Fractal and Wavelet Image Compression Techniques

Excerpt

This book is a tutorial text that examines the techniques behind fractal and wavelet approaches to image compression. The field of image compression has experienced an explosion of interest recently because of the growth of the Internet and other multimedia applications. While standard image and data compression methods exist and are in extensive use today, the demand for ever increasing storage requirements and transmission speed have spurred continued research for improved methods. Fractals and wavelets provide two different avenues for such research. For scientists, engineers, students and researchers interested in learning more about fractal and wavelet image compression, this book provides both an introduction to the subject matter and implementation details sufficient for beginning their own investigations into these exciting new technologies.

Prior knowledge of image compression, fractal geometry or wavelet concepts is not necessary to benefit from this book. The level of mathematical presentation is accessible to advanced undergraduate or beginning graduate students in technical fields. Mathematical concepts that would be helpful to know include the idea of convergence of a sequence, multiple integrals, linear independence and basis vectors. Experienced image processing practitioners will probably be disappointed at the minimal amount of coverage devoted to traditional techniques such as the discrete cosine transform and entropy coding. These topics are covered in depth in other books. For example, entropy coding, which can be applied to the output of any compression algorithm, including fractal and wavelet approaches, is not included in the system applications developed here. The present book focuses on the mathematical aspects of fractal and wavelet image compression.

In addition to learning the theory behind fractal and wavelet image compression, readers of this book will have access to software that will enable them to explore these ideas on their own. The software accompanying this book can be found on the web at http://spiedigitallibrary.org/ebooks/spie/tutorial_texts/tt40/tt40_supplemental as a supplemental file. Details on how to use the software, and how it is constructed, are covered in the book's Appendixes A, B, and C. Three complete Windows-compatible software systems are included with the accompanying software. The IFS System allows readers to create their own fractal images using iterated function systems. The IMG System compresses images using fractal techniques, displays the decoded images, and computes the error between the original and decoded images through image subtraction. The WAV System performs similar functions on images using wavelet techniques and, in addition, displays the wavelet transform of an image. Each system uses a standard Windows interface and includes options for saving and retrieving information from files. The programs run on 32-bit Windows systems, including Windows NT, 95 and 98. Finally, to enable readers to explore beyond the boundaries of the included software, complete C/C++ source code is provided.

The source code for the accompanying software is written in a combination of C and C++. It is not necessary to know either of these languages to benefit from the ideas of this book or to run the programs included with the software. There are a few code examples listed with the text. For the most part, the computational code is written in C. When there is an obvious benefit to exploiting the object-oriented characteristics of C++, then that language is used. In either case, the computational code is kept separate from the user-interface and display code modules that access Windows. Thus, the computational source code, with perhaps minor modifications, should be portable to other platforms, such as UNIX. The user-interface code, where there is an obvious benefit to using object-oriented properties such as inheritance, is written in C++. The source code includes its own C++ application framework for developing simple Windows applications. It does not depend on Microsoft's Foundation Classes (MFC) or other third-party frameworks. The code here was developed using Borland's C++ for Windows, version 4.5. It has also been compiled with Symantec C++ 7.2 and Microsoft Visual C++ 4.0. It should be possible to re-compile the code with any C++ compiler that accesses the Windows Application Programming Interface (API) and supports development of 32-bit Windows applications from source code files.

Stephen T. Welstead

October 1999