CODEWITHSUNDEEP
matlabmathimage-processingsignal-processingconvolution
Diego Catalano
Diego Catalano

Reputation: 689

Convolution in Matlab hands on

I got the matrix below:

 9 18 27 36 45
 0  0  0  0  0
 0  0  0  0  0
 0  0  0  0  0
 0  0  0  0  0

and the kernel:

-0.5+0.8662i 1 -0.5-0.8662i

I'm trying to perform the convolution using valid mode:

ans = conv2(matrix,kernel,'valid');

The matlab returns:

0.0000+15.5916i 0.0000+15.5916i 0.0000+15.5916i

My question is how I can achieve the same results like matlab. I'm trying to do in the matlab in the first point, but the results is different.

a =     matrix(1,1) * kernel(1);
a = a + matrix(1,2) * kernel(2);
a = a + matrix(1,3) * kernel(3);

Result: 0-15.5916i

For some reason the sign of the imaginary is positive using convolution. Why ?

Upvotes: 5

Views: 303

Answers (2)

eigenchris
eigenchris

Reputation: 5821

I believe convolution is usually performed by "flipping" the kernel (left-right, up-down) and then sliding it across the matrix to perform a sum of multiplications.

In other words, what matlab is actually computing is:

a =     matrix(1,1) * kernel(3);
a = a + matrix(1,2) * kernel(2);
a = a + matrix(1,3) * kernel(1);

Upvotes: 7

Luis Mendo
Luis Mendo

Reputation: 112659

In the convolution process the kernel is flipped. So you have to flip it too in your check; that is, swap kernel(1) and kernel(3), as follows:

>> a =     matrix(1,1) * kernel(3);
>> a = a + matrix(1,2) * kernel(2);
>> a = a + matrix(1,3) * kernel(1)
a =
  27.0000 +15.5916i

This is in accordance with the result of the convolution:

>> A = conv2(matrix,kernel,'valid');
>> A(1,1)
ans =
  27.0000 +15.5916i

Upvotes: 6

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