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The Sobel Gradient Operator
If the directional derivative is thought of as a vector, two perpendicular derivatives can be combined to calculate the magnitude of the brightness gradient independent of its orientation. This is the widely used Sobel gradient operator, which applies the kernel in the vertical and horizontal directions to each pixel using brightness rather than color values, and then takes the square root of the squares of the magnitude of the two results to form a new image. This interactive tutorial illustrates the application of the Sobel gradient filter to delineate steps and edges in an image, applying the process to the brightness values only.
The tutorial initializes with a randomly selected specimen appearing in the Specimen Image window. The Choose A Specimen pull-down menu provides a selection of specimen images, in addition to the initial randomly chosen one. The Horizontal Derivative and Vertical Derivative buttons show the result of applying a directional derivative to the image in either direction, while the Sobel Gradient button shows the result of combining the two individual derivatives as vectors to outline steps and edges in the Filtered Image shown on the right. For color images, the processing is applied only to the pixel brightness values.
Contributing Authors
John C. Russ - Materials Science and Engineering Dept., North Carolina State University, Raleigh, North Carolina, 27695.
Matthew Parry-Hill, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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