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This page is a WWW version of a multimedia application for teaching wavelets theory and its applications in image processing.

It is intended for engineers and students with a basic background in signal processing and mathematics. The issue was to teach abstract concepts poorly illustrated on paper. This courseware takes advantage of animation, graphics, written and spoken (only CDROM version) text and interactive simulations [1,2].

Additionally, we include papers in PostScript version that describe related topics and links to other wavelet and image processing pages.

Before you start learning have a look a the contents of the course.

Keywords : multimedia, education, image processing.

This page is optimized for Netscape 4.0 or Microsoft Explorer 4.0. Recommended resolution: 1024*768. Displays best with 24 bit color on Windows platform. To see animations you need a WWW browser and Macromedia Shockwave plug-in.

Wavelets theory is based on advanced, abstract and rather complex mathematical concepts. Paper books can at best explain it with written text and static illustrations [3]. In contrast, multimedia allows enhanced communication and explanation such as spoken comments played while displaying a figure, or interactive illustrations. Therefore, our purpose was not to develop an electronic copy of a paper book. We aimed at taking full pedagogical advantage of multimedia capabilities to make learning easier and more attractive. The purpose of our work was to present in a pedagogical way a few chosen subjects from image processing domain. We focused on two related domains: Fourier and wavelet transforms of two-dimensional signal and their applications.

      We start the course with the properties of two-dimensional Fourier transform. Then, we introduce wavelet transform  as a tool that is usually more powerful in some applications than well-known and often used Fourier transform. We define the basic notations, present different types of wavelets and explain how we can create a wavelet. We present the wavelet transform and its application - the Fast Wavelet Transform (FWT). The next section is related to the decomposition  and the reconstruction  that show the basic and inverse wavelet transform operating in two-dimensional space (images). The next part deals with multiresolution analysis  (MRA) as a very big advantage of wavelets. It let us look at the signals from different resolution ranges. The last part is devoted to wavelet compression and presents different compression methods.

Each article (lesson) of the course consists of several subsections (plans) explaining related subjects. Each part (article) starts with an example of an addressed problem, the resolution of which is presented as a challenge. The mathematical theory is then introduced and illustrated with processed images. Finally, interactive simulations allow students to test their knowledge.

We tried to eliminate unnecessary words that could lead to confusions by using only short sentences elaborated to convey as much information as possible. Throughout the course, previously introduced salient information is recalled, and complex points are explained several times in various ways. A great attention was paid to avoid any gap between successive parts. Written explanations are completed by a voice (only CDROM version) that gives additional information. This allows to communicate with students having different preferred sense perception: images and written texts for those with easier visual perception, and spoken explanation for those preferring to listen. Teaching efficiency is achieved by the following strategies [4, 5, 6]:

• Interest stimulation: To capture students' attention, we try to face them with a challenge right at the beginning of each part of the course, and we give them some hints towards the solution.
• Multilevel reading: Detailed explanations can be obtained by clicking on a question mark icon. This allows users to focus on issues in which they have a particular interest.
• Living presentations: Complex equations and formulas are explained with animated illustrations built on simple examples. Mathematical algorithms with repeated operations can be easily explained by displaying the computation in progress along with spoken explanations.
• Interactivity: Students can change parameters in formulas and observe how the results are altered. A user friendly point-and-click graphical interface lets users control the parameters of interactive simulations.

Development tools

This courseware was created with Macromedia Director 5.0 [7]. Because it does not provide an efficient support for image processing, all the animated illustrations have been pre-computed for a limited number of parameter combinations. Khoros [8] and Matlab [9] have been used for this purpose. The CDROM version requires Windows 95 / NT on a Pentium PC or OS-MAC on a PowerPC, SVGA, a sound card, and 70 Mb available on disk.

Network version needs WWW browser with the Macromedia Shockwave plug-in.

This courseware is being extended with simulations written in Java. Java applets can be run on many different platforms, either locally or over a network link. Most importantly, Java programs allow some data processing in real time, which removes the limitation on the number of combinations of parameters in simulations. The software could be distributed as a part of a course on picture processing on CDROM or be made accessible via Internet using a standard WWW browser with the Macromedia Shockwave plug-in.

This courseware has been developed in the framework of ERNEST project [10] of the Groupe des Ecoles des Télécommunications.

 

Copyright 1999 Wojciech Maziarz. All rights reserved. Please do not replicate this page without prior consent. All logos, names, and trademarks are properties of their respective companies.

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1. Krystian MIKOLAJCZYK, Wojciech MAZIARZ, Patrick HORAIN, A multimedia course on wavelets, Actes Forum, Colloque International sur les Nouvelles Technologies de l'Information et de la Communication dans les Formations d'Ingénieurs et dans l'Industrie (NTICF'98), Rouen, France, 18-20 November 1998, AVI files.
2. Krystian MIKOLAJCZYK, Wojciech MAZIARZ, A multimedia courseware on wavelets, ECMCS'99, EURASIP Conference, DSP for Multimedia Communications and Services, Krakow, 24-26 June 1999.
3. Alain FOURNIER, Wavelets and their Applications in Computer Graphics, SIGGRAPH'94 Course Notes, 1994.
4. Alain GÉRARD, Réseaux et multimédia dans l'éducation, Rapport d'étude remis au 1er Ministre, 97.
5. Les ressources multimédias en éducation, Rencontres de l'Orme, Marseille, 1995.
6. K. BEATTIE (ed.), Interactive multimedia in university education designing for change in teaching and learning, IFIP TC3/WG3.2 Working Conference, Melbourne, 1994.
7. Macromedia, on the WWW at: http://www.macromedia.com.
8. Khoral Reasearch Inc., Creators of Khoros Technology, on the WWW at: http://www.khoral.com.
9. The MathWorks Inc., Developers of Matlab & Simulink, on the WWW at: http://www.mathworks.com.
10. ERNEST, Expérimentation du Réseau National de l'Enseignement Supérieur des Télécommunications, on the WWW at: http://www.int-evry.fr/ernest.