Abstract
The introduction of lifting implementations for image wavelet decomposition generated possibilities of several applications and several adaptive decomposition variations. The prediction step of a lifting stage constitutes the interesting part of the decomposition since it aims to reduce the energy of one of the decomposition bands by making predictions using the other decomposition band. In that aspect, more successful predictions yield better efficiency in terms of reduced energy in the lower band. In this work, we present a prediction filter whose prediction domain pixels are selected adaptively according to the local edge characteristics of the image. By judicuously selecting the prediction domain from pixels that are expected to have closer relation to the estimated pixel, the prediction error signal energy is reduced. In order to keep the adaptation rule symmetric for the encoder and the decoder sides, lossless compression applications are examined. Experimental results show that the proposed algorithm provides good compression results. Furthermore, the edge calculation is computationally inexpensive and comparable to the famous Daubechies 5/3 lifting implementation.
Highlights
In [1], it has been shown that any DWT filter bank can be decomposed into series of lifting/dual-lifting steps
The lifting implementation of Daubechies 5/3 wavelet has attracted a wide range of interest in various applications due to its rational filter tap coefficients which are useful in real-time implementations
A novel prediction filter that directionally adapts its domain according to the local edge characteristics and its application to lossless image coding are presented
Summary
In [1], it has been shown that any DWT filter bank can be decomposed into series of lifting/dual-lifting steps. The lifting implementation of this wavelet contains filters with coefficients that can be written as dyadic rationals of two leading to a multiplication free realization of the filter bank [1, 12]. Since the left and right neighbors of a pixel are naturally closely related to the center pixel, the average of these neighbors constitutes a good estimation for the estimated pixel This implementation is mostly used for image decomposition, it is purely one dimensional. Since the right and left neighbor pixel values are naturally related with the pixel value between them, x0[m, 2n] = (x[m, 2n − 1] + x[m, 2n + 1])/2 will be an accurate estimate of x[m, 2n] By subtracting this prediction value from the true value of x[m, 2n], a small residue is obtained. It is illustrated that the proposed edge-adapted decomposition method yields better estimation results with reduced prediction error energy, yielding to better lossless compression
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