If at least of one of the two "things" is symmetrical, then it doesn't matter which you use. In signal processing, the convolution is performed to obtain the output of an LTI system. The correlation auto, or cross correlation usually is calculated to be used later to do some other calculations. You have to be careful not to confuse correlation, covariance, and correlation coefficient. The correlation does not necessarily have to be between -1 and 1.
The thing we have to remember is that the real operation to be done in statistical signal processing to analize how related are two random variables is the "Covariance", not the correlation. But for most applications where a signal is captured by a sensor and transformed into a voltage and the digitized with an ADC, you can assume that the signal is zero mean, hence the correlation is equal to the covariance.
Keep Signal Processing aside, if you just try to understand what is happening in Convolution and Correlation, both are very similar operations. The only difference is in Convolution, one of the variable is inverted flipped before performing the accumulation of the product.
See that i am not using the word signal anywhere above. I am only talking in terms of the operations performed. Convolution operation is used to calculate the output of a Linear Time Invariant System LTI system given an input singal x and impulse response of the system h. To understand why only Convolution operation is used to get the output of an LTI system, there is big derivation.
Please find the derivation here. Correlation operation is used to find the similarity between the two signals x and y. More the value of correlation, more is the similarity between the two signals. So, from signal analysis point of view, Convolution operation is not used. Only correlation is used from signal analysis point of view. Whereas convolution is used from System analysis point of view. Best way to understand the operations of convolution and correlation is to understand what happens when two convolution and correlation is done between two continuous variables like shown in the diagrams in the question.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. The difference between convolution and cross-correlation from a signal-analysis point of view Ask Question. Asked 5 years, 11 months ago. Active 2 years, 2 months ago.
Viewed 73k times. It seems like these two terms has a lot of use, so, what is that use? Improve this question. MathBgu MathBgu 1 1 gold badge 5 5 silver badges 5 5 bronze badges. Add a comment. Active Oldest Votes. Improve this answer. MBaz MBaz Thanks a lot for your clear and bright answer! The actual kernel numeric values are represented as the variables a, b, c, d, e, f, g, h, and i, shown on the right. These numeric values in the kernel are what a CNN learns during the process of training.
For this piece of the image, I wrote out the indexes of each of the pixels. These are not the pixel values — they are just the [i, j] coordinates of each pixel. What this initially seems to suggest is that in order to obtain the value at index [m,n] in the output y , we need to look at all of the pixels in the image. After all, i and j are indexing into the image, and the sums go across values of i and j from minus infinity to positive infinity.
So, we are only going to end up looking at the pixels of the image for which the kernel part of the equation h [m-i,n-j] is still valid.
On the left of the blue line, we have the values of m, n, i, and j plugged straight in to the convolution equation in a systematic way. The equations above might seem like a lot of mumbo-jumbo, but if we organize them into a picture, we can suddenly see why they are cool.
In the picture below, I show the lower right-hand corner of the image x with the relevant pixel indices written out explicitly. Here are the equations for cross-correlation and convolution side-by-side, so you can compare them:. That one difference ends up determining a whether the kernel is flipped and b what pixels are processed for each element of the output map.
As a further summary of the matter, here are two figures showing what part of the input image is used to create different parts of the output map, for cross-correlation vs. Once again, we can use the math above to fill in a picture showing us what is happening at the level of the image and the kernel. Image Source: Peggy Bacon in mid-air backflip. Remember…real convolution flips the kernel.
You must be logged in to post a comment. Home About Contact Search. Search for: Search. Date: July 26, Author: Rachel Draelos. First, a little motivation on this topic… Motivation It is necessary to understand the difference between convolution and cross-correlation in order to understand backpropagation in CNNs , which is necessary to understand deconvnets a CNN visualization technique , which is necessary to understand the difference between deconvnets and saliency maps more visualization , which is necessary to understand guided backpropagation more visualization , which is necessary to understand Grad-CAM more visualization , which is necessary to understand Guided Attention Inference Networks a method built off of Grad-CAM that includes a new way to train attention maps.
Jeevan Joishi on 27 Jan Vote 8. Theoretically, convolution are linear operations on the signal or signal modifiers, whereas correlation is a measure of similarity between two signals. As you rightly mentioned, the basic difference between convolution and correlation is that the convolution process rotates the matrix by degrees.
Most of the time the choice of using the convolution and correlation is up to the preference of the users, and it is identical when the kernel is symmetrical.
Also, correlation or auto-correlation is the measure of similarity of signal with itself which has a different time lag between them. Cross-correlation is a way of finding similarity between two different signals.
Kenny on 27 Feb Vote 0. Edited: Kenny on 27 Feb I'm thinking that 'convolution' is a mathematical process or manipulation done on numbers, or a sequence of numbers etc, while correlation is about determining similarity or likeness between maybe a set of values when compared with a given reference set of values.
The results of a convolution process is maybe ONE tool or mathematical manipulation process for seeing if there is any degree of relation or similarity aka correlation between data sets. So, if you 'convolve' one particular set of values from a 'reference' time sequence with some other similar sequence, the plotted result could give you a visual indication of similarity between the data sets.
And if a person isn't around to look at the results, then a computer program could search through the result to see if there are relatively large enough 'peaks' in the results of the convolution so can get a computer to do the assessing of the results.
And, then there are cases involving lots of measurements on 1 quantity to get an average value to present to somebody. And lots of measurements on a different other quantity. In that case, there are matrix correlation methods involving these other statistical values like covariance, mean etc, which involve a correlation method, but not using any convolution method. See Also.
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