Digitalisation de partitions et de tessellations

International audienceCette étude concerne le partitionnement d'un ensemble de telle sorte que les séparations entre classes soient matérialisées. On le résoud, dans les cas continu et discret, au moyen de hiérarchies de tesselations dont les classes sont des ouverts réguliers. Dans le cas discret, le passage partition→tessellation s'exprime par des topologies d'Alexandrov, et débouche sur des doubles résolutions. Les ambiguités de configurations diagonales ne sont levées que par la trame triangulaire à deux dimensions, et cubique centrée à trois dimensions. Seules ces trames préservent la connexité des classes dans les hiérarchies, et l'on peut alors introduire des fonctions de saillance. On montre enfin que les seules partitions euclidiennes expérimentalement accessibles sont les tesselations

Energetic Order for Optimization on Hierarchies of Partitions: Continuous hierarchy and Lagrange optimization

In the current technical note we provide a topological generalization of hierarchy of partitions(HOP) structure, and the implications over the axioms of h-increasingness and scale increasingness [13]. Further in this study we will explicit the Lagrange optimization in the optimal cuts problem and the conditions necessary on the energy to obtain a global optimum using the a dynamic program. Further a general multi-constraint optimization problem is considered with multiple Lagrangian multipliers, leading to a general version of scale increasingness that orders cuts, by ordered tuples of multipliers. The report also differentiates Inf-Modularity and Submodularity and their space of application. The final demonstration on wavering hierarchies show how one can relax conditions on the hierarchical structure

Ground truth energies for hierarchies of segmentations

International audienceIn evaluating a hierarchy of segmentations H of an image by ground truth G, which can be partitions of the space or sets, we look for the optimal partition in H that " fits" G best. Two energies on partial partitions express the proximity from H to G, and G to H. They derive from a local version of the Hausdor distance. Then the problem amounts to nding the cut of the hierarchy which minimizes the said energy. This cuts provide global similarity measures of precision and recall. This allows to contrast two input hierarchies with respect to the G, and also to describe how to compose energies from di erent ground truths. Results are demonstrated over the Berkeley database

Unsupervised clustering of hyperspectral images of brain tissues by hierarchical non-negative matrix factorization

International audienceHyperspectral images of high spatial and spectral resolutions are employed to perform the challenging task of brain tissue characterization and subsequent segmentation for visualization of in-vivo images. Each pixel is a high-dimensional spectrum. Working on the hypothesis of pure-pixels on account of high spectral resolution, we perform unsupervised clustering by hierarchical non-negative matrix factorization to identify the pure-pixel spectral signatures of blood, brain tissues, tumor and other materials. This subspace clustering was further used to train a random forest for subsequent classification of test set images constituent of in-vivo and ex-vivo images. Unsupervised hierarchical clustering helps visualize tissue structure in in-vivo test images and provides a inter-operative tool for surgeons. Furthermore the study also provides a preliminary study of the classification and sources of errors in the classification process

What makes the pregnant women revisit public hospitals for research? Participant engagement and retention trial in a public hospital (PERTH): an RCT protocol.

BACKGROUND: Cohort studies have public health importance as they effectively provide evidence on determinants of health from a life course perspective. Researchers often confront the poor follow-up rates as a major challenge in the successful conduct of cohort studies. We are currently recruiting in a birth cohort study, titled as "Maternal Antecedents of Adiposity and Studying the Transgenerational role of Hyperglycemia and Insulin" (MAASTHI) in a public hospital; with the aim of assessing maternal glycemic levels on the risk of adverse fetal outcomes. Nested within the ongoing cohort, the proposed trial aims to evaluate the effectiveness of two interventions in improving the follow-up in the cohort study in a public hospital. METHODS: A randomized trial of 795 pregnant women, with 265 women each in three arms observed through pregnancy, until their baby is 14 weeks old. The comparator group receives a standard leaflet, with details on the importance of glucose testing and regular follow up in pregnancy. Intervention arm-1 will receive the standard leaflet plus individualized messages, through an Interactive Voice Response (IVR) system; a type of computer-linked telephone intervention system to remind the participants about the lab test and follow-up dates. Intervention arm- 2 will have the opportunity to attend Mother and Baby Affairs (MBA) workshops, which will provide information on Gestational Diabetes Mellitus (GDM) screening and management to pregnant women and personalized counselling services. The outcome of interest is the difference in the proportion of participants completing follow-up at different points in time, among three arms. DISCUSSION: Between the two interventions (IVR and MBA), the study results would uncover the contextually specific, timely intervention, which can increase the proportion of pregnant women followed up in public hospitals. If effective, this study will provide information on an effective intervention, useful in ensuring the success of longitudinal follow-up in the public hospitals. TRIAL REGISTRATION: NCT03088501 , Date Registered: 16/03/2017

L’optimization par trellis-énergetique

Hierarchical segmentation has been a model which both identifies with the construct of extracting a tree structured model of the image, while also interpreting it as an optimization problem of the optimal scale selection. Hierarchical processing is an emerging field of problems in computer vision and hyper-spectral image processing community, on account of its ability to structure high-dimensional data. Chapter 1 discusses two important concepts of Braids and Energetic lattices. Braids of partitions is a richer hierarchical partition model that provides multiple locally non-nested partitioning, while being globally a hierarchical partitioning of the space. The problem of optimization on hierarchies and further braids are non-tractable due the combinatorial nature of the problem. We provide conditions, of h-increasingness, scale-increasingness on the energy defined on partitions, to extract unique and monotonically ordered minimal partitions. Furthermore these conditions are found to be coherent with the Braid structure to perform constrained optimization on hierarchies, and more generally Braids. Chapter 2 demonstrates the Energetic lattice, and how it generalizes the Lagrangian formulation of the constrained optimization problem on hierarchies. Finally in Chapter 3 we apply the method of optimization using energetic lattices to the problem of extraction of segmentations from a hierarchy, that are proximal to a ground truth set. Chapter 4 we show how one moves from the energetic lattice on hierarchies and braids, to a numerical lattice of Jordan Curves which define a continous model of hierarchical segmentation. This model enables also to compose different functions and hierarchiesLa segmentation hiérarchique est une méthode pour produire des partitions qui représentent une même image de manière de moins en moins fine. En même temps, elle sert d'entrée à la recherche d'une partition optimale, qui combine des extraits des diverses partitions en divers endroits. Le traitement hiérarchique des images est un domaine émergent en vision par ordinateur, et en particulier dans la communauté qui étudie les images hyperspectrales et les SIG, du fait de son capacité à structurer des données hyper-dimensionnelles. Le chapitre 1 porte sur les deux concepts fondamentaux de tresse et de treillis énergétique. La tresse est une notion plus riche que celle de hiérarchie de partitions, en ce qu'elle incorpore, en plus, des partitions qui ne sont pas emboîtées les unes dans les autres, tout en s'appuyant globalement sur une hiérarchie. Le treillis énergétique est une structure mixte qui regroupe une tresse avec une énergie, et permet d'y définir des éléments maximaux et minimaux. Lorsqu'on se donne une énergie, trouver la partition formée de classes de la tresse (ou de la hiérarchie) qui minimise cette énergie est un problème insoluble, de par sa complexité combinatoriale. Nous donnons les deux conditions de h-croissance et de croissance d'échelle, qui garantissent l'existence, l'unicité et la monotonie des solutions, et conduisent à un algorithme qui les détermine en deux passes de lecture des données. Le chapitre 2 reste dans le cadre précédent, mais étudie plus spécifiquement l'optimisation sous contrainte. Il débouche sur trois généralisations du modèle Lagrangien. Le chapitre 3 applique l'optimisation par treillis énergétique au cas de figure où l'énergie est introduite par une « vérité terrain », c'est à dire par un jeu de dessins manuel, que les partitions optimales doivent serrer au plus près. Enfin, le chapitre 4 passe des treillis énergétiques à ceux des courbes de Jordan dans le plan euclidien, qui définissent un modèle continu de segmentations hiérarchiques. Il permet entre autres de composer les hiérarchies avec diverses fonctions numérique

Energetic Order for Optimization on Hierarchies of Partitions: Continuous hierarchy and Lagrange optimization

In the current technical note we provide a topological generalization of hierarchy of partitions(HOP) structure, and the implications over the axioms of h-increasingness and scale increasingness [13]. Further in this study we will explicit the Lagrange optimization in the optimal cuts problem and the conditions necessary on the energy to obtain a global optimum using the a dynamic program. Further a general multi-constraint optimization problem is considered with multiple Lagrangian multipliers, leading to a general version of scale increasingness that orders cuts, by ordered tuples of multipliers. The report also differentiates Inf-Modularity and Submodularity and their space of application. The final demonstration on wavering hierarchies show how one can relax conditions on the hierarchical structure

L'optimisation contrainte sur des hiérarchies et tresses de partitions

International audienceThis theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results to a larger family of partitions, namely the braid [9]. Secondly, the paper shows the dependence of valid constraint function values and multiplier values in a Lagrangian optimization framework. Lastly, but most importantly, it also proposes the energetic order and energetic lattice based solutions for the constraint optimization problem. This approach operates on a partition based constraint thus ensuring the existence of a valid multiplier and constraint value

Digitization of Partitions and Tessellations

International audienceWe study hierarchies of partitions in a topological space where the interiors of the classes and their frontiers are simultaneously represented. In both continuous and discrete spaces our approach rests on tessellations whose classes are R-open sets. In the discrete case, the passage from partitions to tessellations is expressed by the Alexandrov topology and yields double resolutions. A new topology is proposed to remove the ambiguities of the diagonal configurations. It leads to the triangular grid in Z^2 and the centered cubic grid in Z^3 , which are the only translation invariant grids which preserve connectivity and permit the use of saliency functions