# How to use convolution on a 2d matrix with a kernel?

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Thomas Nell on 28 Oct 2020
Answered: Rishabh Mishra on 6 Nov 2020
Dear Mathworks community,
I have the following function which i plan on using for a 2d matrix with a 2d kernel. The code is as follows:
function [filtered] = basic_convolution(image,kernel)
dimensions = size(image);
dimensions2 = size(kernel);
image2 = zeros(dimensions(1),dimensions(2));
for i = 1:dimensions(1)
for j = 1:dimensions(2)
accumulator = 0;
for k = 1:dimensions2(1)
for l = 1:dimensions2(2)
if [i j] == [k l]
result = image(i,j) * kernel(k,l);
accumulator = accumulator + result;
else
end
end
end
image2(i,j) = accumulator;
end
end
filtered = image2;
end
What I cant figure out is how to apply this to the whole matrix and not a portion. Also, when the resulting image comes out I find that the pixel in the new image isnt the sum of the area multiplied by the matrix, but the individual components which have been multiplied by the kernel. I am aware of the command conv, but in the specification for this code I am not allowed to use it. Also, border handling isnt required at this stage of the code - ill add that in later. If you guys could point out the error in my code I would be super grateful.
Thanks!!

Rishabh Mishra on 6 Nov 2020
Hi,
I have made some changes to the code provided by you, the remaining code remains same. The edited code will perform convolution of 2 matrices (kernel on image) and provide you with required filtered matrix. I have also added some comments for reference.
function [filtered] = basic_convolution(image,kernel)
dimensions = size(image);
dimensions2 = size(kernel);
% define kernel center indices
kernelCenter_x = dimensions2(1)/2;
kernelCenter_y = dimensions2(2)/2;
image2 = zeros(dimensions(1),dimensions(2));
for i = 1:dimensions(1)
for j = 1:dimensions(2)
for k = 1:dimensions2(1)
for l = 1:dimensions2(2)
% New changes are added below
ii = i+(k-kernelCenter_x);
jj = j+(l-kernelCenter_y);
if (ii >= 1 && ii <= dimensions(1) && jj >= 1 && jj <= dimensions(2))
image2(i,j) = image2(i,j) + image(ii,jj)* kernel(k,l);
end
end
end
end
filtered = image2;
end
end
Feel free to reach out for any further queries regarding the above code.
Hope this helps.

R2019b

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