Hierarchical quantization indexing for wavelet and wavelet packet image coding

In this paper, we introduce the quantization index hierarchy, which is used for efficient coding of quantized wavelet and wavelet packet coefficients. A hierarchical classification map is defined in each wavelet subband, which describes the quantized data through a series of index classes. Going from bottom to the top of the tree, neighboring coefficients are combined to form classes that represent some statistics of the quantization indices of these coefficients. Higher levels of the tree are constructed iteratively by repeating this class assignment to partition the coefficients into larger subsets. The class assignments are optimized using a rate-distortion cost analysis. The optimized tree is coded hierarchically from top to bottom by coding the class membership information at each level of the tree. Context-adaptive arithmetic coding is used to improve coding efficiency. The developed algorithm produces PSNR results that are better than the state-of-art wavelet-based and wavelet packet-based coders in literature.     

Tree coding of image subbands

The authors consider the encoding of image subbands with a tree code that is asymptotically optimal for Gaussian sources and the mean squared error (MSE) distortion measure. They first prove that optimal encoding of ideally filtered subbands of a Gaussian image source achieves the rate distortion bound for the MSE distortion measure. The optimal rate and distortion allocation among the subbands is a by-product of this proof. A bound is derived which shows that subband coding is closer than full-band coding to the rate distortion bound for a finite length sequence. The tree codes are then applied to encode the image subbands, both nonadaptively and adaptively. Since the tree codes are stochastic and the search of the code tree is selective, a relatively few reproduction symbols may have an associated squared error a hundred times larger than the target for the subband. Correcting these symbols through a postcoding procedure improves the signal-to-noise ratio and visual quality significantly, with a marginal increase in total rate.     

Vector quantization for entropy coding of image subbands

Vector quantization for entropy coding of image subbands is investigated. Rate distortion curves are computed with mean square error as a distortion criterion. The authors show that full-search entropy-constrained vector quantization of image subbands results in the best performance, but is computationally expensive. Lattice quantizers yield a coding efficiency almost indistinguishable from optimum full-search entropy-constrained vector quantization. Orthogonal lattice quantizers were found to perform almost as well as lattice quantizers derived from dense sphere packings. An optimum bit allocation rule based on a Lagrange multiplier formulation is applied to subband coding. Coding results are shown for a still image.     

An efficient VLSI architecture for 2-D wavelet image coding withnovel image scan

A folded very large scale integration (VLSI) architecture is presented for the implementation of the two-dimensional discrete wavelet transform, without constraints on the choice of the wavelet-filter bank. The proposed architecture is dedicated to flexible block-oriented image processing, such as adaptive vector quantization used in wavelet image coding. We show that reading the image along a two-dimensional (2-D) pseudo-fractal scan creates a very modular and regular data flow and, therefore, considerably reduces the folding complexity and memory requirements for VLSI implementation. This leads to significant area savings for on-chip storage (up to a factor of two) and reduces the power consumption. Furthermore, data scheduling and memory management remain very simple. The end result is an efficient VLSI implementation with a reduced area cost compared to the conventional approaches, reading the input data line by line     

Curved wavelet transform for image coding.

The conventional two-dimensional wavelet transform used in existing image coders is usually performed through one-dimensional (1-D) filtering in the vertical and horizontal directions, which cannot efficiently represent edges and lines in images. The curved wavelet transform presented in this paper is carried out by applying 1-D filters along curves, rather than being restricted to vertical and horizontal straight lines. The curves are determined based on image content and are usually parallel to edges and lines in the image to be coded. The pixels along these curves can be well represented by a small number of wavelet coefficients. The curved wavelet transform is used to construct a new image coder. The code-stream syntax of the new coder is the same as that of JPEG2000, except that a new marker segment is added to the tile headers. Results of image coding and subjective quality assessment show that the new image coder performs better than, or as well as, JPEG2000. It is particularly efficient for images that contain sharp edges and can provide a PSNR gain of up to 1.67 dB for natural images compared with JPEG2000.     

Space-frequency quantization for wavelet image coding

A new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application. We develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive, often outperforming the very best coding algorithms in the literature.     

Adaptive directional lifting-based wavelet transform for image coding.

We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.     

Peak transform for efficient image representation and coding.

In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation and coding. The proposed PT is able to convert high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality. We believe that the concept explored in this work, designing a nonlinear transform to convert hard-to-compress signals into easy ones, is very useful. We hope this work would motivate more research work along this direction.     

Nonlinear image representation for efficient perceptual coding.

Image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized. The success of such a system depends on two properties of the representation. First, the coding rate is minimized only if the elements of the representation are statistically independent. Second, the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent. We argue that linear transforms cannot achieve either of these goals and propose, instead, an adaptive nonlinear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood. We then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements. We develop an efficient method of inverting this transformation, and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images.     

