Characterization of Dirac-structure edges with wavelet transform

This paper aims at studying the characterization of Dirac-structure edges with wavelet transform, and selecting the suitable wavelet functions to detect them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are presented: (1) slope invariant: the local maximum modulus of the wavelet transform of a Dirac-structure edge is independent on the slope of the edge; (2) grey-level invariant: the local maximum modulus of the wavelet transform with respect to a Dirac-structure edge takes place at the same points when the images with different grey-levels are processed; and (3) width light-dependent: for various widths of the Dirac-structure edge images, the location of maximum modulus of the wavelet transform varies lightly under the certain circumscription that the scale of the wavelet transform is larger than the width of the Dirac-structure edges. It is important, in practice, to select the suitable wavelet functions, according to the structures of edges. For example, Haar wavelet is better to represent brick-like images than other wavelets. A mapping technique is applied in this paper to construct such a wavelet function. In this way, a low-pass function is mapped onto a wavelet function by a derivation operation. In this paper, the quadratic spline wavelet is utilized to characterize the Dirac-structure edges and a novel algorithm to extract the Dirac-structure edges by wavelet transform is also developed.