A translation- and scale-invariant adaptive wavelet transform

This paper presents a new approach to deal with the translation- and scale-invariant problem of the discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonormal wavelet,...

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Bibliographic Details
Published in:IEEE transactions on image processing 2000-12, Vol.9 (12), p.2100-2108
Main Authors: Huilin Xiong, Tianxu Zhang, Moon, Y.S.
Format: Article
Language:English
Subjects:
Adaptive filters
Applied sciences
Computers in experimental physics
Continuous wavelet transforms
Data compression
Decomposition
Discrete wavelet transforms
Entropy
Exact sciences and technology
Image processing
Impulse response
Information, signal and communications theory
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Invariants
Moon
Pattern recognition
Physics
Signal processing
Stability
Surface layer
Tasks
Telecommunications and information theory
Texture
Wavelet
Wavelet coefficients
Wavelet transforms
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Summary:This paper presents a new approach to deal with the translation- and scale-invariant problem of the discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonormal wavelet, we adaptively renormalized a signal. The renormalized signal is then decomposed by using the algorithm of the conventional DWT. The final wavelet transform coefficients, called adaptive wavelet invariant moments (AWIM), are proved to be both translation- and scale-invariant. Furthermore, as an application, we define a new textural feature in the framework of our adaptive wavelet decomposition, show its stability to shift and scaling, and demonstrate its efficiency for the task of scale-invariant texture identification.
ISSN:1057-7149
1941-0042
DOI:10.1109/83.887977