Multimedia Applications of the Wavelet Transform Inauguraldissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften der Universit ¨ at Mannheim vorgelegt von Dipl.–Math. oec. Claudia Kerstin Schremmer aus Detmold Mannheim, 2001 Dekan: Professor Dr. Herbert Popp, Universit¨at Mannheim Referent: Professor Dr. Wolfgang Effelsberg, Universit¨at Mannheim Korreferent: Professor Dr. Gabriele Steidl, Universit¨at Mannheim Tag der m ¨undlichen Pr¨ufung: 08. Februar 2002 If we knew what we were doing, it would not be called research, would it? — Albert Einstein Abstract This dissertation investigates novel applications of the wavelet transform in the analysis and compres- sion of audio, still images, and video. In a second focal point, we evaluate the didactic potential of multimedia–enhanced teaching material for higher education. Most recently, some theoretical surveys have been published on the potential for a wavelet–based restoration of noisy audio signals. Based on these, we have developed a wavelet–based denoising program for audio signals that allows flexible parameter settings. It is suited for the demonstration of the potential of wavelet–based denoising algorithms as well as for use in teaching. The multiscale property of the wavelet transform can successfully be exploited for the detection of semantic structures in still images. For example, a comparison of the coefficients in the transformed domain allows the analysis and extraction of a predominant structure. This idea forms the basis of our semiautomatic edge detection algorithm that was developed during the present work. A number of empirical evaluations of potential parameter settings for the convolution–based wavelet transform and the resulting recommendations follow. In the context of the teleteaching project Virtuelle Hochschule Oberrhein, i.e., Virtual University of the Upper Rhine Valley (VIROR), which aims to establish a semi–virtual university, many lectures and seminars were transmitted between remote locations. We thus encountered the problem of scalability of a video stream for different access bandwidths in the Internet. A substantial contribution of this dissertation is the introduction of the wavelet transform into hierarchical video coding and the recom- mendation of parameter settings based on empirical surveys. Furthermore, a prototype implementa- tion of a hierarchical client–server video program proves the principal feasibility of a wavelet–based, nearly arbitrarily scalable application. Mathematical transformations of digital signals constitute a commonly underestimated problem for students in their first semesters of study. Motivated by the VIROR project, we spent a considerable amount of time and effort on the exploration of approaches to enhance mathematical topics with multimedia; both the technical design and the didactic integration into the curriculum are discussed. In a large field trial on traditional teaching versus multimedia–enhanced teaching, in which the students were assigned to different learning settings, not only the motivation, but the objective knowledge gained by the students was measured. This allows us to objectively rate positive the efficiency of the teaching modules developed in the scope of this dissertation. II ABSTRACT Kurzfassung Die vorliegende Dissertation untersucht neue Einsatzm¨oglichkeiten der Wavelet–Transformation f¨ur die Analyse und Kompression der multimedialen Anwendungen Audio, Standbild und Video. In einem weiteren Schwerpunkt evaluieren wir das didaktische Potential multimedial angereicherten Lehrmaterials f¨ur die universit¨are Lehre. In j¨ungster Zeit sind einige theoretische Arbeiten ¨uber Wavelet–basierte Restaurationsverfahren von verrauschten Audiosignalen ver¨offentlicht worden. Hierauf aufbauend haben wir ein Wavelet– basiertes Entrauschungsprogramm f¨ur Audiosignale entwickelt. Es erlaubt eine sehr flexible Auswahl von Parametern, und eignet sich daher sowohl zur Demonstration der M¨achtigkeit Wavelet–basierter Entrauschungsans¨atze, als auch zum Einsatz in der Lehre. Die Multiskaleneigenschaft der Wavelet–Transformation kann bei der Standbildanalyse erfolgreich genutzt werden, um semantische Strukturen eines Bildes zu erkennen. So erlaubt ein Vergleich der Koeffizienten im transformierten Raum die Analyse und Extraktion einer vorherrschenden Struk- tur. Diese Idee liegt unserem im Zuge der vorliegenden Arbeit entstandenen halbautomatischen Kantensegmentierungsalgorithmus zugrunde. Eine Reihe empirischer Evaluationen ¨uber m¨ogliche Parametereinstellungen der Faltungs–basierten Wavelet–Transformation mit daraus resultierenden Empfehlungen schließen sich an. Im Zusammenhang mit dem Teleteaching–Projekt Virtuelle Hochschule Oberrhein (VIROR), das den Aufbau einer semi–virtuellen Universit¨at verfolgt, werden viele Vorlesungen und Seminare zwischen entfernten Orten ¨ubertragen. Dabei stießen wir auf das Problem der Skalierbarkeit von Videostr¨omen f¨ur unterschiedliche Zugangsbandbreiten im Internet. Ein wichtiger Beitrag dieser Dissertation ist, die M¨oglichkeiten der Wavelet–Transformation f¨ur die hierarchische Videokodierung aufzuzeigen und durch empirische Studien belegte Parameterempfehlungen auszusprechen. Eine prototypische Im- plementierung einer hierarchischen Client–Server Videoanwendung beweist zudem die prinzipielle Realisierbarkeit einer Wavelet–basierten, fast beliebig skalierbaren Anwendung. Mathematische Transformationen digitaler Signale stellen f¨ur Studierende der Anfangssemester eine h¨aufig untersch¨atzte Schwierigkeit dar. Angeregt durch das VIROR Projekt setzen wir uns in einem weiteren Teil dieser Dissertation mit den M¨oglichkeiten einer multimedialen Aufbereitung mathema- tischer Sachverhalte auseinander; sowohl die technische Gestaltung als auch eine didaktische Integra- tion in den Unterrichtsbetrieb werden er¨ortert. In einem groß angelegten Feldversuch Traditionelle Lehre versus Multimedia–gest ¨ utzte Lehre wurden nicht nur die Motivation, sondern auch der objektive Lernerfolg von Studierenden gemessen, die unterschiedlichen Lernszenarien zugeordnet waren. Dies erlaubt eine objektive positive Bewertung der Effizienz der im Rahmen dieser Dissertation entstande- nen Lehrmodule. IV KURZFASSUNG A few words. . . ofacknowledgment usuallyare placed at this location. And I also wish to express my gratitude to all those who contributed to the formation of this dissertation. The presented work took shape during my employment as a research assistant in the teleteaching project VIROR and at the Department Praktische Informatik IV, where Prof. Dr. Wolfgang Effelsberg accepted me into his research group on multimedia techniques and computer networks. In this team, I encountered a delightful job surrounding where cooperation, commitment, and freedom of thought were lived and breathed. Prof. Effelsberg not only was my intellectual mentor for this work, he also actively used the teaching modules which were developed during my job title in his lectures. The feedback of the students facilitated their steady improvement. By the way, Prof. Effelsberg was my ‘test subject’ for both the digital teaching video and the lecture which was stacked up against it for the evaluation introduced in Part III of this work. I am heartily obliged to him for my initiation into the world of science, for tips and clues which have influenced the theme of this work, and for his unfailing support. Prof. Dr. Gabriele Steidl deserves many thanks for having overtaken the co–advising. I am beholden to my colleagues Stefan Richter, J¨urgen Vogel, Martin Mauve, Nicolai Scheele, J¨org Widmer, Volker Hilt, Dirk Farin, and Christian Liebig, as well as to the ‘alumni’ Werner Geyer and Oliver Schuster for their offers of help in the controversy with my ideas. Be it through precise thematic advice and discussions or through small joint projects which led to common contributions to scientific conferences. Most notably, I want to show my gratitude to Christoph Kuhm¨unch, Gerald K¨uhne, and Thomas Haenselmann, who exchanged many ideas with me in form and content and thus facilitated their final transcription. Christoph Kuhm¨unch and Gert–jan Los sacrificed a share of their week–ends to cross–read my manuscript, to find redundancies and to debug unclear passages. Our system admin- istrator Walter M¨uller managed the almost flawlessly smooth functioning of the computer systems and our more than unusual secretary Betty Haire Weyerer thoroughly and critically read through my publications in the English language, including the present one, and corrected my ‘Genglish’, i.e., German–English expressions. I particularly enjoyed the coaching of ‘Studienarbeiten’, i.e., students’ implementation work, and diploma theses. Among them, I want to name my very first student, Corinna Dietrich, with whom I grew at the task; Holger Wons, Susanne Krabbe, and Christoph Esser signed as contract students at our department after finishing their task — it seems that they had enjoyed it; Sonja Meyer, Timo M¨uller, Andreas Prassas, Julia Schneider, and Tillmann Schulz helped me to explore different aspects of signal processing, even if not all of their work was related to the presented topic. I owe appreciation to my diploma students Florian B¨omers, Uwe Bosecker, Holger F¨ußler, and Alexander Holzinger for their thorough exploration of and work on facets of the wavelet theory which fit well into the overall picture VI A FEW WORDS of the presented work. They all contributed to my dissertation with their questions and encouragement, with their implementations and suggestions. The project VIROR permitted me to get in contact with the department Erziehungswissenschaft II of the University of Mannheim. I appreciated this interdisciplinary cooperation especially on a personal level, and it most probably is this climate on a personal niveau which allowed us to cooperate so well scientifically. Here I want to especially thank Holger Horz, and I wish him all the best for his own dissertation project. In some periods of the formation process of this work, I needed encouraging words more than techni- cal input. Therefore, I want to express my gratitude to my parents, my sister, and my friends for their trust in my abilities and their appeals to my self–assertiveness. My mother, who always reminded me that there is more to life than work, and my father, who exemplified how to question the circumstances and to believe that rules need not always be unchangeable. That the presented work was started, let alone pushed through and completed, is due to Peter Kappelmann, who gives me so much more than a simple life companionship. He makes my life colorful and exciting. This work is dedicated to him. Claudia Schremmer [...]... overview of the development of the wavelet theory precedes the introduction of the (one dimensional) continuous wavelet transform Here, the denition of a wavelet and basic properties are given and sample wavelets illustrate the concepts of these functions After dening the integral wavelet transform, we review the fact that a particular subclass of wavelets that meet our requirements forms a basis for the. .. reviews the fundamentals of the wavelet theory: We discuss the timefrequency resolution of the wavelet transform and compare it to the common shorttime Fourier transform The multiscale property of the dyadic wavelet transform forms the basis for our further research on multimedia applications; it is introduced, explained, and visualized in many different, yet each time enhanced, tableaux An example of the. .. reviews the theory of wavelets and the dyadic wavelet transform and thus provides a mathematical foundation for the following The second part presents our contributions to novel uses of the wavelet transform for the coding of audio, still images, and video The nal part addresses the teaching aspect with regard to students in their rst semesters of study, where we propose new approaches to multimediaenhanced... understanding of the wavelet transform Yet the implementation of the new image coding standard JPEG2000 with its two suggested standard lters is outlined After a brief introduction into the fundamentals of multimedia coding in Chapter 4, Chapter 5 presents the theory of waveletbased audio denoising Furthermore, we present our implementation of a waveletbased audio denoising tool Extending the wavelet transform. .. until the early beginning of the ắẳth century (e.g., Haar wavelet, 1910) Most of the work was done around the ẵ ẳs, though at that time, the separate efforts did not appear to be parts of a coherent theory Daubechies compares the history of wavelets to a tree with many roots growing in distinct directions The trunk of the tree denotes the joint forces of scientists from different branches of study in the. .. example of the Haar transform aims to render intuitive the idea of lowpass and highpass ltering of a signal before we discuss the general theoretical foundation of lter banks in Chapter 2 Practical considerations for the use of wavelets in multimedia are discussed in Chapter 3 We focus on the convolutionbased implementation of the wavelet transform since we consider the discussion of all these parameters... property of the wavelet transform allows us to track a predominant structure of a signal in the various scales We will make use of this observation to develop a waveletbased algorithm for the semiautomatic edge detection in still images Hence, we will show that the wavelet transform allows a semantic interpretation of an image Various evaluations on the setting of the parameters for the wavelet transform. .. This is where the research on a representation of digital data enters that best mirrors human perception Due to its property of preserving both time, respectively, location, and frequency information of a transformed signal, the wavelet transform renders good services Furthermore, the zooming property of the wavelet transform shifts the focus of attention to different scales Wavelet applications encompass... in the development of a wavelet theory The branches are the different directions and applications which incorporate wavelet methods One of the wavelet roots was put down around 1981 by Morlet [MAFG82] [GGM85] At that time, the standard tool for timefrequency analysis was the shorttime Fourier transform However, as the size of the analyzing window is xed, it has the disadvantage of being imprecise about... of less complexity Furthermore, rather than denoting a specic function, the term wavelet denotes a class of functions This has the drawback that a specic function still has to be selected for the transformation process At the same time, it offers the advantage to select a transformationwavelet according to both the signal under consideration and the purpose of the transformation, and thus to achieve . Properties of the Short–time Fourier Transform . . . 15 1.4.3 Properties of the Wavelet Transform . . . 16 X TABLE OF CONTENTS 1.5 SamplingGridoftheWaveletTransform. for their thorough exploration of and work on facets of the wavelet theory which fit well into the overall picture VI A FEW WORDS of the presented work. They