1. Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision¶

1.1 Other Textbooks by the Author¶

The author also has the following (open-access) textbooks:

This textbook provides a comprehensive introduction to multiresolution signal and geometry processing. It covers a very broad range of topics, including:

• one-dimensional multirate signal processing
• one-dimensional multirate filter banks (and transmultiplexers)
• univariate wavelet systems (2-scale and M-scale cases, orthonormal and biorthogonal cases)
• multidimensional multirate signal processing
• multidimensional multirate filter banks
• multivariate wavelet systems
• subdivision surfaces and subdivision wavelets
• JPEG 2000
• Computational Geometry Algorithms Library (CGAL)
• Open Graphics Library (OpenGL) and OpenGL Utility Toolkit (GLUT)
• functional analysis
• geometry processing

For additional information about the contents of the textbook, refer to the Textbook Abstract section.

1.4 Textbook Abstract¶

The abstract for the textbook is as follows:

This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.

1.5 Textbook and Lecture Slides License¶

The textbook and lecture slides are each licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. This license allows for a work to be distributed freely, subject to certain quite reasonable conditions (e.g., no commercial use). Refer to the above link for more details on the license.

1.6 Obtaining the Textbook and Lecture Slides (E-Book and Print)¶

Each of the textbook and lecture slide documents is identifed by a version number (such as "2013-09-26"). The version number appears on most pages of the document, allowing different versions to be easily distinguished.

All versions of the textbook and lectures slides that are currently available are listed below. All versions of these documents are available in electronic form (i.e., PDF format) for download from this web page. (See below.) Some versions of these documents are also available in print form via online order from the University of Victoria Bookstore.

It is strongly recommended that the most recent version of the textbook be employed whenever possible, as it will typically contain new and improved material as well as corrections that older versions lack.

The available versions of the textbook are as follows:

• M. D. Adams, Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision (Version 2013-09-26), University of Victoria, Victoria, BC, Canada, Sept. 2013, xxxviii + 538 pages. ISBN 978-1-55058-508-7 (PDF). ISBN 978-1-55058-507-0 (paperback).

The available versions of the lecture slides are as follows:

• M. D. Adams, Lecture Slides for Multiresolution Signal and Geometry Processing (Version 2015-02-03), University of Victoria, Victoria, BC, Canada, Feb. 2015, xi+587 pages. ISBN 978-1-55058-536-0 (PDF). ISBN 978-1-55058-535-3 (paperback).
• Version 2013-09-26
• M. D. Adams, Lecture Slides for Multiresolution Signal and Geometry Processing (Version 2013-09-26), University of Victoria, Victoria, BC, Canada, Sept. 2013, 570 pages. ISBN 978-1-55058-522-3 (PDF). ISBN 978-1-55058-521-6 (paperback).

1.7 Software¶

The Signal Processing Library (SPL) mentioned in one of the appendices of the textbook is available for download from the SPL web site.

1.8 Information for Instructors¶

A solutions manual and lecture slides have also been developed for the textbook. The solutions manual is only available to instructors, and requires proof of faculty status. If you are an instructor who is interested in using the textbook to teach one of your courses, please contact the author for more information regarding the solutions manual. An electronic copy of the lecture slides can be downloaded from the Obtaining the Textbook and Lecture Slides section of this web page.

1.9 Solutions Manual¶

The solutions manual presents complete solutions for the problem sets appearing in the textbook. Each problem from the textbook is given along with a detailed solution.

Proof of faculty status is required in order to obtain the solutions manual. All versions of the solutions manual in e-book form can be requested directly from the author. The versions of the solutions manual published by the University of Victoria can be ordered in paperback from the University of Victoria Bookstore.

The versions available are as follows: