An edge detection algorithm based on the regularization theory in which the smoothness is controlled spatially over the image space is presented. The algorithm starts with an oversmoothed regularized solution and iteratively refines the surface around discontinuities using the knowledge on the structure of discontinuities exhibited in the error signal between the image data and the previous regularized solution. The spatial control of smoothness is shown to resolve the conflict between detection and localization criteria. The adaptive nature of the algorithm eliminates the need to select image-dependent parameters and enables the extraction of multiscale features from the image. The computational aspects of the algorithm as well as its performance on real and synthetic images are considered.
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