CONVOLUTION IN MATLAB

                 Let us try to understand convolution by performing spatial averaging on a matrix without using MATLAB built in function ‘conv2()’.

%CONVOLUTION IN MATLAB

%INPUT  MATRIX

A = zeros(5);

A(:) = 1:25;

%KERNEL

avg3 = ones(3)/9;

%CONVOLUTION

Result = conv2(A,avg3,'same');

display(Result);

Steps to be performed:

NOTE :

To define a kernel for spatial averaging, fill the kernel with ones and divide it by the number of elements in it.

For instance, consider kernel of size 4x4 , fill the  matrix with ones and divide it by 16. i.e the total number of elements in the matrix.

MATLAB CODE:

%INPUT  MATRIX

A = zeros(5);

A(:) = 1:25;

%KERNEL

avg3 = ones(3)/9;

%PAD THE MATRIX WITH ZEROS

B = padarray(A,[1 1]);

% PRE-ALLOCATE THE MATRIX

Output = zeros([size(A,1) size(A,2)]);

%PERFORM COONVOLUTION

for i = 1:size(B,1)-2

    for j = 1:size(B,2)-2

        Temp = B(i:i+2,j:j+2).*avg3;

        Output(i,j) = sum(Temp(:));

    end

 end

display(Output);