Modélisation, Analyse, Représentation des Images Numériques Approche combinatoire de l’imagerie

My research are focused on combinatorial image processing. My approach is to propose mathematical models to abstract physical reality. This abstraction allows to define new techniques leading to original solutions for some problems. In this context, I propose a topological model of image, regions segmentation based on statistical criteria and combinatorial algorithms, and a bound representation based on combinatorial maps.Mes travaux de recherche sont basés sur une approche combinatoire et discrète de l’imagerie. Ma démarche est de proposer des définitions de modèles mathématiques fournissant une abstraction de la réalité physique, cette abstraction permettant de définir des nouvelles techniques amenant des solutions originales à des problèmes posés. Dans ce cadre, je me suis plus particulièrement intéressé à la définition d’un modèle formel d’image, à la segmentation en régions par des techniques algorithmiques et statistiques, et à la structuration du résultat à l’aide d’une représentation combinatoire

Approche interpixel en analyse d'images : une topologie et des algorithmes de segmentation

Any image segmentation process aims at obtaining the features of the image entities. Most of the existing segmentation methods take into account only the materialized elements composing the image set: pixels or voxels.We suggest to deal with border elements, localized between the pixels or voxels, in order to study the links and connections between those base elements. Thus we can define a topology closely bound to image analysis processing: the star-topology. An important feature of this topology is that all classical theorems of the IR^n classical geometry can be directly translated into our frame.We associate to this topological study an inter pixel edge detector and segmentations algorithms making a perfect cooperation edge-region. Moreover we develop an extension of the region adjacency graph, the "boudary graph" which fits as well as the above results into our general framework of combinatoric methods in image analysis.Le but de tout processus de segmentation d'images est la caractérisation des entités représentées dans l'image. La plupart des méthodes existantes s'appuient sur les seuls éléments matérialisés formant l'ensemble Image : les pixels ou les voxels.Nous proposons de prendre en compte les éléments de bord des pixels ou des voxels afin d'étudier les liaisons et connexions entre ces derniers. Ceci nous permet de définir une topologie adaptée à l'analyse d'images : la star-topologie. Un résultat important de cette topologie est qu'elle permet de récupérer sans peine les théorèmes de la géométrie classique sur IR^n.Nous associons à cette étude topologique un détecteur de contours en interpixel et des algorithmes de segmentation exhibant un coopération parfaite région-contour. En outre le graphe des frontières, extension proposée du graphe d'adjacence, s'inscrit lui-aussi dans le cadre d'une approche globale combinatoire en analyse d'images

Adaptive Discrete Laplace Operator

International audienceDiffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, gener- alizing the operator defined on meshes. We study its eigenvalues and eigenvectors recovering interesting geometrical informations. We discuss its convergence towards the usual Laplacian operator especially on lat- tice of diamonds. We extend this definition to 3D shapes. Finally we use this Laplacian in classical but adaptive denoising of pictures preserving zones of interest like thin structures

Discrete Circles: an arithmetical approach with non-constant thickness

International audienceIn the present paper, we introduce an arithmetical definition of discrete circles with a non-constant thickness and we exhibit different classes of them depending on the arithmetical discrete lines. On the one hand, it results in the characterization of regular discrete circles with integer parameters as well as J. Bresenham's circles. As far as we know, it is the first arithmetical definition of the latter one. On the other hand, we introduce new discrete circles, actually the thinnest ones for the usual discrete connectedness relations

Volume Segmentation of 3-dimensional Images

We present a practical method to segment large medical images that takes the whole 3-dimensional structure into account. We use a Union-Find data structure to record and maintain the necessary information during the segmentation process. Due to the large data size, we are forced to divide our process in two parts: a "weak segmentation" of the individual sections and a global integration of all the data. This method shows good results on computer tomographies

Memory Management for Union-Find Algorithms

We provide a general tool to improve the real time performance of a broad class of Union-Find algorithms. This is done by minimizing the random access memory that is used and thus to avoid the well-known von~Neumann bottleneck of synchronizing CPU and memory. A main application to image segmentation algorithms is demonstrated where the real time performance is drastically improved

Amélioration de l'invisibilité par adaptation de la quantification aux données à insérer

Cet article présente une amélioration pour les méthodes d'insertion de données basées sur la DCT : l'adaptation de la quantification à l'insertion de données cachées. Les méthodes actuelles n'intègrent l'information secrète qu'après l'étape de quantification de la compression JPEG. La robustesse au format JPEG est bien obtenue, mais l'image subit deux pertes d'information successives : la quantification et l'insertion des données. En adaptant la quantification au message secret, nous réduisons les variations induites et donc, améliorons la qualité de l'image compressée et marquée vis-à-vis de l'originale

Hyperspectral image segmentation: the butterfly approach

International audienceFew methods are proposed in the litterature for coupling the spectral and the spatial dimension available on hyperspectral images. This paper proposes a generic segmentation scheme named butterfly based on an iterative process and a cross analysis of spectral and spatial information. Indeed, spatial and spatial structures are extracted in spatial and spectral space respectively both taking into account the other one. To apply this layout on hyperspectral imgages, we focus particulary on spatial and spectral structures i.e. topologic concepts and latent variable for the spatial and the spectral space respectively. Moreover, a cooperation scheme with these structures is proposed. Finally, results obtained on real hyperspectral images using this specific implementation of the butterfly approach are presented and discussed

Image segmentation using a generic, fast and non-parametric approach

International audienceIn this paper, we investigate image segmentation by region merging. Given any similarity measure between regions , satisfying some weak constraints, we give a general predicate for answering if two regions are to be merged or not during the segmentation process. Our predicate is generic and has six properties. The first one is its inde-pendance with respect to the similarity measure, that leads to a user-independant and adaptative predicate. Second, it is non-parametric, and does not rely on any assumption concerning the image. Third, due to its weak constraints, knowledge may be included in the predicate to fit better to the user's behaviour. Fourth, provided the similarity is well-chosen by the user, we are able to upperbound one type of error made during the image segmentation. Fifth, it does not rely on a particular segmentation algorithm and can be used with almost all region-merging algorithms in various application domains. Sixth, it is calculated quickly, and can lead with appropriated algorithms to very efficient segmentation