Métamorphose de maillage 3D

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 processusThis 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 processEVRY-INT (912282302) / SudocSudocFranceF

Numerical and variational aspects of mesh parameterization and editing

A surface parameterization is a smooth one-to-one mapping between the surface and a parametric domain. Typically, surfaces with disk topology are mapped onto the plane and genus-zero surfaces onto the sphere. As any attempt to flatten a non-trivial surface onto the plane will inevitably induce a certain amount of distortion, the main concern of research on this topic is to minimize parametric distortion. This thesis aims at presenting a balanced blend of mathematical rigor and engineering intuition to address the challenges raised by the mesh parameterization problem. We study the numerical aspects of mesh parameterization in the light of parallel developments in both mathematics and engineering. Furthermore, we introduce the concept of quasi-harmonic maps for reducing distortion in the fixed boundary case and extend it to both the free boundary and the spherical case. Thinking of parameterization in a more general sense as the construction of one or several scalar fields on a surface, we explore the potential of this construction for mesh deformation and surface matching. We propose an \u27;on-surface parameterization\u27; for guiding the deformation process and performing surface matching. A direct harmonic interpolation in the quaternion domain is also shown to give promising results for deformation transfer.Eine Flächenparameterisierung ist eine globale bijektive Abbildung zwischen der Fläche und einem zugehörigen parametrischen Gebiet. Gewöhnlich werden Flächen mit scheibenförmiger Topologie auf eine Kreisscheibe und Flächen mit Genus Null auf eine Sphäre abgebildet. Das Hauptinteresse der Forschung an diesem Thema ist die Minimierung der parametrischen Verzerrung, die unweigerlich bei jedem Versuch, eine nicht triviale Fläche über einer Ebene zu parameterisieren, erzeugt wird. Diese Arbeit strebt zur Behandlung des Parametrisierungsproblems eine ausgeglichene Mischung zwischen mathematischer Präzision und ingenieurwissenschaftlicher Intuition an. Wir behandeln dabei die numerischen Aspekte des Parameterisierungsproblems im Hinblick auf die aktuellen parallelen Entwicklungen in der Mathematik und den Ingenieurwissenschaften. Weiterhin führen wir das Konzept der quasi-harmonischen Abbildungen ein, um die Verzerrung bei gegebenen Randbedingungen zu verringern. Anschließend verallgemeinern wir dieses Konzept auf den sphärischen Fall und auf den Fall mit freien Randbedingungen. Durch allgemeinere Betrachtung der Parameterisierung als Konstruktion eines oder mehrerer skalarer Felder auf einer Fläche ergibt sich ein neuer Ansatz zur Netzdeformation und der Erzeugung von Flächenkorrespondenzen. Wir stellen eine \u27;on-surface parameterization\u27; vor, welche den Deformationsprozess leitet und Flächenkorrespondenzen erstellt. Darüber hinaus zeigt eine direkte harmonische Interpolation in der Domäne der Quaternionen auch vielversprechende Resultate für die Übertragung von Deformationen

Structural Surface Mapping for Shape Analysis

Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing. This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure

Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing