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Sobel operator
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== Example == The result of the Sobel–Feldman operator is a 2-dimensional map of the gradient at each point. It can be processed and viewed as though it is itself an image, with the areas of high gradient (the likely edges) visible as white lines. The following images illustrate this, by showing the computation of the Sobel–Feldman operator on a simple image. {| |[[Image:Bikesgray.jpg|thumb|200px|Grayscale test image of brick wall and bike rack]] |[[Image:Bikesgraysobel.jpg|thumb|200px|Normalized gradient magnitude from Sobel–Feldman operator]] |- |[[Image:Bikesgraygv.jpg|thumb|200px|Normalized ''x''-gradient from Sobel–Feldman operator]] |[[Image:Bikesgraygh.jpg|thumb|200px|Normalized ''y''-gradient from Sobel–Feldman operator]] |} The images below illustrate the change in the direction of the gradient on a grayscale circle. When the sign of <math>\mathbf{G_x}</math> and <math>\mathbf{G_y}</math> are the same the gradient's angle is positive, and negative when different. In the example below the red and yellow colors on the edge of the circle indicate positive angles, and the blue and cyan colors indicate negative angles. The vertical edges on the left and right sides of the circle have an angle of 0 because there is no local change in <math>\mathbf{G_y}</math>. The horizontal edges at the top and bottom sides of the circle have angles of −{{sfrac|{{pi}}|2}} and {{sfrac|{{pi}}|2}} respectively because there is no local change in <math>\mathbf{G_x}</math>. The negative angle for top edge signifies the transition is from a bright to dark region, and the positive angle for the bottom edge signifies a transition from a dark to bright region. All other pixels are marked as black due to no local change in either <math>\mathbf{G_x}</math> or <math>\mathbf{G_y}</math>, and thus the angle is not defined. Since the angle is a function of the ratio of <math>\mathbf{G_y}</math> to <math>\mathbf{G_x}</math> pixels with small rates of change can still have a large angle response. As a result noise can have a large angle response which is typically undesired. When using gradient angle information for image processing applications effort should be made to remove [[image noise]] to reduce this false response. {| |[[File:Black Circle.jpg|thumb|150px|Grayscale image of a black circle with a white background.]] |[[File:Sobel_Operator_Gradient_Angle.JPG|thumb|180px|The direction of the Sobel operator's gradient.]] |}
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