Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

Compressed Random-Access Trees for Spatially Coherent Data

International audienceAdaptive multiresolution hierarchies are highly efficient at representing spatially coherent graphics data. We introduce a framework for compressing such adaptive hierarchies using a compact randomly-accessible tree structure. Prior schemes have explored compressed trees, but nearly all involve entropy coding of a sequential traversal, thus preventing fine-grain random queries required by rendering algorithms. Instead, we use fixed-rate encoding for both the tree topology and its data. Key elements include the replacement of pointers by local offsets, a forested mipmap structure, vector quantization of inter-level residuals, and efficient coding of partially defined data. Both the offsets and codebook indices are stored as byte records for easy parsing by either CPU or GPU shaders. We show that continuous mipmapping over an adaptive tree is more efficient using primal subdivision than traditional dual subdivision. Finally, we demonstrate efficient compression of many data types including light maps, alpha mattes, distance fields, and HDR images

Signal processing for high-definition television

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.Includes bibliographical references (p. 60-62).by Peter Monta.Ph.D

A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

Wavelet-Neural Network Based Image Compression System for Colour Images

There are many images used by human being, such as medical, satellite, telescope, painting, and graphic or animation generated by computer images. In order to use these images practically, image compression method has an essential role for transmission and storage purposes. In this research, a wavelet based image compression technique is used. There are various wavelet filters available. The selection of filters has considerable impact on the compression performance. The filter which is suitable for one image may not be the best for another. The image characteristics are expected to be parameters that can be used to select the available wavelet filter. The main objective of this research is to develop an automatic wavelet-based colour image compression system using neural network. The system should select the appropriate wavelet for the image compression based on the image features. In order to reach the main goal, this study observes the cause-effect relation of image features on the wavelet codec (compression-decompression) performance. The images are compressed by applying different families of wavelets. Statistical hypothesis testing by non parametric test is used to establish the cause-effect relation between image features and the wavelet codec performance measurements. The image features used are image gradient, namely image activity measurement (IAM) and spatial frequency (SF) values of each colour component. This research is also carried out to select the most appropriate wavelet for colour image compression, based on certain image features using artificial neural network (ANN) as a tool. The IAM and SF values are used as the input; therefore, the wavelet filters are used as the output or target in the network training. This research has asserted that there are the cause-effect relations between image features and the wavelet codec performance measurements. Furthermore, the study reveals that the parameters in this investigation can be used for the selection of appropriate wavelet filters. An automatic wavelet-based colour image compression system using neural network is developed. The system can give considerably good results

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications