The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream In addition to producing a fully embedded bit stream, the EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source The EZW algorithm is based on four key concepts: (1) a discrete wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, (3) entropy-coded successive-approximation quantization, and (4) universal lossless data compression which is achieved via adaptive arithmetic coding >

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Sig%20Pro41,%203445.pdf

Embedded image coding using zerotrees of wavelet coefficients

Quantization is a process that maps a continous or discrete set of values into approximations that belong to a smaller set. Quantization is a lossy: some information about the original data is lost in the process. The key to a successful quantization is therefore the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.

Quantization

An approach to image coding based on a fractal theory of iterated contractive transformations defined piecewise is described. The main characteristics of this approach are that it relies on the assumption that image redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis, and it approximates an original image by a fractal image, obtained from a finite number of iterations of an image transformation called a fractal code. This approach is referred to as fractal block coding. The general coding-decoding system is based on the construction, for an image to be encoded, of a fractal code-a contractive image transformation for which the original image is an approximate fixed point-which, when applied iteratively on any initial image of the decoder, produces a sequence of images which converges to a fractal approximation of the original. The design of a system for the encoding of monochrome digital images at rates below 1 b/pixel is described. Ideas and extensions from the work of other researchers are presented. >

Fractal image coding: a review

The generalized Lloyd algorithm plays an important role in the design of vector quantizers (VQ) and in feature clustering for pattern recognition. In the VQ context, this algorithm provides a procedure to iteratively improve a codebook and results in a local minimum that minimizes the average distortion function. We propose an efficient method to obtain a good initial codebook that can accelerate the convergence of the generalized Lloyd algorithm and achieve a better local minimum as well. >

/pdf/a-new-initialization-technique-for-generalized-lloyd-2frje5uqm2.pdf

A new initialization technique for generalized Lloyd iteration

The quadtree data structure is commonly used in image coding to decompose an image into separate spatial regions to adaptively identify the type of quantizer used in various regions of an image. The authors describe the theory needed to construct quadtree data structures that optimally allocate rate, given a set of quantizers. A Lagrange multiplier method finds these optimal rate allocations with no monotonicity restrictions. They use the theory to derive a new quadtree construction method that uses a stepwise search to find the overall optimal quadtree structure. The search can be driven with either actual measured quantizer performance or ensemble average predicted performance. They apply this theory to the design of a motion compensated interframe video coding system using a quadtree with vector quantization. >

Efficient quadtree coding of images and video

High-quality variable-rate image compression is achieved by segmenting an image into regions of different sizes, classifying each region into one of several perceptually distinct categories, and using a distinct coding procedure for each category Segmentation is performed with a quadtree data structure by isolating the perceptually more important areas of the image into small regions and separately identifying larger random texture blocks Since the important regions have been isolated, the remaining parts of the image can be coded at a lower rate than would be otherwise possible High-quality coding results are achieved at rates between 035 and 07 b/p depending on the nature of the original image, and satisfactory results have been obtained at 025 b/p >

Image compression with variable block size segmentation

The authors present a unified formulation and study of vector quantizer design methods that couple stochastic relaxation (SR) techniques with the generalized Lloyd algorithm. Two new SR techniques are investigated and compared: simulated annealing (SA) and a reduced-complexity approach that modifies the traditional acceptance criterion for simulated annealing to an unconditional acceptance of perturbations. It is shown that four existing techniques all fit into a general methodology for vector quantizer design aimed at finding a globally optimal solution. Comparisons of the algorithms' performances when quantizing Gauss-Markov processes, speech, and image sources are given. The SA method is guaranteed to perform in a globally optimal manner, and the SR technique gives empirical results equivalent to those of SA. Both techniques result in significantly better performance than that obtained with the generalized Lloyd algorithm. >

Globally optimal vector quantizer design by stochastic relaxation

A central issue in the use of vector quantization (VQ) for speech or image compression is the specification of the codebook. The traditional method for VQ codebook design is to use the Generalized Lloyd Algorithm (GLA), an iterative optimization procedure where an initial codebook is continually refined so that each iteration reduces the distortion involved in coding a given training set. However, this algorithm easily gets trapped in local minima of the distortion, resulting in a suboptimal codebook. Simulated Annealing (SA) is a procedure that employs randomness in a search algorithm and tends to skirt relatively poor local minima in favor of better ones. By altering the GLA with techniques motivated by SA we are able to improve the quality of the codebwks by reducing the distortion involved in coding the training set. Results are presented in the context of image coding using VQ.

http://ieeexplore.ieee.org/iel2/723/5035/00196808.pdf

M9.6 simulated annealing and codebook design

This paper presents a unified formulation and study of vector quantizer design methods that couple stochastic re- laxation (SR) techniques with the generalized Lloyd algorithm. Two new SR techniques are investigated and compared: simu- lated annealing (SA), and a reduced-complexity approach that modifies the traditional acceptance criterion for simulated an- nealing to an unconditional acceptance of perturbations. It is shown that four existing techniques all fit into a general meth- odology for vector quantizer design aimed at finding a globally optimal solution. Comparisons of each algorithms' perfor- mance when quantizing Gauss-Markov processes, speech, and image sources are given. The SA method is guaranteed to per- form in a globally optimal manner, and the SR technique gives empirical results equivalent to those of SA. Both techniques re- sult in significantly better performance than that obtained with the generalized Lloyd algorithm.

http://ieeexplore.ieee.org/iel4/78/3524/00124941.pdf

Jacques Vaisey

Papers

Image compression with variable block size segmentation

Globally optimal vector quantizer design by stochastic relaxation

M9.6 simulated annealing and codebook design

Globally Optimal Vector Quantizer Design by