Pyramids of n-Dimensional Generalized Maps

International audienceGraph pyramids are often used for representing irregular pyramids. Combinatorial pyramids have been recently defined for this purpose. We define here pyramids of n-dimensional generalized maps. This is the main contribution of this work: a generic definition in any dimension which extend and generalize the previous works. Moreover, such pyramids explicitly represent more topological information than graph pyramids. A pyramid can be implemented in several ways, and three representations are discussed in this paper

Generalized Map Pyramid for Multi-level 3D Image Segmentation

International audienceGraph pyramids are often used to represent an image with various levels of details. Generalized pyramids have been recently defined in order to deal with images in any dimension. In this work, we show how to use generalized pyramids to represent 3D multi-level segmented images. We show how to construct such a pyramid, by alternating segmentation and simplification steps. We present how cells to be removed are marked: by using an homogeneous criterion to mark faces and the cell degree to mark other cells. When the pyramid is constructed, the main problem consists in retrieving information on regions. In this work, we show how to retrieve two types of information. The first one is the low level cells that are merged into a unique high level cell. The second one is the inter-voxel cells that compose a given region

Receptive Fields for Generalized Map Pyramids: The Notion of Generalized Orbit

International audienceA pyramid of n-dimensional generalized maps is a hierarchical data structure. It can be used, for instance, in order to represent an irregular pyramid of n-dimensional images. A pyramid of generalized maps can be built by successively removing and/or contracting cells of any dimension. In this paper, we define generalized orbits, which extend the classical notion of receptive fields. Generalized orbits allow to establish the correspondence between a cell of a pyramid level and the set of cells of previous levels, the removal or contraction of which have led to the creation of this cell. In order to define generalized orbits, we extend, for generalized map pyramids, the notion of connecting walk defined by Brun and Kropatsch

Définition et étude des pyramides généralisées D (application pour la segmentation multi-échelle d'images 3D)

Dans ce travail, nous nous intéressons à la modélisation géométrique hiérarchique à base topologique en proposant la définition d'un modèle générique en dimension quelconque, et en montrant une application possible en segmentation multi-échelle d'images 3D. Dans la première partie de cette thèse, nous définissons et étudions les pyramides généralisées nD. C'est un modèle topologique hiérarchique générique qui représente toutes les cellules d'une subdivision ainsi que les relations d'adjacence et d'incidence existant entre celles-ci. Nous proposons et comparons trois représentations possibles de ces pyramides. Afin de retrouver les informations correspondant à une cellule, nous définissons la notion d'orbite généralisée étendant celle de champ récepteur. Nous définissons également une opération de modification locale d'un niveau de la pyramide permettant de conserver la cohérence du modèle en propageant les modifications aux niveaux supérieurs. Dans la deuxième partie de ce travail, nous montrons comment utiliser ce modèle dans le cadre d'une segmentation multi-échelle d'images 3D. Nous définissons les propriétés que doit satisfaire la pyramide, puis nous donnons les algorithmes qui permettent de construire une telle pyramide. Nous montrons ensuite comment utiliser les orbites généralisées afin de retrouver les voxels ou éléments inter-voxels composant une région ou son bord. Enfin nous définissons une opération permettant de modifier localement le critère de segmentation d'un ensemble de régions. Cette opération est basée sur celle définie dans la première partie afin de conserver les contraintes de cohérence.In this work, we are interested in the hierarchical geometrical modeling with a topological basis. We propose the definition of a generic model in any dimension, and we show a possible application in multi-level segmentation of 3D images. In the first part of this work, we define and study the nD generalized pyramids. This is a generic hierarchical topological model which represents all the cells of a subdivision as well as the adjacency and incidence relations existing between these cells. We propose and compare three possible representations of these pyramids. In order to retrieve the information which corresponds to a cell, we define the notion of generalized orbit. This notion extends the notion of receptive field. We also define a local modification operation of a pyramid level allowing to preserve the model coherence by propagating the modifications at the upper levels. In the second part of this work, we show how to use this model in the case of a multi-level segmentation of 3D images. We define the properties which have to be respected by the pyramid, and we give the algorithms that allow to construct such a pyramid. Then, we show how to use the generalized orbits in order to retrieve the voxels or the inter-voxel elements which compose a region or its boundary. Finally we define an operation allowing to locally modify the segmentation criterion of a region set. This operation is based on the operation defined in the first part in order to preserve the coherence constraints.POITIERS-BU Sciences (861942102) / SudocSudocFranceF

Sotrovimab therapy elicits antiviral activities against Omicron BQ.1.1 and XBB.1.5 in sera of immunocompromised patients [letter]

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