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

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!!

Answer 1

[Rishabh Mishra]

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.