Convolution vs Correlation - what is the main difference?

Hi, I'm still confused on the correlation vs convolution. The difference is only the position of the kernel at 180 degree rotation whereas the rest are the same. In most of the convolution example, the image is directly multiply and sum from the kernel. No rotation is performed? Is there a rotation in the first place prior to given kernel?

In image processing the correlation is used to check the similarity of the images. Why convolution cannot be used to measure too?

Thanks

Answer 1

[Mehmed Saad]

Take a complex number as an example

s = [1+1j 2-2j];

How convolution is performed (i am convolving s with itself)

you take the time reversal of the your signal and shift it,move it on the other signal from left to right while summing them

conv(s,s)
ans =

   0.0000 + 2.0000i   8.0000 + 0.0000i   0.0000 - 8.0000i

In correlation you take the conjugate of your signal and shift it,,move it on the other signal from left to right while summing them

xcorr(s,s)
ans =

   0.0000 + 4.0000i  10.0000 + 0.0000i   0.0000 - 4.0000i

what convolution did is it expresses how the shape of one signal is modified by the other

what correlation did is it maximizes the output value

How to Perform Correlation through Convolution

In convolution we flip the signal,shift it and move

In correlation we conj the signal shift it and move

so the difference is one flips it and the other conjugates it

In order to perform Correlation through convolution

1. flip the signal by yourself
2. take conjugate of signal by yourself

conv(s,fliplr(conj(s)))
ans =

   0.0000 + 4.0000i  10.0000 + 0.0000i   0.0000 - 4.0000i

same result as correlation

when you flip the signal and feed it to convolution block, it flips it again (as it is a part of convolution) .

Hope this was helpfull for you