A Principle Discussion of Edge Detection based on Gaussian Wavelet

Abstract

Edge detection is an image processing technique for finding the boundaries of objects within images. It works by detecting discontinuities in brightness. In this paper, we develop the Canny edge detector, introduce wavelet basis functions of nth Gaussian derivative and utilize them to extract the edge. At first, the principle of the edge detection by the wavelet transform is given briefly and new basis of wavelet functions are introduced and admissibility conditions of them are discussed. Then, the theoretical edge detection analysis of three significant edge types (step, ramp and stage) via new wavelet basis functions is studied, and relevant formulas are derived. The theory of the step response in the x, y and arbitrary direction is given and the effect of smoothing filter is obtained. We show that all introduced wavelet functions can detect the breakpoint of the step function. A model of the ramp function is presented and an approximation of it is used to simplify the results