A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

International audienceIn this paper we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modeling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimising CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models

A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

International audienceIn this paper we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modeling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimising CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models

From motion capture to interactive virtual worlds : towards unconstrained motion-capture algorithms for real-time performance-driven character animation

This dissertation takes performance-driven character animation as a representative application and advances motion capture algorithms and animation methods to meet its high demands. Existing approaches have either coarse resolution and restricted capture volume, require expensive and complex multi-camera systems, or use intrusive suits and controllers. For motion capture, set-up time is reduced using fewer cameras, accuracy is increased despite occlusions and general environments, initialization is automated, and free roaming is enabled by egocentric cameras. For animation, increased robustness enables the use of low-cost sensors input, custom control gesture definition is guided to support novice users, and animation expressiveness is increased. The important contributions are: 1) an analytic and differentiable visibility model for pose optimization under strong occlusions, 2) a volumetric contour model for automatic actor initialization in general scenes, 3) a method to annotate and augment image-pose databases automatically, 4) the utilization of unlabeled examples for character control, and 5) the generalization and disambiguation of cyclical gestures for faithful character animation. In summary, the whole process of human motion capture, processing, and application to animation is advanced. These advances on the state of the art have the potential to improve many interactive applications, within and outside virtual reality.Diese Arbeit befasst sich mit Performance-driven Character Animation, insbesondere werden Motion Capture-Algorithmen entwickelt um den hohen Anforderungen dieser Beispielanwendung gerecht zu werden. Existierende Methoden haben entweder eine geringe Genauigkeit und einen eingeschränkten Aufnahmebereich oder benötigen teure Multi-Kamera-Systeme, oder benutzen störende Controller und spezielle Anzüge. Für Motion Capture wird die Setup-Zeit verkürzt, die Genauigkeit für Verdeckungen und generelle Umgebungen erhöht, die Initialisierung automatisiert, und Bewegungseinschränkung verringert. Für Character Animation wird die Robustheit für ungenaue Sensoren erhöht, Hilfe für benutzerdefinierte Gestendefinition geboten, und die Ausdrucksstärke der Animation verbessert. Die wichtigsten Beiträge sind: 1) ein analytisches und differenzierbares Sichtbarkeitsmodell für Rekonstruktionen unter starken Verdeckungen, 2) ein volumetrisches Konturenmodell für automatische Körpermodellinitialisierung in genereller Umgebung, 3) eine Methode zur automatischen Annotation von Posen und Augmentation von Bildern in großen Datenbanken, 4) das Nutzen von Beispielbewegungen für Character Animation, und 5) die Generalisierung und Übertragung von zyklischen Gesten für genaue Charakteranimation. Es wird der gesamte Prozess erweitert, von Motion Capture bis hin zu Charakteranimation. Die Verbesserungen sind für viele interaktive Anwendungen geeignet, innerhalb und außerhalb von virtueller Realität