Hierarchical morphological segmentation for image sequence coding

This paper deals with a hierarchical morphological segmentation algorithm for image sequence coding. Mathematical morphology is very attractive for this purpose because it efficiently deals with geometrical features such as size, shape, contrast, or connectivity that can be considered as segmentation-oriented features. The algorithm follows a top-down procedure. It first takes into account the global information and produces a coarse segmentation, that is, with a small number of regions. Then, the segmentation quality is improved by introducing regions corresponding to more local information. The algorithm, considering sequences as being functions on a 3-D space, directly segments 3-D regions. A 3-D approach is used to get a segmentation that is stable in time and to directly solve the region correspondence problem. Each segmentation stage relies on four basic steps: simplification, marker extraction, decision, and quality estimation. The simplification removes information from the sequence to make it easier to segment. Morphological filters based on partial reconstruction are proven to be very efficient for this purpose, especially in the case of sequences. The marker extraction identifies the presence of homogeneous 3-D regions. It is based on constrained flat region labeling and morphological contrast extraction. The goal of the decision is to precisely locate the contours of regions detected by the marker extraction. This decision is performed by a modified watershed algorithm. Finally, the quality estimation concentrates on the coding residue, all the information about the 3-D regions that have not been properly segmented and therefore coded. The procedure allows the introduction of the texture and contour coding schemes within the segmentation algorithm. The coding residue is transmitted to the next segmentation stage to improve the segmentation and coding quality. Finally, segmentation and coding examples are presented to show the validity and interest of the coding approach.     

Hierarchical finite-state vector quantization for image coding

The hierarchical finite-state vector quantization (HFSVQ) introduced in the paper is an improvement of the finite state vector quantization combined with hierarchical multirate image coding. Based on an understanding of the perception of human eye and the structural features of images, the HFSVQ technique employs different coding rates and different numbers of the predictive states for representative vector selection. The bit rate used to encode images is very low while the reconstructed images can still achieve a satisfactory perceptual quality     

Hierarchical multirate vector quantization for image coding

The hierarchical multirate vector quantization (HMVQ) introduced in this paper is an improved form of vector quantization for digital image coding. The HMVQ uses block segmentation and a structure tree to divide an original image into several layers and sub-layers according to their grey scale contrast within blocks of a certain size. Variant bit-rates are used for block coding of different layers with the same codebook. The HMVQ technique provides high encoded image quality with very low bit-rates. The processing time for codebook generation is considerably reduced by using layer by layer optimization and subsampling in low detail regions. This technique also demonstrates flexibility of accurate reproduction in different detail regions.     

面向多用户的高动态范围视频动态范围可分级编码

提出了面向多用户的高动态范围(HDR,high dynamic range) 视频动态范围可分级编码方法,并利用视觉掩蔽特性抑制了噪声,提高了动态范围可 分级编码的效率。首先,考虑HDR视频感知特性,提出了动态范围可分级模型(DRSM,dynamic range scalable model),将不同动态范围级的HDR视频分解成为一个标准动态范围(SDR,s tandard dynamic range) 视频和多个残差信号帧(RSFs,residual signal frames)序列。然后,结合亮度掩蔽效应和 人眼感知特性,对 RSFs进行量化和滤波处理,滤除残差中的零散数据点,保留RSFs相邻动态范围级之间的整体 差异信息, 提高RSFs的编码效率。最后,在解码端重建得到SDR视频和各个动态范围级的HDR视频,以适 应多用 户端MDR显示设备。结果表明,所提出方法能在保持重建HDR视频的主观感知质量的同时降低 编码码率, 并在全帧内预测编码模式下,相同HDR-VDP-2.2和PSNR分值时,BD-rate (Bjntegaard D elta rate)平均节省了32.03%和31.28%,其编 码率失真性能有明显提升。     

适宜图像编码的双正交小波基的选择

提出一种新的选择适合图橡编码应用的双正交小波基的方法。通过用几个已证实是与图像编码密切相关的小波基评价标准对小波进行全面评价，选出了一些适宜图像编码应用的双正交小波基，并作了编码模拟检验。     

Nonlinear wavelet transforms for image coding via lifting

We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.     

A NEW FRACTAL ZEROTREE CODING FOR WAVELET IMAGE

Based on the mechanisms underlying the performance of fractal and Discrete Wavelet Transform(DWT), one method using fractal-based self-quantization coding way to code different subband coefficients of DWT is presented. Within this method finer coefficients are fractal encoded according to the successive coarser ones. Self-similarities inherent between parent and their children at the same spatial location of the adjacent scales of similar orientation are exploited to predict variation of information across wavelet scales. On the other hand, with respect to Human Visual System(HVS) model, we assign different error thresholds to different decomposition scales, and different shape of range blocks to different orientations of the same scale, by which the perceptually lossless high compression ratio can be achieved and the matching processing can be quickened dramatically.     

Spatial coefficient partitioning for lossless wavelet image coding

In pyramidal wavelet representation, an image is decomposed into multiresolution and multifrequency subbands with sets of tree-structured coefficients, i.e. a spatial orientation tree which consists of coefficients at different resolutions and different orientations but associated with the same spatial location. The magnitudes of the coefficients in these trees measure the signal activity level of the corresponding spatial areas. A novel coefficient partitioning algorithm is introduced for splitting the coefficients into two sets using a spatial orientation tree data structure. By splitting the coefficients, the overall theoretical entropy is reduced due to the different probability distributions for the two coefficient sets. In the spatial domain, it is equivalent to identifying smooth regions of the image. A lossless coder based on this spatial coefficient partitioning has a better coding performance than other wavelet-based lossless image coders such as S + P and JPEG-2000.     

Methods for improving the tone mapping for backward compatible high dynamic range image and video coding

Backward compatibility for high dynamic range image and video compression forms one of the essential requirements in the transition phase from low dynamic range (LDR) displays to high dynamic range (HDR) displays. In a recent work [1], the problems of tone mapping and HDR video coding are originally fused together in the same mathematical framework, and an optimized solution for tone mapping is achieved in terms of the mean square error (MSE) of the logarithm of luminance values. In this paper, we improve this pioneer study in three aspects by considering its three shortcomings. First, the proposed method [1] works over the logarithms of luminance values which are not uniform with respect to Human Visual System (HVS) sensitivity. We propose to use the perceptually uniform luminance values as an alternative for the optimization of tone mapping curve. Second, the proposed method [1] does not take the quality of the resulting tone mapped images into account during the formulation in contrary to the main goal of tone mapping research. We include the LDR image quality as a constraint to the optimization problem and develop a generic methodology to compromise the trade-off between HDR and LDR image qualities for coding. Third, the proposed method [1] simply applies a low-pass filter to the generated tone curves for video frames to avoid flickering during the adaptation of the method to the video. We instead include an HVS based flickering constraint to the optimization and derive a methodology to compromise the trade-off between the rate-distortion performance and flickering distortion. The superiority of the proposed methodologies is verified with experiments on HDR images and video sequences.     

A fast and low memory image coding algorithm based on lifting wavelet transform and modified SPIHT

Due to its excellent rate–distortion performance, set partitioning in hierarchical trees (SPIHT) has become the state-of-the-art algorithm for image compression. However, the algorithm does not fully provide the desired features of progressive transmission, spatial scalability and optimal visual quality, at very low bit rate coding. Furthermore, the use of three linked lists for recording the coordinates of wavelet coefficients and tree sets during the coding process becomes the bottleneck of a fast implementation of the SPIHT. In this paper, we propose a listless modified SPIHT (LMSPIHT) approach, which is a fast and low memory image coding algorithm based on the lifting wavelet transform. The LMSPIHT jointly considers the advantages of progressive transmission, spatial scalability, and incorporates human visual system (HVS) characteristics in the coding scheme; thus it outperforms the traditional SPIHT algorithm at low bit rate coding. Compared with the SPIHT algorithm, LMSPIHT provides a better compression performance and a superior perceptual performance with low coding complexity. The compression efficiency of LMSPIHT comes from three aspects. The lifting scheme lowers the number of arithmetic operations of the wavelet transform. Moreover, a significance reordering of the modified SPIHT ensures that it codes more significant information belonging to the lower frequency bands earlier in the bit stream than that of the SPIHT to better exploit the energy compaction of the wavelet coefficients. HVS characteristics are employed to improve the perceptual quality of the compressed image by placing more coding artifacts in the less visually significant regions of the image. Finally, a listless implementation structure further reduces the amount of memory and improves the speed of compression by more than 51% for a 512×512 image, as compared with that of the SPIHT algorithm.     

An adaptive edge model in the wavelet domain for wavelet image coding

State-of-art wavelet coders owe their performance to smart ideas for exploiting inter and intra-band dependencies of wavelet coefficients. We claim that developing more efficient coders requires us to look at the main source of these dependencies; i.e., highly localized information around edges. This paper investigates the structural relationships among wavelet coefficients based on an idealized view of edge behavior, and proposes a simple edge model that explains the roots of existing dependencies. We describe how the model is used to approximate and estimate the significant wavelet coefficients. Simulations support its relevance for understanding and analyzing edge information. Specifically, model-based estimation within the space-frequency quantization (SFQ) framework increases the peak signal-to-noise ratio (PSNR) by up to 0.3 dB over the original SFQ coding algorithm. Despite being simple, the model provides valuable insights into the problem of edge-based adaptive modeling of value and location information in the wavelet domain.