Abstract
In this paper, we propose multiresolution edge detection techniques for noiseless images and noisy ones which are contaminated by additive Gaussian noise or multiplicative noise. For edge detection, they determine automatically the resolution of a pixel by using pertinent discontinuity measures. The mode of the discontinuity measure γ calculated over the (2 p + 1) × (2 p + 1) windows is used to determine the resolution of a given pixel and the edge operator with a varying scale is applied to the pixel depending on its resolution. For noiseless images and noisy images contaminated by additive Gaussian noise, the local variance γ a is used as an edgeness measure. For multiplicative speckle images, the statistical quantities such as the ratio γ s of the variance to mean-square, or the maximum difference γ d between the real and theoretical cumulative density functions (CDF's) are employed as discontinuity measures. The application of the proposed pixelwise resolution determination algorithm to the conventional Canny and LoG edge detectors, for example, gives the proposed multiresolution edge detection techniques. Their effectiveness is shown via computer simulations.
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