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This algorithm seeks to create a thresholding surface (also referred to as an active surface) derived from the initial image topology by means which minimize the image gradient, resulting in a smoothed image which can be used for adaptive thresholding. Unlike approaches which interpolate through points usually associated with high gradient values, each image point is uniquely characterized by a quadratic cost function determined by the gradient at that point along with a constraining potential determined by the image intensity. Minimization is achieved by allowing each point to deviate from its initial value so as to minimize the gradient, as balanced by a constraining potential which seeks to minimize the amount of deviation. The cost function also contains terms which cause the gradient of the thresholding surface to closely parallel those of the image in regions of near uniform intensity (where the absolute values of the gradients are small). This is done to reduce the effects of ghosting (or false segmenting) when thresholding, an important feature of this approach. Image binarization is achieved by comparing the values of the original image points with those of the thresholding surface; values above a given threshold are considered part of the foreground, while those below are considered part of the background.
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