- #1

fog37

- 1,568

- 108

- TL;DR Summary
- understand the difference between convolution and cross-correlation results

Hello,

Convolution is essentially superposition. Conceptually, a copy of the same mask/filter is essentially placed at every point in the signal (1D, 2D, ect.). Once all these convolution masks are in place, we just compute the sum and get the convolved signal. The integral formula for convolution, which implies rotating by 180 degrees the mask, is less intuitive.

Let's now talk about cross-correlation. In this case, we don't place the mask at EVERY point in the input signal but simply slide the mask around and calculate the inner product with the overlapped area and move on to the next input signal area....The correlation map looks therefore very different from a convolution operation. The integral formula for cross- correlation seems very similar (the mask is not rotated) to the convolution integral but the concept is quite different.

Concetually, convolution places the mask everywhere in the input signal, does the inner product, and sum everything up. Cross-correlation simply perform the inner product area by area...

What actually occurs in deep learning and CNN (convolutional neural networks) is really

Convolution is essentially superposition. Conceptually, a copy of the same mask/filter is essentially placed at every point in the signal (1D, 2D, ect.). Once all these convolution masks are in place, we just compute the sum and get the convolved signal. The integral formula for convolution, which implies rotating by 180 degrees the mask, is less intuitive.

Let's now talk about cross-correlation. In this case, we don't place the mask at EVERY point in the input signal but simply slide the mask around and calculate the inner product with the overlapped area and move on to the next input signal area....The correlation map looks therefore very different from a convolution operation. The integral formula for cross- correlation seems very similar (the mask is not rotated) to the convolution integral but the concept is quite different.

Concetually, convolution places the mask everywhere in the input signal, does the inner product, and sum everything up. Cross-correlation simply perform the inner product area by area...

What actually occurs in deep learning and CNN (convolutional neural networks) is really

__and not convolution, correct?__**cross-correlation**