The Sobel operator is a classic edge-detection linear filter that is based on a simple 3x3 kernel that has the following structure:
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-1 |
0 |
1 |
|
-2 |
0 |
2 |
|
-1 |
0 |
1 |
|
-1 |
-2 |
-1 |
|
0 |
0 |
0 |
|
1 |
2 |
1 |
If we view the image as a two-dimensional function, the Sobel operator can then be seen as a measure of the variation of the image in the vertical and horizontal directions. In mathematical terms, this measure is called a gradient, and it is defined as a 2-D vector that is made from the function's first derivatives in two orthogonal directions:
Therefore, the Sobel operator gives you an approximation ...
