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);
