Characterization of Dirac-structure edges with wavelet transform

This paper aims at studying the characterization of Dirac-structure edges w ith wavelet transform, and selecting the suitable wavelet functions to dete ct them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are present ed: 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 re spect to a Dirac-structure edge takes place at the same points when the ima ges with different grey-levels are processed; and 3) width light-dependent: for various widths of the Dirac-structure edge images, the location of max imum modulus of the wavelet transform varies lightly under the certain circ umscription that the scale of the wavelet transform is larger than the widt h of the Dirac-structure edges. It is important, in practice, to select the suitable wavelet functions, according to the structures of edges. For exam ple, Haar wavelet is better to represent brick-like images than other wavel ets. A mapping technique is applied in this paper to construct such a wavel et function. In this way, a low-pass function is mapped onto a wavelet func tion by a derivation operation. In this paper, the quadratic spline wavelet is utilized to characterize the Dirac-structure edges and an novel algorit hm to extract the Dirac-structure edges by wavelet transform is also develo ped.