The Sobel operator is a simple edge detection filter, which is often used in image processing where it is used by using the convolution algorithm as ( Sobel algorithm). This computes the first derivative of the pixel brightness values, at the same time orthogonal to the discharge direction is smoothed.
The algorithm uses a convolution using a 3 x 3 matrix ( convolution matrix ) generating from the original image, a gradient image. This high frequencies are shown in the image gray values . The areas of greatest intensity are where the brightness of the original image most changes and thus represents the largest edges. Therefore, a threshold function is usually applied after the convolution with the Sobel operator. However the algorithm can also be applied to other two-dimensional signals.
From the original image, the area around the point to be considered is for each pixel always only a segment, specifically used. For this purpose, a matrix is defined whose components represent the change in weighting the vicinity of the point. The matrix is usually designed to be symmetrical, so that no change in the environment leads to a zero-sum ( see below). Now, using the Sobeloperatoren and the folded results and calculated:
By utilizing the separability, the computing time can be greatly reduced.
Then all components of the matrix are summed to get their gray value. A directional information can be obtained by combining two results:
The direction of a gradient is obtained by the formula
Where atan2, the " inverse tangent " with two arguments is.
Here, the value describes a vertical edge. Positive values describe a counterclockwise rotation.
The Sobel operator has no perfect rotational symmetry. Take better account of this is with the scratching operator: