Les bases de fonctions sont des outils indispensables de la géométrie numérique puisqu'ils permettent de représenter des fonctions comme des vecteurs, c'est à dire d'appliquer les outils de l'algèbre linéaire à l'analyse fonctionnelle. Dans cette thèse, nous présentons plusieurs constructions de bases de fonctions sur des surfaces pour la géométrie numérique. Nous commençons par présenter les bases de fonctions usuelles des éléments finis et du calcul extérieur discret, leur théorie et leurs limites. Nous étudions ensuite le Laplacien et sa discrétisation, ce qui nous permettra de construire une base de fonctions particulière~: les fonctions propres de l'opérateur de Laplace-Beltrami, ou harmoniques variétés. Celles-ci permettent de généraliser la transformée de Fourier et le filtrage spectral aux fonctions définies sur des surfaces. Nous présentons ensuite des applications de cette base de fonction à la géométrie numérique. En particulier, nous montrons qu'une fois calculée, cette base de fonction permet de filtrer la géométrie en temps interactif. Pour pouvoir définir des bases de fonctions de façon plus indépendante du maillage de la surface, nous nous intéressons ensuite aux paramétrisations globales, et en particulier aux champs de directions à symétries qui permettent de les définir. Ainsi, dans la dernière partie, nous étudions ces champs de directions à symétries, et en particulier leur géométrie et leur topologie. Nous donnons alors des outils pour les construire, les manipuler et les visualiser / Function bases are fundamental objects in geometry processing as they allow to represent functions as vectors, that is to apply tools from linear algebra to functional analysis. In this thesis, we present various constructions of useful functions bases for geometry processing. We start by presenting usual function bases, their theory and limits. We then study the Laplacian operator and its discretization, and use it to define a particular function basis: Laplacian eigenfunctions or Manifold harmonics. The Manifold Hamonics form a function basis that allows to generalize the Fourier transform and spectral filtering on a surface. We present some applications and extensions of this basis for geometry processing. To define function bases in a mesh-independant manner, we need to build a global parameterization, and especially the direction fields required to define them. Thus, in the last part of this thesis we study N-symmetry direction fields on surfaces, and in particular their geometry and topology. We then give tools to build, edit, control and visualize them

<p>Verification of users’ identities are normally carried out via PIN-codes or ID- cards. Biometric identification, identification of unique body features, offers an alternative solution to these methods. </p><p>Fingerprint scanning is the most common biometric identification method used today. It uses a simple and quick method of identification and has therefore been favored instead of other biometric identification methods such as retina scan or signature verification. </p><p>In this report biometric security systems have been evaluated based on fingerprint scanners. The evaluation method focuses on copies of real fingers, artificial fingers, as intrusion method but it also mentions currently used algorithms for identification and strengths and weaknesses in hardware solutions used. </p><p>The artificial fingers used in the evaluation were made of gelatin, as it resembles the surface of human skin in ways of moisture, electric resistance and texture. Artificial fingers were based on ten subjects whose real fingers and artificial counterpart were tested on three different fingerprint scanners. All scanners tested accepted artificial fingers as substitutes for real fingers. Results varied between users and scanners but the artificial fingers were accepted between about one forth and half of the times. </p><p>Techniques used in image enhancement, minutiae analysis and pattern matching are analyzed. Normalization, binarization, quality markup and low pass filtering are described within image enhancement. In minutiae analysis connectivity numbers, point identification and skeletonization (thinning algorithms) are analyzed. Within pattern matching, direction field analysis and principal component analysis are described. Finally combinations of both minutiae analysis and pattern matching, hybrid models, are mentioned. </p><p>Based on experiments made and analysis of used techniques a recommendation for future use and development of fingerprint scanners is made.</p>

Verification of users’ identities are normally carried out via PIN-codes or ID- cards. Biometric identification, identification of unique body features, offers an alternative solution to these methods. Fingerprint scanning is the most common biometric identification method used today. It uses a simple and quick method of identification and has therefore been favored instead of other biometric identification methods such as retina scan or signature verification. In this report biometric security systems have been evaluated based on fingerprint scanners. The evaluation method focuses on copies of real fingers, artificial fingers, as intrusion method but it also mentions currently used algorithms for identification and strengths and weaknesses in hardware solutions used. The artificial fingers used in the evaluation were made of gelatin, as it resembles the surface of human skin in ways of moisture, electric resistance and texture. Artificial fingers were based on ten subjects whose real fingers and artificial counterpart were tested on three different fingerprint scanners. All scanners tested accepted artificial fingers as substitutes for real fingers. Results varied between users and scanners but the artificial fingers were accepted between about one forth and half of the times. Techniques used in image enhancement, minutiae analysis and pattern matching are analyzed. Normalization, binarization, quality markup and low pass filtering are described within image enhancement. In minutiae analysis connectivity numbers, point identification and skeletonization (thinning algorithms) are analyzed. Within pattern matching, direction field analysis and principal component analysis are described. Finally combinations of both minutiae analysis and pattern matching, hybrid models, are mentioned. Based on experiments made and analysis of used techniques a recommendation for future use and development of fingerprint scanners is made.