Convolution in CNN vs Convolution Operator

Are Convolution operation in CNN different from the Convolution operator expressed as:

If they share similarities, what would be those, and could we use the convolution operator as shown above in CNN in a meaningful way?

Hi Ahmed Atif,

Welcome to the community. Sorry for the delayed response.

Well, convolutional operators are just a medium that are used to interpret images with the use of various detectors such as edge detectors, corner detectors etc in a convolutional neural network based model. These mathematical operators help in producing a filtered output with the help of image (as an input) and a filter along.

Now, the variables ‘f’ and ‘g’ that you are talking about, are just the symbols written as (f*g) and are defined as the integral of the product of two functions where one of them is reversed/shifted. This displacement is also known as transformation.

You can have a better idea idea on how operators work in a CNN.

Let us know whether things get clear at your end.

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Rashmi has explained what “convolution” means in the neural network context. The formulation you show is the mathematical definition of the convolution of two continuous functions. That particular formulation is for functions of one variable, but there are more general formulations as well. Here’s the Wikipedia page on convolution. I don’t think there is any real mathematical relationship between that definition of convolution and the Neural Network meaning of convolution. There is a vague similarity in that you are multiplying two things together as you “slide” one over the other. Take a look at the animations on that Wikipedia page. But in the math case, the functions are continuous and the convolution operation is continuous, whereas everything is “discrete” in the CNN case: the “sliding” is done in discrete steps rather than continuously.

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Hi Paul sir,

Yes, you are right! There is no real mathematical relationship between the definition of Convolution & the CNN. I just used it as symbolic representation to make Ahmed Atif understand, how the formula works. I should not have mentioned that.

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