# Correlation and Convolution [duplicate]

Both Correlation and Convolution are displacement function, i.e they are used to slide the filter mask across the image.

Convolution is same as correlation except that the filter mask is rotated 180 degree before computing the sum of products.

We mostly use convolution. why it is widely used? why convolution is preferred over correlation?

We have,

 Convolution in time domain   = Multiplication in Frequency domain


Do we have any similar relation for correlation ?

Correlation in time domain  =  _______________ in Frequency domain ?


## 2 Answers

Please note that for complex-valued signals, complex conjugates are needed for correlation, but neither signal is conjugated in the convolution. So it is only partially true for real valued signals that Convolution is same as correlation except that the filter mask is rotated 180 degree before computing the sum of products.

In image processing, convolve the multiple filters into a single filter is preferred, while correlation is sufficient if you are only find one template for matching purpose. Check this post for its associative property on convolution.

• Thanks for the link..Can u explain what do you mean by multiple filters? – Premnath D Feb 10 '14 at 16:24
• implementation with a series filters. Such as what they did in this paper: ieeexplore.ieee.org/xpl/… – lennon310 Feb 10 '14 at 16:30
• Thank U. I am deleting the post as it is termed as duplicate.. Thank u again for your help – Premnath D Feb 10 '14 at 16:31
• you can keep it if you like to, finally a redirection from your post to another will be made if it is closed – lennon310 Feb 10 '14 at 16:32

Convolution as associative, while correlation is not. The associative property is what allows you to convolve multiple filters into a single one, and then convolve that one filter with the image. That is the big advantage of convolution over correlation.

• Actually I cited your post:) Thanks! +1 – lennon310 Feb 10 '14 at 20:15