix so that we can calculate the pixel
%values of the corner element with the use of the mask above
noisy_image_with_zeros = padarray(noisy_image,[2 2]);
for i=1:m
    for j=1:n
        %temporary variable, var_temp used for calculation
        var_temp = noisy_image_with_zeros(i:i+4 , j:j+4);
        var_temp = double(var_temp);
        conv = var_temp.*mask_matrix;
        gausian_filtered_image(i,j) = sum(conv(:));
    end
end

gausian_filtered_image = uint8(gausian_filtered_image);

% showing here, original and filtered image
figure(1);
set(gcf,'Position',get(0,'Screensize'));
subplot(121),imshow(uint8(original_image)),title('Intact Image');
subplot(122),imshow(gausian_filtered_image),title(' gaussian filtered Image');