Traditional methods of image and video coding rely on linear transformations that focus primarily on high compression. With the increasing demand for digital imagery and video there is now a need for functionality of the compressed information. This dissertation develops a new framework for compression that uses a fractal wavelet method to break the imagery into shape, texture, color, and motion. With this new organization, image information is readily accessible to the user in compressed form. Based on this compression method, we then develop an object-oriented video format. Image analysts tend to break imagery into the categories of shape, texture, color, and motion. Thus, we begin our approach to image compression by finding mathematical methods that preserve shape and texture in an efficient manner. This new non-traditional method begins by using fractals. A fractal is an object which when observed at its smallest level of detail resembles the overall object itself. Some natural examples include ferns, snowflakes, clouds, and mountains. Recently, engineers have applied fixed point theory to describe a method of fractal image compression . Unfortunately fixed point theory only provides a partial description of fractal compression, since it says little about the spatial frequency structure behind the process.

Interest in image compression for internet and other multimedia applications has spurred research into compression techniques that will increase storage capabilities and transmission speed. This tutorial provides a practical guide to fractal and wavelet approaches--two techniques with exciting potential. It is intended for scientists, engineers, researchers, and students. It provides both introductory information and implementation details. Three Windows-compatible software systems are included so that readers can explore the new technologies in depth. Complete C/C++ source code is provided, enabling readers to go beyond the accompanying software. The mathematical presentation is accessible to advanced undergraduate or beginning graduate students in technical fields.

An exciting new development has taken place in the digital era that has captured the imagination and talent of researchers around the globe - wavelet image compression. This technology has deep roots in theories of vision, and promises performance improvements over all other compression methods, such as those based on Fourier transforms, vectors quantizers, fractals, neural nets, and many others. It is this revolutionary new technology that is presented in Wavelet Image and Video Compression, in a form that is accessible to the largest audience possible. Wavelet Image and Video Compression is divided into four parts. Part I, Background Material, introduces the basic mathematical structures that underly image compression algorithms with the intention of providing an easy introduction to the mathematical concepts that are prerequisites for the remainder of the book. It explains such topics as change of bases, scalar and vector quantization, bit allocation and rate-distortion theory, entropy coding, the discrete-cosine transform, wavelet filters and other related topics. Part II, Still Image Coding, presents a spectrum of wavelet still image coding techniques. Part III, Special Topics in Still Image Coding, provides a variety of example coding schemes with a special flavor in either approach or application domain. Part IV, Video Coding, examines wavelet and pyramidal coding techniques for video data. Wavelet Image and Video Compression serves as an excellent reference and may be used as a text for advanced courses covering the subject.

There are several approaches to image compression. The current most popular methods relies on eliminating high frequency components of the signal by storing only the low frequency Fourier coefficients. Other methods use a 'building block' approach, breaking up images into a small number of canonical pieces and storing only a reference to which piece goes where. Our research has focused on a new scheme based on fractals. Our approach to image compression is to tessellate the image with a tiling which varies with the local image complexity, and to check for self similarity amongst the tiles. Self similarities are coded as systems of affine transformations which can be stored far more compactly than the original images on small platforms. An original objective of our Phase II research project was to develop a hardware implementation of our Fractal based algorithm and to investigate various techniques for encoding. During the course of initial investigations it became apparent that the bulk of our efforts should be directed toward speeding up the software algorithms, especially in the decoding and adapting our fractal encoding methods to color images. This is because the most significant commercial applications of image compression require fast decoding.

The explosive growth of multimedia data transmission has generated a critical need for efficient, high-capacity image databases, as well as powerful search engines to retrieve image data from them. This book brings together contributions by an international all-star team of innovators in the field who share their insights into all key aspects of image database and search engine construction. Readers get in-depth discussions of the entire range of crucial image database architecture, indexing and retrieval, transmission, display, and user interface issues. And, using examples from an array of disciplines, the authors present cutting-edge applications in medical imagery, multimedia communications, earth science, remote sensing, and other major application areas.

Abstract: Wavelet-based image and video compression techniques have become popular areas in the research community. In March of 2000, the Joint Pictures Expert Group (JPEG) released JPEG2000. JPEG2000 is a wavelet-based image compression standard and predicted to completely replace the original JPEG standard. In the video compression field, a compression technique called 3D wavelet compression shows promise. Thus, wavelet-based compression techniques have received more attention from the research community. This dissertation involves further investigation of the wavelet transform in the compression of image and video signals, and a rate control method for real-time transfer of wavelet-based compressed video. A pre-processing algorithm based on the wavelet transform is developed for the removal of noise in images prior to compression. The intelligent removal of noise reduces the entropy of the original signal, aiding in compressibility. The proposed wavelet-based denoising method shows a computational speedup of at least an order of magnitude than previously established image denoising methods and a higher peak signal-to-noise ratio (PSNR). A video denoising algorithm is also included which eliminates both intra- and inter-frame noise. The inter-frame noise removal technique estimates the amount of motion in the image sequence. Using motion and noise level estimates, a video denoising technique is established which is robust to various levels of noise corruption and various levels of motion. A virtual-object video compression method is included. Object-based compression methods have come to the forefront of the research community with the adoption of the MPEG-4 (Motion Pictures Expert Group) standard. Object-based compression methods promise higher compression ratios without further cost in reconstructed quality. Results show that virtual-object compression outperforms 3D wavelet compression with an increase in compression ratio and higher PSNR. Finally, a rate-control method is developed for the real-time transmission of wavelet-based compressed video. Wavelet compression schemes demand a rate-control algorithm for real-time video communication systems. Using a leaky-bucket design approach, the proposed rate-control method manages the uncertain factors in both the acquisition time of the group of frames (GoF), computation time of compression/decompression algorithms, and network delay. Results show good management and control of buffers and minimal variance in frame rate.

This book explains the stages necessary to create a wavelet compression system for images and describes state-of-the-art systems used in image compression standards and current research. It starts with a high level discussion of the properties of the wavelet transform, especially the decomposition into multi-resolution subbands. It continues with an exposition of the null-zone, uniform quantization used in most subband coding systems and the optimal allocation of bitrate to the different subbands. Then the image compression systems of the FBI Fingerprint Compression Standard and the JPEG2000 Standard are described in detail. Following that, the set partitioning coders SPECK and SPIHT, and EZW are explained in detail and compared via a fictitious wavelet transform in actions and number of bits coded in a single pass in the top bit plane. The presentation teaches that, besides producing efficient compression, these coding systems, except for the FBI Standard, are capable of writing bit streams that have attributes of rate scalability, resolution scalability, and random access decoding. Many diagrams and tables accompany the text to aid understanding. The book is generous in pointing out references and resources to help the reader who wishes to expand his knowledge, know the origins of the methods, or find resources for running the various algorithms or building his own coding system. Table of Contents: Introduction / Characteristics of the Wavelet Transform / Generic Wavelet-based Coding Systems / The FBI Fingerprint Image Compression Standard / Set Partition Embedded Block (SPECK) Coding / Tree-based Wavelet Transform Coding Systems / Rate Control for Embedded Block Coders / Conclusion