Modélisation des maillages animés 3D par Reeb Graph et son application à l'indexation et la compression

In the last decade, the technological progress in telecommunication, hardware design and multimedia, allows access to an ever finer three-dimensional (3-D) modeling of the world. While most researchers have focused on the field of 3D objects, now it is necessary to turn to 3D time domain (3D+t). 3D dynamic meshes are becoming a media of increasing importance. This 3D content is subject to various processing operations such as indexation, segmentation or compression. However, surface mesh is an extrinsic shape representation. Therefore, it suffers from important variability under different sampling strategies and canonical shape-non-altering surface transformations, such as affine or isometric transformations. Consequently it needs an intrinsic structural descriptor before being processed by one of the aforementioned processing operations. The research topic of this thesis work is the topological modeling based on Reeb graphs. Specifically, we focus on 3D shapes represented by triangulated surfaces. Our objective is to propose a new approach, of Reeb graph construction, which exploits the temporal information. The main contribution consists in defining a new continuous function based on the heat diffusion properties. The latter is computed from the discrete representation of the shape to obtain a topological structure.The restriction of the heat kernel to temporal domain makes the proposed function intrinsic and stable against transformation. Due to the presence of neighborhood information in the heat kernel, the proposed Reeb Graph construction approach can be extremely useful as local shape descriptor for non-rigid shape retrieval. It can also be introduced into a segmentation-based dynamic compression scheme in order to infer the functional parts of a 3D shape by decomposing it into parts of uniform motion. In this context, we apply the concept of Reeb graph in two widely used applications which are pattern recognition and compression.Reeb graph has been known as an interesting candidate for 3D shape intrinsic structural representation. we propose a 3D non rigid shape recognition approach. The main contribution consists in defining a new scalar function to construct the Reeb graph. This function is computed based on the diffusion distance. For matching purpose, the constructed Reeb graph is segmented into Reeb charts, which are associated with a couple of geometrical signatures. The matching between two Reeb charts is performed based on the distances between their corresponding signatures. As a result, the global similarity is estimated based on the minimum distance between Reeb chart pairs. Skeletonisation and segmentation tasks are closely related. Mesh segmentation can be formulated as graph clustering. First we propose an implicit segmentation method which consists in partitioning mesh sequences, with constant connectivity, based on the Reeb graph construction method. Regions are separated according to the values of the proposed continuous function while adding a refinement step based on curvature and boundary information.Intrinsic mesh surface segmentation has been studied in the field of computer vision, especially for compression and simplification purposes. Therefore we present a segmentation-based compression scheme for animated sequences of meshes with constant connectivity. The proposed method exploits the temporal coherence of the geometry component by using the heat diffusion properties during the segmentation process. The motion of the resulting regions is accurately described by 3D affine transforms. These transforms are computed at the first frame to match the subsequent ones. In order to improve the performance of our coding scheme, the quantization of temporal prediction errors is optimized by using a bit allocation procedure. The objective aimed at is to control the compression rate while minimizing the reconstruction error.Le développement fulgurant de réseaux informatiques, a entraîné l'apparition de diverses applications multimédia qui emploient des données 3D dans des multiples contextes. Si la majorité des travaux de recherche sur ces données s'est appuyées sur les modèles statiques, c'est à présent vers Les modèles dynamiques de maillages qu'il faut se tourner. Cependant, le maillage triangulaire est une représentation extrinsèque, sensible face aux différentes transformations affines et isométriques. Par conséquent, il a besoin d'un descripteur structurel intrinsèque. Pour relever ces défis, nous nous concentrons sur la modélisation topologique intrinsèque basée sur les graphes de Reeb. Notre principale contribution consiste à définir une nouvelle fonction continue basée sur les propriétés de diffusion de la chaleur. Ce dernier est calculé comme la distance de diffusion d'un point de la surface aux points localisés aux extrémités du modèle 3D qui représentent l'extremum locales de l'objet . Cette approche de construction de graph de Reeb peut être extrêmement utile comme descripteur de forme locale pour la reconnaissance de forme 3D. Il peut également être introduit dans un système de compression dynamique basée sur la segmentation.Dans une deuxième partie, nous avons proposé d'exploiter la méthode de construction de graphe de Reeb dans un système de reconnaissance de formes 3D non rigides. L'objectif consiste à segmenter le graphe de Reeb en cartes de Reeb définis comme cartes de topologie contrôlée. Chaque carte de Reeb est projetée vers le domaine planaire canonique. Ce dépliage dans le domaine planaire canonique introduit des distorsions d'aire et d'angle. En se basant sur une estimation de distorsion, l'extraction de vecteur caractéristique est effectuée. Nous calculons pour chaque carte un couple de signatures, qui sera utilisé par la suite pour faire l'appariement entre les cartes de Reeb.Dans une troisième partie, nous avons proposé de concevoir une technique de segmentation, des maillages dynamiques 3D. Le processus de segmentation est effectué en fonction des valeurs de la fonction scalaire proposée dans la première partie. Le principe consiste à dériver une segmentation purement topologique qui vise à partitionner le maillage en des régions rigides tout en estimant le mouvement de chaque région au cours du temps. Pour obtenir une bonne répartition des sommets situés sur les frontières des régions, nous avons proposé d'ajouter une étape de raffinement basée sur l'information de la courbure. Chaque limite de région est associée à une valeur de la fonction qui correspond à un point critique. L'objectif visé est de trouver la valeur optimale de cette fonction qui détermine le profil des limites. La technique de segmentation développée est exploitée dans un système de compression sans perte des maillages dynamiques 3D. Il s'agit de partitionner la première trame de la séquence. Chaque région est modélisée par une transformée affine et leurs poids d'animation associés. Le vecteur partition, associant à chaque sommet l'index de la région auquel il appartient, est compressé par un codeur arithmétique. Les deux ensembles des transformées affines et des poids d'animation sont quantifiés uniformément et compressés par un codeur arithmétique. La première trame de la séquence est compressée en appliquant un codeur de maillage statique. L a quantification de l'erreur de prédiction temporelle est optimisée en minimisant l'erreur de reconstruction. Ce processus est effectué sur les données de l'erreur de prédiction, qui est divisé en 3 sous-bandes correspondant aux erreurs de prédiction des 3 coordonnées x, y et z. Le taux de distorsion introduit est déterminé en calculant le pas de quantification, pour chaque sous-bande, afin d'atteindre le débit binaire cible

