This Ph.D. thesis specifically deals with the issue of metamorphosis of 3D objects represented as 3D triangular meshes. The objective is to elaborate a complete 3D mesh morphing methodology which ensures high quality transition sequences, smooth and gradual, consistent with respect to both geometry and topology, and visually pleasant. Our first contributions concern the two different approaches of parameterization: a new barycentric mapping algorithm based on the preservation of the mesh length ratios, and a spherical parameterization technique, exploiting a Gaussian curvature criterion. The experimental evaluation, carried out on 3D models of various shapes, demonstrated a considerably improvement in terms of mesh distortion for both methods. In order to align the features of the two input models, we have considered a warping technique based on the CTPS C2a radial basis function suitable to deform the models embeddings in the parametric domain maintaining a valid mapping through the entire movement process. We show how this technique has to be adapted in order to warp meshes specified in the parametric domains. A final contribution consists of a novel algorithm for constructing a pseudo-metamesh that avoids the complex process of edge intersections encountered in the state-of-the-art. The obtained mesh structure is characterized by a small number of vertices and it is able to approximate both the source and target shapes. The entire mesh morphing framework has been integrated in an interactive application that allows the user to control and visualize all the stages of the morphing process

Cette thèse de doctorat aborde spécifiquement le problème de la métamorphose entre différents maillages 3D, qui peut assurer un niveau élevé de qualité pour la séquence de transition, qui devrait être aussi lisse et progressive que possible, cohérente par rapport à la géométrie et la topologie, et visuellement agréable. Les différentes étapes impliquées dans le processus de transformation sont développées dans cette thèse. Nos premières contributions concernent deux approches différentes des paramétrisations: un algorithme de mappage barycentrique basé sur la préservation des rapports de longueur et une technique de paramétrisation sphérique, exploitant la courbure Gaussien. L'évaluation expérimentale, effectuées sur des modèles 3D de formes variées, démontré une amélioration considérable en termes de distorsion maillage pour les deux méthodes. Afin d’aligner les caractéristiques des deux modèles d'entrée, nous avons considéré une technique de déformation basée sur la fonction radial CTPS C2a approprié pour déformer le mappage dans le domaine paramétrique et maintenir un mappage valide a travers le processus de mouvement. La dernière contribution consiste d’une une nouvelle méthode qui construit un pseudo metamaillage qui évite l'exécution et le suivi des intersections d’arêtes comme rencontrées dans l'état-of-the-art. En outre, notre méthode permet de réduire de manière drastique le nombre de sommets normalement nécessaires dans une structure supermesh. Le cadre générale de métamorphose a été intégré dans une application prototype de morphing qui permet à l'utilisateur d'opérer de façon interactive avec des modèles 3D et de contrôler chaque étape du processus / This Ph.D. thesis specifically deals with the issue of metamorphosis of 3D objects represented as 3D triangular meshes. The objective is to elaborate a complete 3D mesh morphing methodology which ensures high quality transition sequences, smooth and gradual, consistent with respect to both geometry and topology, and visually pleasant. Our first contributions concern the two different approaches of parameterization: a new barycentric mapping algorithm based on the preservation of the mesh length ratios, and a spherical parameterization technique, exploiting a Gaussian curvature criterion. The experimental evaluation, carried out on 3D models of various shapes, demonstrated a considerably improvement in terms of mesh distortion for both methods. In order to align the features of the two input models, we have considered a warping technique based on the CTPS C2a radial basis function suitable to deform the models embeddings in the parametric domain maintaining a valid mapping through the entire movement process. We show how this technique has to be adapted in order to warp meshes specified in the parametric domains. A final contribution consists of a novel algorithm for constructing a pseudo-metamesh that avoids the complex process of edge intersections encountered in the state-of-the-art. The obtained mesh structure is characterized by a small number of vertices and it is able to approximate both the source and target shapes. The entire mesh morphing framework has been integrated in an interactive application that allows the user to control and visualize all the stages of the morphing process

Numerous prediction models of SARS-CoV-2 pandemic were proposed in the past. Unknown parameters of these models are often estimated based on observational data. However, lag in case-reporting, changing testing policy or incompleteness of data lead to biased estimates. Moreover, parametrization is time-dependent due to changing age-structures, emerging virus variants, non-pharmaceutical interventions, and vaccination programs. To cover these aspects, we propose a principled approach to parametrize a SIR-type epidemiologic model by embedding it as a hidden layer into an input-output non-linear dynamical system (IO-NLDS). Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. This includes data issues such as known delays or biases in reporting. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a specific SIR-type model and data of Germany and Saxony demonstrating good prediction performances. Our approach can estimate and compare the relative effectiveness of non-pharmaceutical interventions and provide scenarios of the future course of the epidemic under specified conditions. It can be translated to other data sets, i.e., other countries and other SIR-type models.