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Sobel

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In computer vision, the Sobel operator is a simple edge detection algorithm using the 1st derivative of the intensity information.

The operator uses two 3x3 kernels convolved with the original image to produce a map of intensity gradient. The areas of highest gradient are where the intensity of the image changes rapidly over a few pixels, and are thus likely to represent edges.

Two convolution kernels are needed to detect the first-order derivative of both horizontal and vertical changes in a 2-dimensional image. If we define \mathbf{A}

as the source image, we can compute:


\mathbf{G_x} = \begin{bmatrix} 
-1 & 0 & +1 \\
-2 & 0 & +2 \\
-1 & 0 & +1 
\end{bmatrix} * \mathbf{A}
\ and\ 
\mathbf{G_y} = \begin{bmatrix} 
+1 & +2 & +1 \\
0 & 0 & 0 \\
-1 & -2 & -1 
\end{bmatrix} * \mathbf{A}


Which can then be combined to give the overall magnitudes using:

\mathbf{G} = \sqrt{ \mathbf{G_x}^2 + \mathbf{G_y}^2 }


Using this information, we can also calculate the gradient's direction:

\mathbf{\Theta} = \operatorname{arctan}\left({ \mathbf{G_y} \over \mathbf{G_x} }\right)

Where \Theta

will be 0 for a vertical edge, and will increase for edges anti-clockwise of this.

See alsoEdit

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