DocumentCode :
1395434
Title :
Nonlinear multiresolution signal decomposition schemes. II. Morphological wavelets
Author :
Heijmans, Henk J A M ; Goutsias, John
Author_Institution :
CWI, Amsterdam, Netherlands
Volume :
9
Issue :
11
fYear :
2000
fDate :
11/1/2000 12:00:00 AM
Firstpage :
1897
Lastpage :
1913
Abstract :
For pt.I see ibid., vol.9, no.11, p.1862-76 (2000). 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 (1995, 1996, 1998). The aim of this paper, which is a sequel to 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
Keywords :
Haar transforms; channel bank filters; image resolution; mathematical morphology; nonlinear filters; wavelet transforms; axiomatic framework; lifting scheme; mathematical morphology; max-lifting scheme; morphological Haar wavelet; morphological wavelets; nonlinear extension; nonlinear multiresolution signal decomposition schemes; wavelet decompositions; wavelet transform; Computer science; Image processing; Image reconstruction; Image resolution; Laplace equations; Mathematics; Morphology; Signal processing; Signal resolution; Wavelet transforms;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.877211
Filename :
877211
Link To Document :
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