Implementation of MPEG-4’s Subdivision Surfaces Tools

This work is about the implementation of a MPEG-4 decoder for subdivision surfaces, which are powerful 3D paradigms allowing to compactly represent piecewise smooth surfaces. This ‘study’ will take place in the framework of MPEG-4 AFX, the extension of the MPEG-4 standard including the subdivision surfaces. This document will introduce, with some details, the ‘theory’ of subdivision surfaces in the two forms present in MPEG-4: ‘plain’ and detailed/wavelet subdivision surfaces. It will particularly concentrate on wavelet subdivision surfaces, which permit progressive 3D mesh compression. The first chapter begins with an overview of MPEG-4, more particulary of MPEG-4 Visual. Then, the AFX extension and the role of subdivision surfaces within it are introduced. The second chapter presents the mathematical representation of discrete surfaces and some associated properties, enabling a ‘smoother’ explanation of subdivision surfaces. The third chapter introduces ‘plain’ subdivision surfaces. Some of their properties, such as hierarchical relationships or convergence, are also explored. Ultimately, an example (based on Loop scheme) and the MPEG-4 implementation are discussed. The fourth chapter describes wavelet subdivision surfaces. It also gives a general overview of wavelet theory and its relation with subdivision surfaces. In continuation, a brief summary of different 3D mesh compression methods (both progressive or not) is done. A section then explains, more adequately, wavelet details compression through a hierarchical tree partitioning algorithm. It permits to introduce MPEG-4 wavelet subdivision surfaces implementation, and to propose the addition of a new (and simpler) AFX tool for progressive 3D mesh compression (without view-dependency, and correcting some discrepancies of the current tool concerning progressive transmission). A fifth chapter presents the data structures and the program general structures. It also describes some algorithms used in the actual implementation. The last chapter is a summary of the work done. It also states some of the future work that could be done in this domain, and ends with a short conclusion.