Nonlinear multiresolution signal decomposition schemes-Part II : Morphological wavelets

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...

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Bibliographic Details
Published in:IEEE transactions on image processing 2000-11, Vol.9 (11), p.1897-1913
Main Authors: HEIJMANS, Henk J. A. M, GOUTSIAS, John
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Image processing
Information, signal and communications theory
Pattern recognition. Digital image processing. Computational geometry
Signal processing
Telecommunications and information theory
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Summary: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.
ISSN:1057-7149
1941-0042
DOI:10.1109/83.877211