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The sharpening filter and edge detection kernel relationship?

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From Wikipedia:

(The sharpening filter) is obtained by taking the identity kernel and subtracting an edge detection kernel

Can someone explain to be how is that the case.As for as I understand it, to achieve a sharpening image, you take the original image and add high-contrast edges to it.They even take the example of the matrix:

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Should the matrix

0   -1   0-1   4   -10   -1   0

be the edge detection kernel, according to another Wikipedia article? So, the math should be adding, not subtracting.

Anyway, I am a bit confused here and could use some help. Thank you!


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