A mathematical approach to edge detection in hyperbolic-distributed and Gaussian-distributed pixel-intensity images using hyperbolic and Gaussian masks

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 β=1 and σ=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.