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## 4.1: The Filter-Kernels
There are a variety of different Kernels used for edge detection; some of the most common ones are Sobel, Scharr, and Prewitt - Kernels.
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-Sobel:
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-X-Direction: $\begin{bmatrix}1&0&-1\\2&0&-2\\1&0&-1\end{bmatrix}$ Y-Direction: $\begin{bmatrix}1&2&1\\0&0&0\\-1&-2&-1\end{bmatrix}$
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----
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-Scharr:
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-X-Direction: $\begin{bmatrix}47&0&-47\\162&0&-162\\47&0&-47\end{bmatrix}$ Y-Direction: $\begin{bmatrix}47&162&47\\0&0&0\\-47&-162&-47\end{bmatrix}$
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----
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-Prewitt:
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-X-Direction: $\begin{bmatrix}1&0&-1\\1&0&-1\\1&0&-1\end{bmatrix}$ Y-Direction: $\begin{bmatrix}1&1&1\\0&0&0\\-1&-1&-1\end{bmatrix}$
-
-
+
When applying these Filter-Kernels to an image through __convolution__, you essentially create the derivative of the image.
This is because these Kernels result in higher pixel-values in regions, where the image contains a sharp change in brightness (similar to derivatives in analysis). This "derivation" is performed in X- and Y-direction seperately.