Abstract
This paper mathematically introduces a new hyperbolic distribution and hyperbolic mask for edge detection. Mathematical comparisons between the hyperbolic and Gaussian (Mexican-hat) masks in the time and frequency domain are given for typical scale parameters of @b=1 and @s=2 respectively. Edge-detection error probability as a function of the half mask size m is estimated using both masks in Gaussian- and hyperbolic-distributed pixel-intensity images. Advantages and disadvantages of the masks and both distributions are discussed. Experiments on edge detection in images are presented. The effects of noise are also considered.
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