Mathematical models of classes of objects can significantly contribute to the analysis of digital images. A major problem in modelling is to establish suitable descriptions that cover not only a single object but also the variation that is usually present within a class of objects. The objective of this thesis is to develop more general modelling strategies than commonly used today. In particular, the impact of the human factor in the model creation process should be minimised. It is presumed that the human ability of abstraction imposes undesired constraints on the description. In comparison, common approaches are discussed from the viewpoint of generality. The technique considered introduces appearance space as a common framework to represent both shapes and images. In appearance space, an object is represented by a single point in a high-dimensional vector space. Accordingly, objects subject to variation appear as nonlinear manifolds in appearance space. These manifolds are often characterised by only a few intrinsic dimensions. A model of a class of objects is therefore considered equal to the mathematical description of this manifold. The presence of nonlinearity motivates the use of artificial auto-associative neural networks in the modelling process. The network extracts nonlinear modes of variation from a number of training examples. The procedure is evaluated on both synthetic and natural data of shapes and images and shows promising results as a general approach to object modelling.

New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions. For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.

In this thesis, we study the shape analysis problem and propose new methods for shape description, similarity and recognition. Firstly, we introduce a new shape descriptor in a two-step method. In the first step, the 2-D shape information is mapped into a set of 1-D functions. The mapping is based on the beams, which are originated from a boundary point, connecting that point with the rest of the points on the boundary. At each point, the angle between a pair of beams is taken as a random variable to define the statistics of the topological structure of the boundary. The third order statistics of all the beam angles is used to construct 1-D Beam Angle Statistics (BAS) functions. In the second step, we apply a set of feature extraction methods on BAS functions in order to describe it in a more compact form. BAS functions eliminate the context-dependency of the representation to the data set. BAS function is invariant to translation, rotation and scale. It is insensitive to distortions. No predefined resolution or threshold is required to define the BAS functions. Secondly, we adopt three different similarity distance methods defined on the BAS feature space, namely, Optimal Correspondence of String Subsequences, Dynamic Warping and Cyclic Sequence Matching algorithms. Main goal in these algorithms is to minimize the distance between two BAS features by allowing deformations. Thirdly, we propose a new Hidden Markov Model (HMM)topology for boundary based shape recognition. The proposed topology called Circular HMM is both ergodic and temporal. Therefore, the states can be revisited in finite time intervals while keeping the sequential information in the string, which represents the shape. It is insensitive to size changes. Since it has no starting and terminating state, it is insensitive to the starting point of the shape boundary. Experiments are done on the dataset of MPEG 7 Core Experiments Shape-1. It is observed that BAS descriptor outperforms all the methods in the literature. The Circular HMM gives higher recognition rates than the classical topologies in shape analysis applications.

Les récentes avancées en matière de systèmes d'acquisition et de modélisation ont permis la mise à disposition d'une très grande quantité de données numériques (e.g. images, vidéos, modèles 3D) dans différents domaines d'application. En particulier, la création d'Environnements Virtuels (EVs) nécessite l'exploitation de données nu-mériques pour permettre des simulations et des effets proches de la réalité. Malgré ces avancées, la conception d'EVs dédiés à certaines applications requiert encore de nombreuses et parfois laborieuses étapes de modélisation et de traitement qui impliquent plusieurs experts (e.g. experts du domaine de l'application, experts en modélisation 3D et programmeur d'environnements virtuels, designers et experts communication/marketing). En fonction de l'application visée, le nombre et le profil des experts impliqués peuvent varier. Les limitations et difficultés d'au-jourd'hui sont principalement dues au fait qu'il n'existe aucune relation forte entre les experts du domaine qui ont des besoins, les experts du numérique ainsi que les outils et les modèles qui prennent part au processus de déve-loppement de l'EV. En fait, les outils existants focalisent sur des définitions souvent très détaillées des formes et ne sont pas capables de supporter les processus de créativité et d'innovation pourtant garants du succès d'un pro-duit ou d'une application. De plus, la grande quantité de données numériques aujourd'hui accessible n'est pas réellement exploitée. Clairement, les idées innovantes viennent souvent de la combinaison d'éléments et les don-nées numériques disponibles pourraient être mieux utilisées. Aussi, l'existence de nouveaux outils permettant la réutilisation et la combinaison de ces données serait d'une grande aide lors de la phase de conception conceptuelle de formes et d'EVs. Pour répondre à ces besoins, cette thèse propose une nouvelle approche et un nouvel outil pour la conception conceptuelle d'EVs exploitant au maximum des ressources existantes, en les intégrant et en les combinant tout en conservant leurs propriétés sémantiques. C'est ainsi que le Modèle de Description Générique de Formes (MDGF) est introduit. Ce modèle permet la combinaison de données multimodales (e.g. images et maillages 3D) selon trois niveaux : Conceptuel, Intermédiaire et Données. Le niveau Conceptuel exprime quelles sont les différentes parties de la forme ainsi que la façon dont elles sont combinées. Chaque partie est définie par un Elément qui peut être soit un Composant soit un Groupe de Composants lorsque ceux-ci possèdent des carac-téristiques communes (e.g. comportement, sens). Les Eléments sont liés par des Relations définies au niveau Con-ceptuel là où les experts du domaine interagissent. Chaque Composant est ensuite décrit au niveau Données par sa Géométrie, sa Structure et ses informations Sémantiques potentiellement attachées. Dans l'approche proposée, un Composant est une partie d'image ou une partie d'un maillage triangulaire 3D. Quatre Relations sont proposées (fusion, assemblage, shaping et localisation) et décomposées en un ensemble de Contraintes qui contrôlent la po-sition relative, l'orientation et le facteur d'échelle des Composants au sein de la scène graphique. Les Contraintes sont stockées au niveau Intermédiaire et agissent sur des Entités Clés (e.g. points, des lignes) attachées à la Géo-métrie ou à la Structure des Composants. Toutes ces contraintes sont résolues en minimisant une fonction énergie basée sur des grandeurs physiques. Les concepts du MDGF ont été implémentés et intégrés au sein d'un outil de design conceptuel développé par l'auteur. Différents exemples illustrent le potentiel de l'approche appliquée à différents domaines d'application. / Due to the great advances in acquisition devices and modeling tools, a huge amount of digital data (e.g. images, videos, 3D models) is becoming now available in various application domains. In particular, virtual envi-ronments make use of those digital data allowing more attractive and more effectual communication and simula-tion of real or not (yet) existing environments and objects. Despite those innovations, the design of application-oriented virtual environment still results from a long and tedious iterative modeling and modification process that involves several actors (e.g. experts of the domain, 3D modelers and VR programmers, designers or communica-tions/marketing experts). Depending of the targeted application, the number and the profiles of the involved actors may change. Today's limitations and difficulties are mainly due to the fact there exists no strong relationships between the expert of the domain with creative ideas, the digitally skilled actors, the tools and the shape models taking part to the virtual environment development process. Actually, existing tools mainly focus on the detailed geometric definition of the shapes and are not suitable to effectively support creativity and innovation, which are considered as key elements for successful products and applications. In addition, the huge amount of available digital data is not fully exploited. Clearly, those data could be used as a source of inspiration for new solutions, being innovative ideas frequently coming from the (unforeseen) combination of existing elements. Therefore, the availability of software tools allowing the re-use and combination of such digital data would be an effective support for the conceptual design phase of both single shapes and VR environments. To answer those needs, this thesis proposes a new approach and system for the conceptual design of VRs and associated digital assets by taking existing shape resources, integrating and combining them together while keeping their semantic meanings. To support this, a Generic Shape Description Model (GSDM) is introduced. This model allows the combination of multimodal data (e.g. images and 3D meshes) according to three levels: conceptual, intermediate and data levels. The conceptual level expresses what the different parts of a shape are, and how they are combined together. Each part of a shape is defined by an Element that can either be a Component or a Group of Components when they share common characteristics (e.g. behavior, meaning). Elements are linked with Relations defined at the Concep-tual level where the experts in the domain are acting and exchanging. Each Component is then further described at the data level with its associated Geometry, Structure and potentially attached Semantics. In the proposed ap-proach, a Component is a part of an image or a part of a 3D mesh. Four types of Relation are proposed (merging, assembly, shaping and location) and decomposed in a set of Constraints which control the relative position, orien-tation and scaling of the Components within the 3D viewer. Constraints are stored at the intermediate level and are acting on Key Entities (such as points, a lines, etc.) laying on the Geometry or Structure of the Components. All these constraints are finally solved while minimizing an additional physically-based energy function. At the end, most of the concepts of GSDM have been implemented and integrated into a user-oriented conceptual design tool totally developed by the author. Different examples have been created using this tool demonstrating the potential of the approach proposed in this document.

