I have read many documents about convolution in image processing, and most of them say about its formula, some additional parameters. No one explains the intuition and real meaning behind doing convolution on an image. For example, intuition of derivation on the graph is make it more linear for example.
I think a quick summary of the definition is: convolution is multiplied overlap square between image and kernel, after that sum again and put it into anchor. And this doesn't make any sense with me.
According to this article about convolution I cannot imagine why convolution can do some "unbelievable" things. For example, line and edge detection on the last page of this link. Just choose appropriate convolution kernel can make nice effects (detect line or detect edge).
Can anyone provide some intuition (doesn't need to have to be a neat proof) on how it can do that?