Multiresolution Approaches for Edge Detection and Classification Based on Discrete Wavelet Transform
Guillermo Palacios, José Luis Alapont Ramón, Raquel Lacuest · InTech eBooks · 2011
Detecting edges is a very well known subject in the image#processing field.Edge detection is the process of the localization of significant discontinuities in the grey level image and the identification of the physical phenomena that originated them.Those significant intensity changes occur at different resolution or scales for a given image.As suggested by Rosenfeld and Thurston (Rosenfeld & Thurston, 1976) and Marr (Marr, 1982), we can obtain a description of the image changes at different scales combining the information given by an edge detector applied at different resolutions.This is the aim of the work presented in this paper.The first aspect to be covered by multiresolution analysis is the filter chosen to accomplish the low#pass filtering of the image at different scales.At a single resolution, low pass filtering is imposed because differentiation is an ill#posed problem (Torre & Poggio, 1984).The needed regularization process is implemented by means of a low pass filter.Marr (Marr, 1982) proposed the Gaussian filter because its optimal behaviour in terms of the smoothing and the localization in both the spatial and frequency domains.This filter has been commonly used in edge detectors.In a multiresolution approach the first or second directional derivatives of the low pass filtered image with Gaussians of different widths are used to detect edges.In the Bergholm edge focusing method (Bergholm, 1987) various edge maps extracted at different scales are integrated allowing distinguishing shadows contours from perfect ones using Canny's operator (Canny, 1986) with different widths.Another possibility is to describe the image in terms of the scale space as proposed by Witkin (Witkin, 1983) and to detect edges in terms of the zero crossing of the Laplacian operator with different widths (Park et al., 1995) (Eklundth et al., 1982).Other multiresolution methods have been proposed.Mallat and Zhong (Mallat & Zhong, 1992) related multiscale edge detection with the discrete wavelet transform (DWT).They proposed a wavelet to perform edge detection and they showed that the evolution of wavelet local maxima across scales characterizes the shape of irregular structures.In our work we will use the wavelet#based algorithm proposed by Mallat and Zhong and we will show the condition that must be satisfied by the Gaussian filter to be comparable with the Mallat and Zhong's wavelet.Our aim is to detect and classify different edge types.Various edge profiles have been proposed.Rosenfeld (Rosenfeld & Kak, 1976) proposed the step, www.intechopen.