<p>Detailed characterization of size and shape of polymers, and development of methods to elucidate the mechanisms behind shape transitions are central issues in this thesis. In particular we characterize grafted polymer chains under confinement in terms of the chain entanglement complexity and mean molecular size. Confinement of polymers into small regions can drastically affect the structural and mechanical properties, and make these systems convenient for a large number of applications, including the design of lubricants, coatings, and various biotechnical applications.</p><p>Using Monte Carlo simulations with a model including both persistence length and intramolecular non-bonded interaction, we find two regimes of polymer behaviour: <i>i) soft mushrooms</i>, where confinement successively flattens the chains with accompanying change in the folding complexity, and <i>ii) hard mushrooms </i>where the compact structures appear to resist confinement and the only way to reorganize the entanglements is by flattening under strong confinement. We also show that a simultaneous use of mean molecular size and chain entanglement complexity renders the possibility to create configurational "phase" diagrams for a wide range of polymers. We have further introduced a new descriptor of folding complexity, <i>the path-space ratio</i>, ζ_α which captures essential features of molecular shape beyond those conveyed by mean size and asphericity.</p><p>This thesis also contains results of light scattering measurements on supramolecular complexes formed when mixing an adamantane end-capped star polymer with a β-cyclodextrin polymer. The specific interactions result in an interplay between the association of the end-caps and a strong inclusion interaction between adamantane and β-cyclodextrin.</p>

Detailed characterization of size and shape of polymers, and development of methods to elucidate the mechanisms behind shape transitions are central issues in this thesis. In particular we characterize grafted polymer chains under confinement in terms of the chain entanglement complexity and mean molecular size. Confinement of polymers into small regions can drastically affect the structural and mechanical properties, and make these systems convenient for a large number of applications, including the design of lubricants, coatings, and various biotechnical applications. Using Monte Carlo simulations with a model including both persistence length and intramolecular non-bonded interaction, we find two regimes of polymer behaviour: i) soft mushrooms, where confinement successively flattens the chains with accompanying change in the folding complexity, and ii) hard mushrooms where the compact structures appear to resist confinement and the only way to reorganize the entanglements is by flattening under strong confinement. We also show that a simultaneous use of mean molecular size and chain entanglement complexity renders the possibility to create configurational "phase" diagrams for a wide range of polymers. We have further introduced a new descriptor of folding complexity, the path-space ratio, ζα which captures essential features of molecular shape beyond those conveyed by mean size and asphericity. This thesis also contains results of light scattering measurements on supramolecular complexes formed when mixing an adamantane end-capped star polymer with a β-cyclodextrin polymer. The specific interactions result in an interplay between the association of the end-caps and a strong inclusion interaction between adamantane and β-cyclodextrin.