Segmentation-based 3D dynamic mesh compression scheme

International audienceThis paper presents a novel compression scheme for 3D dynamic meshes. The proposed method mainly uses a segmentation approach which exploits both of temporal and spatial dependencies. The temporal coherence of the geometry component is determined using the heat diffusion properties. The motion of the resulting regions is accurately described by 3D affine transforms. These transforms are computed at the first frame to match the subsequent ones. The temporal prediction errors are then encoded. Comparative coding test, for 3D dynamic meshes, were conducted to evaluate the coding efficiency of the proposed compression scheme. Simulations demonstrate that the rate/distortion results are competitive when compared to the state of the art

Kinematic Reeb Graph Extraction Based on Heat Diffusion

International audienceThis paper presents a new approach of Reeb graph extraction adapted to 3D dynamic triangular Meshes. Particularly, we propose a new continuous scalar function, used for Reeb graph construction. This function is based on the heat diffusion properties. The restriction of the heat kernel to temporal domain makes the scalar function intrinsic and stable against perturbations. Due to the presence of neighborhood information in the heat kernel associated to each vertex, the proposed Reeb Graph extraction can be extremely useful as local shape descriptor for non-rigid shape retrieval. Experiments show that the proposed structural analysis technique achieves high accuracy and stability under topology changes and various perturbations through time

Phase-shifting digital holographic data compression

International audienceModern holography for 3D imaging allows to reconstruct all the parallaxes that are needed for a truly immersive visualisation. Nevertheless, it possess huge amount of data which induces higher transmission and storage requirements. To gain more popularity and acceptance, digital holography demands development of efficient coding schemes that provide significant data compression at low computation cost. Another issue that needs to be tackled when designing holography coding algorithms is interoperability with commonly used formats. In light of this, the upcoming JPEG Pleno standard aims to develop a standard framework for the representation and exchange of new imaging modalities such as holographic imaging while maintaining backward compatibility with the legacy JPEG decoders. This paper summarize the early work on lossy compression of computer graphic holograms and analyse the efficiency of additional methods that may exhibit good satisfactory coding performance while considering the backward compatibility with legacy JPEG decoders. To validate our findings, the results of our tests are shown and interpreted. Finally, we also outline the emerging trends for future researches

Global three‐dimensional‐mesh indexing based on structural analysis and geometrical signatures

This study presents a new local feature matching approach that relies upon Reeb graph (RG)‐based representation as well as a simple and accurate similarity estimation. The central contribution of this work is to reinforce the topological consistency conditions of the graph‐based description. Formally, the RGs are enriched with geometry signatures based on parameterisation approaches. After RG construction, the shape is segmented into Reeb charts of controlled topology mapped to its canonical planar domain. Then, two stretching signatures, corresponding to the area and angle distortion, are determined and taken as three‐dimensional‐shape descriptor. The similarity estimation is performed in two steps. The first one consists in forming the pairs of similar Reeb charts, according to the minimal distance between their corresponding signatures. The second step is to measure the global similarity which quantifies the similitude degree between all the matched Reeb charts. Retrieval experiments conducted on four publicly available databases have shown that the proposed matching scheme yields satisfactory results. Among observations, it can be noticed that despite its rapidity, the method provides an overall retrieval efficiency gain compared to very recent state‐of‐the‐art methods

Rate-Distortion Optimized Compression Algorithm for 3D Triangular Mesh Sequences

International audienceThis paper presents a new segmentation-based compression scheme for 3D dynamic models. The segmentation process is preformed based on the heat diffusion properties, while exploit- ing temporal and spatial dependencies of the geometry component. 3D affine transforms are used to describe the motion clusters. Weighting of these affine transforms allows to faithfully determine the vertex motions in each cluster. Indeed, both of affine transforms and weighting parameters are determined in order to estimate the positions of vertices in each frame, and consequently compute the temporal prediction errors to be quantized and encoded. In order to improve the coding efficiency, the prediction error quantization is op- timized using a rate control mechanism. Comparative coding tests, for 3D mesh sequences, were conducted to evaluate the coding performance and examine the effectiveness of the proposed coder. The experiments have shown that our codec provides very satisfactory results when compared to the state of the art