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Person# Laurent Balmelli

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Related publications (14)

Related research domains (4)

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Computer graphics

Computer graphics deals with generating s and art with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing.

Rate–distortion theory

Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per symbol, as measured by the rate R, that should be communicated over a channel, so that the source (input signal) can be approximately reconstructed at the receiver (output signal) without exceeding an expected distortion D. Rate–distortion theory gives an analytical expression for how much compression can be achieved using lossy compression methods.

The thesis studies the optimization of a specific type of computer graphic representation: polygon-based, textured models. More precisely, we focus on meshes having 4-8 connectivity. We study a progressive and adaptive representation for textured 4-8 meshes suitable for transmission. Our results are valid for 4-8 meshes built from matrices of amplitudes, or given as approximations of a subdivision surface. In the latter case, the models can have arbitrary topology. In order to clarify our goals, we first describe a transmission system for computer graphics models (Chapter 1). Then, we review approximation techniques (Chapter 2) and study the computational properties of 4-8 meshes (Chapter 3). We provide an efficient method to store and access our dataset (Chapter 4). We address the problem of 4-8 mesh simplification and give an efficient θ(n log n) algorithm to compute progressive and adaptive representations of 4-8 meshes using global error (Chapter 5). We study the joint optimization of mesh and texture (Chapter 6). Finally, we conclude and give future research directions (Chapter 7).

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Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such as efficient processing, compact storage and numerical robustness. A mesh having subdivision connectivity can be described using a tree structure and recent work exploits this inherent hierarchy in applications such as progressive terrain visualization, surface compression and transmission. We propose a hierarchical, fine to coarse (i.e., using vertex decimation) algorithm to reduce the number of vertices in meshes whose connectivity is based on quadrilateral quadrisection (e.g., subdivision surfaces obtained from Catmull–Clark or 4-8 subdivision rules). Our method is derived from optimal tree pruning algorithms used in modeling of adaptive quantizers for compression. The main advantage of our method is that it allows control of the global error of the approximation, whereas previous methods are based on local error heuristics only. We present a set of operations allowing the use of global error and use them to build an O(nlogn) simplification algorithm transforming an input mesh of n vertices into a multiresolution hierarchy. Note that a single approximation having k

Martin Vetterli, Thomas Liebling, Laurent Balmelli

Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such as efficient processing, compact storage and numerical robustness. A mesh having subdivision connectivity can be described using a tree structure and recent work exploits this inherent hierarchy in applications such as progressive terrain visualization, surface compression and transmission. We propose a hierarchical, fine to coarse (i.e., using vertex decimation) algorithm to reduce the number of vertices in meshes whose connectivity is based on quadrilateral quadrisection (e.g., subdivision surfaces obtained from Catmull–Clark or 4-8 subdivision rules). Our method is derived from optimal tree pruning algorithms used in modeling of adaptive quantizers for compression. The main advantage of our method is that it allows control of the global error of the approximation, whereas previous methods are based on local error heuristics only. We present a set of operations allowing the use of global error and use them to build an O(nlogn) simplification algorithm transforming an input mesh of n vertices into a multiresolution hierarchy. Note that a single approximation having k

2003