TY - JOUR
T1 - Characterization of Dirac-structure edges with wavelet transform
AU - Tang, Yuan Y.
AU - Yang, Lihua
AU - Liu, Jiming
N1 - Funding Information:
Manuscript received August 10, 1998; revised October 31, 1999. This work was supported by research grants received from Research Grant Council (RGC) of Hong Kong, and Faculty Research Grant (FRG) of Hong Kong Baptist University, and by the National Natural Science Foundation of China (19871095) and the Guangdong Provincial Natural Science Foundation of China (990227). This paper was recommended by Associate Editor P. Willett.
PY - 2000/2
Y1 - 2000/2
N2 - 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 an novel algorithm to extract the Dirac-structure edges by wavelet transform is also developed.
AB - 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 an novel algorithm to extract the Dirac-structure edges by wavelet transform is also developed.
UR - http://www.scopus.com/inward/record.url?scp=0033905230&partnerID=8YFLogxK
U2 - 10.1109/3477.826950
DO - 10.1109/3477.826950
M3 - Journal article
AN - SCOPUS:0033905230
SN - 1083-4419
VL - 30
SP - 93
EP - 109
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IS - 1
ER -