La pathologie numérique s’est développée ces dernières années grâce à l’avancée récente des algorithmes d’analyse d’images et de la puissance de calcul. Notamment, elle se base de plus en plus sur les images histologiques. Ce format de données a la particularité de révéler les objets biologiques recherchés par les experts en utilisant des marqueurs spécifiques tout en conservant la plus intacte possible l’architecture du tissu. De nombreuses méthodes d’aide au diagnostic à partir de ces images se sont récemment développées afin de guider les pathologistes avec des mesures quantitatives dans l’établissement d’un diagnostic. Les travaux présentés dans cette thèse visent à adresser les défis liés à l’analyse d’images histologiques, et à développer un modèle d’aide au diagnostic se basant principalement sur les relations spatiales, une information que les méthodes existantes n’exploitent que rarement. Une technique d’analyse de la texture à plusieurs échelles est tout d’abord proposée afin de détecter la présence de tissu malades dans les images. Un descripteur d’objets, baptisé Force Histogram Decomposition (FHD), est ensuite introduit dans le but d’extraire les formes et l’organisation spatiale des régions définissant un objet. Finalement, les images histologiques sont décrites par les FHD mesurées à partir de leurs différents types de tissus et des objets biologiques marqués qu’ils contiennent. Les expérimentations intermédiaires ont montré que les FHD parviennent à correctement reconnaitre des objets sur fonds uniformes y compris dans les cas où les relations spatiales ne contiennent à priori pas d’informations pertinentes. De même, la méthode d’analyse de la texture s’avère satisfaisante dans deux types d’applications médicales différents, les images histologiques et celles de fond d’œil, et ses performances sont mises en évidence au travers d’une comparaison avec les méthodes similaires classiquement utilisées pour l’aide au diagnostic. Enfin, la méthode dans son ensemble a été appliquée à l’aide au diagnostic pour établir la sévérité d’un cancer via deux ensembles d’images histologiques, un de foies métastasés de souris dans le contexte du projet ANR SPIRIT, et l’autre de seins humains dans le cadre du challenge CPR 2014 : Nuclear Atypia. L’analyse des relations spatiales et des formes à deux échelles parvient à correctement reconnaitre les grades du cancer métastasé dans 87, 0 % des cas et fourni des indications quant au degré d’atypie nucléaire. Ce qui prouve de fait l’efficacité de la méthode et l’intérêt d’encoder l’organisation spatiale dans ce type d’images particulier. / During the last decade, digital pathology has been improved thanks to the advance of image analysis algorithms and calculus power. Particularly, it is more and more based on histology images. This modality of images presents the advantage of showing only the biological objects targeted by the pathologists using specific stains while preserving as unharmed as possible the tissue structure. Numerous computer-aided diagnosis methods using these images have been developed this past few years in order to assist the medical experts with quantitative measurements. The studies presented in this thesis aim at adressing the challenges related to histology image analysis, as well as at developing an assisted diagnosis model mainly based on spatial relations, an information that currently used methods rarely use. A multiscale texture analysis is first proposed and applied to detect the presence of diseased tissue. A descriptor named Force Histogram Decomposition (FHD) is then introduced in order to extract the shapes and spatial organisation of regions within an object. Finally, histology images are described by the FHD measured on their different types of tissue and also on the stained biological objects inside every types of tissue. Preliminary studies showed that the FHD are able to accurately recognise objects on uniform backgrounds, including when spatial relations are supposed to hold no relevant information. Besides, the texture analysis method proved to be satisfactory in two different medical applications, namely histology images and fundus photographies. The performance of these methods are highlighted by a comparison with the usual approaches in their respectives fields. Finally, the complete method has been applied to assess the severity of cancers on two sets of histology images. The first one is given as part of the ANR project SPIRIT and presents metastatic mice livers. The other one comes from the challenge ICPR 2014 : Nuclear Atypia and contains human breast tissues. The analysis of spatial relations and shapes at two different scales achieves a correct recognition of metastatic cancer grades of 87.0 % and gives insight about the nuclear atypia grade. This proves the efficiency of the method as well as the relevance of measuring the spatial organisation in this particular type of images.