Nonlinear multiresolution signal decomposition schemes - Part II: morphological wavelets

被引:177
作者
Heijmans, HJAM [1 ]
Goutsias, J
机构
[1] Ctr Math & Comp Sci, NL-1090 GB Amsterdam, Netherlands
[2] Johns Hopkins Univ, Dept Elect & Comp Engn, Baltimore, MD 21218 USA
[3] Johns Hopkins Univ, Ctr Imaging Sci, Baltimore, MD 21218 USA
基金
美国国家科学基金会;
关键词
coupled and uncoupled wavelet decomposition; lifting scheme; mathematical morphology; max-lifting; morphological operators; multiresolution signal decomposition; nonlinear wavelet transform;
D O I
10.1109/83.877211
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens, The aim of this paper, which is a sequel of a previous paper devoted exclusively to the pyramid transform, is to present an axiomatic framework encompassing most existing linear and nonlinear wavelet decompositions. Furthermore, it introduces some, thus far unknown, wavelets based on mathematical morphology, such as the morphological Haar wavelet, both in one and two dimensions. A general and flexible approach for the construction of nonlinear (morphological) wavelets is provided by the lifting scheme. This paper briefly discusses one example, the max-lifting scheme, which has the intriguing property that preserves local maxima in a signal over a range of scales, depending on how local or global these maxima are.
引用
收藏
页码:1897 / 1913
页数:17
相关论文
共 46 条
[1]  
Alvarez Luis, 1994, ACTA NUMER, V3, P1
[2]   EVOLUTION-EQUATIONS FOR CONTINUOUS-SCALE MORPHOLOGICAL FILTERING [J].
BROCKETT, RW ;
MARAGOS, P .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1994, 42 (12) :3377-3386
[3]  
BRUEKERS FAML, 1992, IEEE J SEL AREA COMM, V10, P130
[4]   THE LAPLACIAN PYRAMID AS A COMPACT IMAGE CODE [J].
BURT, PJ ;
ADELSON, EH .
IEEE TRANSACTIONS ON COMMUNICATIONS, 1983, 31 (04) :532-540
[5]   Wavelet transforms that map integers to integers [J].
Calderbank, AR ;
Daubechies, I ;
Sweldens, W ;
Yeo, BL .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1998, 5 (03) :332-369
[6]   Adaptive morphological representation of signals: Polynomial and wavelet methods [J].
Cha, HT ;
Chaparro, LF .
MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 1997, 8 (03) :249-271
[7]   HUMAN AND MACHINE RECOGNITION OF FACES - A SURVEY [J].
CHELLAPPA, R ;
WILSON, CL ;
SIROHEY, S .
PROCEEDINGS OF THE IEEE, 1995, 83 (05) :705-740
[8]  
CLAYPOOLE R, 1997, P 31 AS C SIGN SYST, V1, P662
[9]   Lifting construction of non-linear wavelet transforms [J].
Claypoole, RL ;
Baraniuk, RG ;
Nowak, RD .
PROCEEDINGS OF THE IEEE-SP INTERNATIONAL SYMPOSIUM ON TIME-FREQUENCY AND TIME-SCALE ANALYSIS, 1998, :49-52
[10]  
CLAYPOOLE RL, 1999, 9304 RIC U DEP EL CO