Journal of Visual Communication and Image Representation
A reduced-complexity image coding scheme using decision-directed wavelet-based contourlet transform
Highlights
► We propose 3 enhanced tools for wavelet-based contourlet transform coding scheme. ► First, we propose short length 2-D filters for directional transform. ► Then, we propose an algorithm to find out proper subbands for directional transform. ► Finally, we fine-tune context tables for arithmetic coder. ► We saves about 92% run time and provide comparable coding performance.
Introduction
Wavelet-based image coding method becomes a popular image compression topic in recent years [1], [2]. For example, it was adopted by JPEG2000 [2] as an international image coding standard. Typical wavelet-based image coding scheme consists of three stages: two-dimensional discrete wavelet transform (2-D DWT), quantization, and arithmetic coding [2]. A digital image is first transformed by 2-D DWT to produce a set of transform coefficients. After quantization, these coefficients are compressed to a binary stream by an entropy coding tool.
However, the 2-D DWT is inefficient in representing the edge signals that are not aligned with the vertical or the horizontal axes [3]. Many 2-D directional transforms have thus been developed to solve this problem [5], [6], [7], [8], [11], [12], [13], [14], [15], [16], [17]. Among them, the wavelet-based contourlet transform (WBCT) [17] technique has the critical-sampling property, consumes comparatively less computational power, and requires no side information for decoding. Therefore, we focus on WBCT in this study.
The arithmetic coding methods [9], [10], [18], [19], [26], [27], [28] are commonly adopted to compress the transformed/quantized coefficients. Particularly, the embedded block coding with optimized truncation (EBCOT) [9] technique was adopted by JPEG2000. It was originally designed for intra-subband coding. In this study, we adopt ESCOT (3-D embedded subband coding with optimized truncation) [26], which is an extension of EBCOT to inter-frame video coding, because our future work is targeting at video coding.
Combining WBCT and ESCOT, a WBCT image coding scheme can achieve a better coding performance than a regular 2-D DWT image coding scheme. However, there are a few issues in the existing WBCT coding schemes. They need a large amount of computations because the existing WBCT directional filters have a large support. And, we found that for a specific picture, some WBCT frequency subbands do not need further directional transform. Furthermore, the context table in ESCOT needs adjustment to match the characteristics of quantized WBCT coefficients.
To solve these issues, we propose three tools in this paper to enhance the WBCT image coding scheme. First, we suggest a set of short-length 2-D directional filters [30] and verify their performance. Second, we design a mean-shift-based decision scheme to dynamically select the proper subbands for directional transform [31]. Third, we re-design the context tables of ESCOT to match the data directionality. With these tools, our proposed scheme reduces 92% or higher the computational complexity of the original WBCT image coding scheme at similar visual quality [30].
The rest of this paper is organized as follows. Literature reviews and detailed problem statements are given in Section 2 and Section 3 describes the use of short-length 2-D filters. Section 4 presents a mean-shift-based decision algorithm for choosing the proper subbands for directional transform. Section 5 illustrates new entropy-coding context tables that are optimized for compressing the filtered coefficients. Experimental results are shown in Section 6. Finally, Section 7 concludes this paper.
Section snippets
Literature reviews and problem statements
Wavelet-based image coding systems typically consist of transform, quantization, and entropy coding. In this section, we briefly review the evolvement of directional transforms from 2-D DWT to WBCT. Then, we summarize the operations of ESCOT. When we put these two elements together, they form a conventional WBCT scheme.
Short-length 2-D filters
To reduce computational load of the current WBCT, we design new short-length 2-D filters (SLF). The design procedure is as follows. We first choose an appropriate 1-D filter, up-sample it, and map it to a 2-D filter.
We begin our design from a 1-D type-II linear phase finite impulse response filter [23], [25]. Eq. (1) is a 1-D prototype filter β(z), wherein the coefficients {vk} satisfy (2) so that β(ej0) = 1. When N1 = 1 (short filter), β(z) has a wide transition band. To keep a good balance
Mean-shift-based decision on subband selection
In the WBCT image coding scheme, we apply the directional transform to the LH1, HL1, and HH1 subbands. Yet, only the subband signal with significant energy in that direction would benefit from the directional transform. We thus try to locate the subbands with this property. Essentially, we identify the energy peaks and find their locations.
Mean shift technique is adopted to locate the energy peaks in the frequency spectrum. Mean shift is an iterative, nonparametric estimator of the peak
New ZC context tables for ESCOT
Arithmetic coding methods encode the transformed/quantized coefficients into a bit-stream. ESCOT is a bit-plane coding method and it uses its neighbors for the context model. Let the sequence xN = {xN, xN-1, …, x2, x1} represents one bit-plane of a coefficient block. Because the bit-plane consists of binary symbols, i.e., xi ϵ {0, 1}, the minimum code length of a binary sequence estimated based on the information theory is shown in (37), wherein P(xi|xi-1) is the conditional probability of xi
Experimental results
We have discussed the three proposed tools that enhance a WBCT image coding scheme in computation and/or complexity reduction. They are short length 2-D filters, a mean-shift-based decision, and new ZC context tables for ESCOT. In this section, we examine the impact of each tool towards the system performance. And, putting them together, we compare the overall performance between the 2-D DWT image coding scheme, the original WBCT image coding scheme, and the proposed WBCT image coding scheme
Conclusions
The WBCT-based image coding approach is explored in this paper. We propose three components to enhance its performance. First, we design a short-length filter set (SLF) to speed up the filtering process. It provides similar coding performance but requires only 10% of computational complexity of the original long-length filters (LLF). Second, we construct a mean-shift-based decision process to decide if a higher subband (HH1, HL1, or LH1) is appropriate for directional decomposition. Threshold
Acknowledgements
The first author would like to thank Dr. Jang-Jer Tsai for his valuable suggestions on improving the quality of this paper. This work was supported in parts by the NSC, Taiwan under Grant 98-2221-E-009-076, by the MOEA, Taiwan under Grant 99-EC-17-A-01-I1-0016, and by the Intelligent Information Communications Research Center, NCTU.
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