Shape representation and analysis of 2D compact sets by shape diagrams

Shape diagrams are shape representations in the Euclidean plane introduced for studying 3D and 2D compact sets. A compact set is represented by a point within a shape diagram whose coordinates are morphological functionals defined from geometrical functionals and inequalities. Classically, the geometrical functionals for 2D sets are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. The purpose of this paper is to present a particular shape diagram for which mathematical properties have been well-defined and to analyse the shape of several families of 2D sets for the discrimination of convex and non convex sets as well as the discrimination of similar sets

Shape diagrams for 2D compact sets - Part III: convexity discrimination for analytic and discretized simply connected sets.

International audienceShape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The two first parts of this study are published in previous papers [8, 9]. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets

Shape diagrams for 2D compact sets - Part I: analytic convex sets. Australian Journal of

International audienceShape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirty-one shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirty-one shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers [19, 20]. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively

Shape diagrams for 2D compact sets - Part II: analytic simply connected sets.

International audienceShape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The first part of this study is published in a previous paper [16]. It focused on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The purpose of this paper is to present the second part, by focusing on analytic simply connected compact sets. The third part of the comparative study is published in a following paper [17]. It is focused on convexity discrimination for analytic and discretized simply connected compact sets

General adaptive neighborhood-based Minkowski maps for gray-tone image analysis.

In quantitative image analysis, Minkowski functionals are standard parameters for topological and geometrical measurements. Nevertheless, they are often limited to binary images and achieved in a global and monoscale way. The use of General Adaptive Neighborhoods (GANs) enables to overcome these limitations. The GANs are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, according to three (GAN) axiomatic criteria: a criterion function (luminance, contrast, . . . ), an homogeneity tolerance with respect to this criterion, and an algebraic model for the image space. Thus, the GANs are simultaneously adaptive with the analyzing scales, the spatial structures and the image intensities. The aim of this paper is to introduce the GAN-based Minkowski functionals, which allow a gray-tone image analysis to be realized in a local, adaptive and multiscale way. The Minkowski functionals are computed on the GAN of each point of the image, enabling to define the so-called Minkowski maps which assign the geometrical or the topological functional to each point. The impact of the GAN characteristics, as well as the impact of multiscale morphological transformations, is analyzed in a qualitative way through these maps. The GAN-based Minkowski maps are illustrated on the test image 'Lena' and also applied in the biomedical and materials areas

Fonctionnelles et fonctions de Minkowski à voisinages adaptatifs généraux pour l'analyse des images à tons de gris

http://documents.irevues.inist.fr/handle/2042/29071 http://hdl.handle.net/2042/29071 | DOI : 10.4267/2042/29071International audienceEn analyse d'image, les fonctionnelles de Minkowski sont des paramètres standards de mesures topologiques et géométriques d'objets. Néanmoins, elles sont souvent limitées aux images binaires, et déterminées de manière globale et mono-échelle. L'utilisation des Voisinages Adaptatifs Généraux (VAG), simultanément adaptatifs avec les échelles d'analyse, les structures spatiales et les intensités des images, permet de pallier ces limites. Une analyse locale, adaptative et multi-échelle des images à tons de gris est donc proposée sous forme de cartographies des fonctionnelles de Minkowski à VAG. Les VAG sont des voisinages définis en chaque point du support spatial d'une image à tons de gris, homogènes par rapport à un critère d'analyse suivant une tolérance d'homogénéité. Les fonctionnelles de Minkowski sont calculées pour chaque VAG de l'image, permettant de définir les cartographies des fonctionnelles de Minkowski adaptatives. A chaque point de l'image est donc attribuée une fonctionnelle topologique ou géométrique de la structure locale de l'image. Par ailleurs, l'évolution de la tolérance d'homogénéité permet de définir des cartographies multi-échelles. De plus, les cartographies sont analysées de manière qualitative sous l'influence d'une transformation morphologique multi-échelle (dilatation/érosion, ouverture/fermeture par reconstruction,...) ================================== In quantitative image analysis, Minkowski functionals are standard parameters for topological and geometrical measurements. Nevertheless, they are often limited to binary images and achieved in a global and monoscale way. The use of General Adaptive Neighborhoods (GANs), simultaneously adaptive with the analyzing scales, the spatial structures and the image intensities, enables to overcome these limitations. The GAN-based Minkowski functionals are introduced, which allow a gray-tone image analysis to be realized in a local, adaptive and multiscale way. The GANs are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, homogeneous with respect to a criterion function according to an homogeneity tolerance. The Minkowski functionals are computed on the GAN of each point of the image, enabling to define the so-called Minkowski maps which assign the geometrical or the topological functional to each point. Also, the evolution of the GAN homogeneity tolerance allows the multiscale Minkowski maps to be defined. Futhermore, the impact of multiscale morphological transformations (dilation/erosion, opening/closing by reconstruction, . . . ), is analyzed in a qualitative way through these maps

Analyse morphométrique d'images à tons de gris par diagrammes de forme

Session "Posters"National audienceLes diagrammes de forme sont des représentations introduites pour étudier les ensembles connexes compacts: un tel ensemble est représenté par un point dans le plan euclidien dont les coordonnées sont deux fonctionnelles morphométriques. Néanmoins, les diagrammes de forme sont souvent limités à l'analyse globale et mono-échelle d'image binaire. L'utilisation des Voisinages Adaptatifs Généraux (VAG) permet de pallier ces limites. Les VAG sont des voisinages spatiaux, définis autour de chaque point du support spatial d'une image à niveaux de gris, simultanément adatatifs avec les échelles d'analyse, les structures spatiales, et les intensités de l'image. Ce papier vise à introduire les diagrammes de forme à VAG, qui permettent d'analyser les images à niveaux de gris de manière locale, adaptative et multi-échelle. Les fonctionnelles morphométriques sont calculées pour le VAG de chaque point du support spatial de l'image, définissant les diagrammes de forme à VAG. Des distributions morphométriques des structures locales de l'image sont obtenues, permettant par exemple de les classifie

Integral Geometry and General Adaptive Neighborhoods for Multiscale Image Analysis

International audienceIn quantitative image analysis, Minkowski functionals are becoming standard parameters for topological and geometrical measurements. Nevertheless, they are limited to binary images or to sections of gray-tone images and are achieved in a global and monoscale way. The use of General Adaptive Neighborhoods (GANs) enables to overcome these limitations. The GANs are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, according to three (GAN) axiomatic criteria: a criterion function (luminance, contrast, ...), an homogeneity tolerance with respect to this criterion, and an algebraic model for the image space. Thus, the GANs are simultaneously adaptive with the analyzing scales, the spatial structures and the image intensities. This paper aims to introduce the GAN-based Minkowski functionals, which allow a gray-tone image analysis to be realized in a local, adaptive and multiscale way. The Minkowski functionals are computed on the GAN of each point of the spatial support of a gray-tone image, enabling to define the so-called Minkowski maps by assigning the Minkowski functional value to each point. The histograms of these maps provide a statistical distribution of the topology and geometry of the gray-tone image structures, and not only of the image intensities. The impact of the GAN characteristics, as well as the impact of multiscale transformations, are analyzed in a qualitative global and local way through these GAN-based Minkowski maps and histograms. This multiscale image analysis is illustrated on the test image 'Lena' and also applied in both the biomedical and materials areas

Exposition prénatale aux perturbateurs endocriniens et risque sur le neurodéveloppement : étude de fratries exposées au diéthylstilbestrol

Many endocrine disruptors are found in our environment. They act on hormonal receptors, on their action and synthesis. They may alter neuronal transmission and neuronal formation. A lot of neurodevelopmental diseases have a growing prevalence, raising many questions about a possible association with endocrine disruptors. One of their action mechanisms may be an effect on DNA methylation of the developing brain.Objectives: To study neurodevelopmental characteristics and the epigenetic signature of patients exposed in utero to diethylstilbestrol. To identify differentially methylated regions in neurodevelopmental related genes, which could lead to a psychiatric vulnerability.Materials and Methods: We recruited 75 siblings from 31 families, in which at least one member was exposed in utero to diethylstilbestrol. A psychiatric evaluation was assessed with standardized questionnaires. We used the Infinium HumanMethylation450 BeadChip and analyzed the methylation variations of 411 947 CpG loci.Results: We found clinical differences in non-specific psychiatric symptoms and in neurological soft signs, such as lateralization, associated with the exposure. We found several biological pathways in which methylation modifications were associated to diethylstilbestrol exposure. These pathways are implicated in neurodevelopmental pathways, general metabolism and oncogenesis mostly.Conclusion : Prenatal diethylstilbestrol exposure seems associated with non-specific psychiatric symptoms, lateralization abnormalities and methylation alterations in genes that participate to pathways known to be involved in psychiatric diseases, notably in neurotransmitters signalization.De nombreux perturbateurs endocriniens sont retrouvés dans notre environnement. Ils interfèrent sur l’action des récepteurs hormonaux. Plusieurs travaux argumentent qu’ils altéreraient la formation des réseaux neuronaux. Un parallèle a été évoqué avec l’augmentation de la prévalence des troubles neurodéveloppementaux. Un mécanisme d’action évoqué est un effet sur la méthylation de l’ADN dans le cerveau en maturation.Objectifs : Étudier les caractéristiques neurodéveloppementales et la signature épigénétique des patients exposés in utero au diéthylstilbestrol. Identifier des régions de méthylation différentielles sur des gènes impliqués dans le neurodéveloppement, pouvant mener à une vulnérabilité psychiatrique.Matériels et méthodes: Nous avons recruté 75 frères et sœurs issus de 31 familles dont au moins un membre fut exposé in utero au diéthylstilbestrol. Une évaluation neuropsychiatrique a été réalisée. Nous avons utilisé une puce de méthylation et avons analysé les variations de méthylation de 411 947 CpG.Résultats: Nous avons observé des différences significatives au niveau de symptômes psychiatriques aspécifiques et de signes neurologiques mineurs, tels que la latéralisation, associées à l’exposition. Plusieurs réseaux biologiques présentant des modifications de méthylation sont associés à l’exposition. Ils concernent les fonctions neurodéveloppementales, le métabolisme et l’oncogenèse.Conclusion : L’exposition au diéthylstilbestrol paraît associée à des profils cliniques aspécifiques, à des troubles de la latéralisation, et à des altérations de méthylation au sein de réseaux biologiques spécifiques

Prevention of oil spills by tankers : feasibility study of a safety and environmental index (SEI)

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1995.Includes bibliographical references (leaves 70-71).by Laurent Rivollier.M.S