High-pass Subbands Research Articles

Subband correlation of Daubechies wavelet representations

We investigate the correlation characteristics of multiresolution image representations using compactly supported Daubechies wavelets. Subband correlation of two images consists of crosscorrelation of respective low-pass (approximation) and high-pass (detail) subbands generated from wavelet transform. Based on subband correlation, a fast algorithm for target localization and image registration is provided. In particular, a peak of approximation-subband correlation at a resolution level provides a guide for candidate location at the next finer resolution level, thereby confining the searching region and accelerating the matching. The presence of a sharp correlation peak in detail- subband correlation provides a precise location. Using N-order Daubechies wavelets with N= (1,2,3,4,5), the effects of the following aspects on subband correlation are investigated: (1) support length of wavelet filters, (2) random noises and static clutter, and (3) the in-plane rotation. Simulations show that approximation-subband correlation is relatively stable to random noises and static clutter whereas the detail- subband correlation is unstable to periodic translations, and the degradation of subband correlation is mainly attributable to the translation sensitivity.

Binary subband decomposition and concatenated arithmetic coding

This paper proposes a new subband coding approach to compression of document images, which is based on nonlinear binary subband decomposition followed by the concatenated arithmetic coding. We choose to use the sampling-exclusive OR (XOR) subband decomposition to exploit its beneficial characteristics to conserve the alphabet size of symbols and provide a small region of support while providing the perfect reconstruction property. We propose a concatenated arithmetic coding scheme to alleviate the degradation of predictability caused by subband decomposition, where three high-pass subband coefficients at the same location are concatenated and then encoded by an octave arithmetic coder. The proposed concatenated arithmetic coding is performed based on a conditioning context properly selected by exploiting the nature of the sampling-XOR subband filter bank as well as taking the advantage of noncausal prediction capability of subband coding. We also introduce a unicolor map to efficiently represent large uniform regions frequently appearing in document images. Simulation results show that each of the functional blocks proposed in the paper performs very well, and consequently, the proposed subband coder provides good compression of document images.

The translation sensitivity of wavelet-based registration

This paper studies the effects of image translation on wavelet-based image registration. The main result is that the normalized correlation coefficients of low-pass Haar and Daubechies wavelet subbands are essentially insensitive to translations for features larger than twice the wavelet blocksize. The third-level low-pass subbands produce a correlation peak that varies with translation from 0.7 and 1.0 with an average in excess of 0.9. Translation sensitivity is limited to the high-pass subband and even this subband is potentially useful. The correlation peak for high-pass subbands derived from first and second-level low-pass subbands ranges from about 0.0 to 1.0 with an average of about 0.5 for Daubechies and 0.7 for Haar. We use a mathematical model to develop these results, and confirm them on real data.

Subband coding of images using asymmetrical filter banks

We address the problem of the choice of subband filters in the context of image coding. The ringing effects that occur in subband-based compression schemes are the major unpleasant distortions. A new set of two-band filter banks suitable for image coding applications is presented. The basic properties of these filters are linear phase, perfect reconstruction, asymmetric length, and maximum regularity. The better overall performances compared to the classical QMF subband filters are explained. The asymmetry of the filter lengths results in a better compaction of the energy, especially in the highpass subbands. Moreover, the quantization error is reduced due to the short lowpass synthesis filter. The undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter. The proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images, which explains the better coding performance.