. Performances-d-'un-système-de-tatouage-dépendent-d-'un-compromis-entre-la-robustesse, Elles sont généralement mesurées par la robustesse pour une fidélité et une capacité données Cette mesure correspondàcorrespondà un unique point de fonctionnement, et ne rend pas compte de l'ensemble des performances possibles De plus, cette mesure nécessite la sélection d'une métrique de distorsion Dans le cadre du tatouage 3D, cette tâche est complexe, et introduit souvent un biais en faveur d'un système Afin d'´ eviter cesprobì emes, les performances ontétéontété mesurées sur les seules fonctions d'extraction plutôt qu'` a l'´ echelle d'un système complet. Dans le protocole expérimental proposé, plusieurs types d'attaques sont appliqués aux treize maillages d'une base de données. La robustesse facè a l'ajout de bruit, au lissage, au rognage où a la pose est ainsi testée, Les performances d'une fonction d'extraction correspondentàcorrespondentà la stabilité du signal porteur du tatouage après de telles attaques. Cette stabilité est d'abord mesurée localement sur chaque sommet

. En-particulier, A l'inverse, les distance radiales, entre le centre de gravité et les sommets, présentent une très large stabilité, excepté facè a la pose et au rognage Les distances géodésiques, calculées entre tous les sommets du maillage et un sommet de référence, sont modérément stables facè a toutes les attaques testées. Les courbures principales présentent une très forte instabilité face aux attaques valumétriques, mais résistent au rognage. A l'inverse, la norme des coefficients spectraux est robuste aux attaques valumétriques, mais très instable face au rognage où a la simplification

. La-méthode-proposée-débute-par-un-ré-´-echantillonnement-de-la-surface, avant de construire un nuage de points associés au demi-diamètre estimé pour chaqué echantillon. L'´ epaisseur locale est Protection parétalementparétalement La transformée parétalementparétalement constitue un paramètre secret du système de tatouage. La direction de projection, associéè a une suite de classes de l'histogramme des distances radiales, est pseudoaléatoire . Sans la clé secrète, l'attaquant ne peut pas projeter le signal porteur du tatouage et récupérer le message. Cependant, si l'adversaire accumule des observations du signal tatoué, il peut estimer statistiquement la direction de projection par une analyse en composante principale

Q. Le-tatouage and . La-plupart, Pour résisterrésisterà ce type d'attaque, des mécanismes de " resynchronisation implicite " ontétéontété proposés Le maillage est d'abord segmenté demanì ere canonique en fonction de ses points d'intérêt, puis le message estentì erement inséré dans chacun des segments. Il suffit qu'un seul soit préservé par le rognage pour décoder correctement le tatouage. Cette approche présente néanmoins des inconvénients : la segmentation peutêtrepeutêtre elle-même affectée par le rognage, et les points d'intérêts sont difficilesàdifficilesà localiser de façon robuste et précise Stability and computation of medial axes, a state-of-the-art report, Les performances de ces Bibliography [ABE09] Dominique Attali Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, pp.109-125, 2009.

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