Graph-based morphological processing of multivariate microscopy images and data bases

International audienceThe extension of lattice based operators to manifolds is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a manifold by its rank suitable for classical morphological processing. Manifold learning is considered as the basis for the construction of a complete lattice. The whole processing of multivariate functions is expressed on graphs to have a formalism that can be applied on images, region adjacency graphs, and image databases. Several examples in microscopy do illustrate the benefits of the proposed approach

Tabu search model selection for SVM

International audienceA model selection method based on tabu search is proposed to build support vector machines (binary decision functions) of reduced complexity and efficient generalization. The aim is to build a fast and efficient support vector machines classifier. A criterion is defined to evaluate the decision function quality which blends recognition rate and the complexity of a binary decision functions together. The selection of the simplification level by vector quantization, of a feature subset and of support vector machines hyperparameters are performed by tabu search method to optimize the defined decision function quality criterion in order to find a good sub-optimal model on tractable times

Lifting scheme on graphs with application to image representation

International audienceWe propose a new multiscale transform for scalar functions defined on the vertex set of a general undirected weighted graph. The transform is based on an adaption of the lifting scheme to graphs. One of the difficulties in applying directly the lifting scheme to graphs is the partitioning of the vertex set. We follow a recent greedy approach and extend it to a multilevel transform. We carefully examine each step of the algorithm, in particular its effect on the underlying basis. We finally investigate the use of the proposed transform to image representation by computing M-term nonlinear approximation errors. We provide a comparison with standard orthogonal and biorthogonal wavelet transforms

PDEs level sets on weighted graphs

International audienceIn this paper we propose an adaptation of PDEs level sets over weighted graphs of arbitrary structure, based on PdEs and using a framework of discrete operators. A general PDEs level sets formulation is presented and an algorithm to solve such equation is described. Some transcriptions of well-known models under this formalism, as the mean-curvature-motion or active contours, are also provided. Then, we present several applications of our formalism, including image segmentation with active contours, using weighted graphs of arbitrary topologies

Nonlocal PdES on graphs for active contours models with applications to image segmentation and data clustering

International audienceWe propose a transcription on graphs of recent continuous global active contours proposed for image segmentation to address the problem of binary partitioning of data represented by graphs. To do so, using the framework of Partial difference Equations (PdEs), we propose a family of nonlocal regularization functionals that verify the co-area formula on graphs. The gradients of a sub-graph are introduced and their properties studied. Relations, for the case of a sub-graph, between the introduced nonlocal regularization functionals and nonlocal discrete perimeters are exhibited and the co-area formula on graphs is introduced. Finally, nonlocal global minimizers can be considered on graphs with the associated energies. Experiments show the benefits of the approach for nonlocal image segmentation and high dimensional data clustering

Segmentation of color images : applications to cellular microscopy

A morphological method for the color segmentation of cytological images is presented. This method is mainly based on watershed whose potential function blend local and global informations. The method uses a priori informations for the frame of the method. The paper is based on three parts. In a first part, the frame of a morphological segmentation method is recalled. Secondly, our morphological method of color segmentation is presented and its corresponding methodology of utilization is developped. All importants points of our morphological method are exposed : choice of the color space, choice of the color gradient, etc. Finally, the usefulness of the segmentation method is illustrated on images from serous cytology.Nous proposons une méthode morphologique de segmentation d'images couleur de cytologie. Cette méthode est basée sur la ligne de partage des eaux utilisant une fonction de potentiel couleur combinant informations locale et globale. Cette méthode de segmentation utilise des informations a priori pour élaborer l'utilisation de la méthode. L'article s'articule autour de trois parties. Dans une première partie, nous rappellerons tout d'abord la structure d'une segmentation morphologique couleur. Dans une deuxième partie, nous exposerons notre méthode morphologique de segmentation couleur ainsi que sa méthodologie d'utilisation précisant tous les points importants et leur mise au point (choix de l'espace couleur, choix du gradient, etc.). Dans une dernière partie nous verrons une illustration de la méthode de segmentation sur des images de la cytologie des séreuses

Segmentation d'images par morphologie mathématique et classification de données par réseaux de neurones : Application à la classification de cellules en cytologie des séreuses

In this work, we studied the various stages useful for the development of a computer vision system : the segmentation of images, the characterization of objects and the classification of data. We developed sufficiently general original techniques allowing to carry out each one of these stages.We will first of all present a method of segmentation of images color of microscopy based on a watershed using of local and global information. In order to be able to adapt the critical points of the method, we defined a strategy of optimization which makes it possible to define the way to approach and to optimize them. We are more particularly interested in the choice of color space and in the obtaining of the markers. In particular, we defined a strategy for the choice of a color space using a color contrast measure based on a priori information.We detail then a neural network architecture. Its principle consists in simplifying the task of the classifior by dividing the problem to be solved. Architecture that we defined makes it possible to simplify the recognition of the data, to improve the training, to simplify the structure of the neural networks used but mainly to increase the recognition rate of the classifior. We illustrated these properties by experiments on various data bases.Finally, we present the development of a screening assistance system by computer cell sorting. This system carries out the synthesis of the methods suggested in the first two parts. It is completely autonomous and allows the recognition of the cells in a highly reliable way (94.5% of the abnormal cells and 99% of the normal cells).Dans ce travail, nous avons étudié les différentes étapes utiles à l'élaboration d'un système de vision par ordinateur : la segmentation d'images, la caractérisation d'objets et la classification de données. Nous avons développé des techniques originales suffisamment générales permettant de réaliser chacune de ces étapes.Nous exposerons tout d'abord une méthode de segmentation d'images couleur de microscopie basée sur une ligne de partage des eaux utilisant des informations locales et globales. Afin de pouvoir adapter les points critiques de la méthode, nous avons défini une stratégie d'optimisation qui permet de définir la façon de les aborder et de les optimiser. Nous nous sommes plus particulièrement intéressés au choix de l'espace couleur et à l'obtention de marqueurs. En particulier, nous avons défini une stratégie de choix de l'espace couleur basée sur une mesure du contraste couleur à partir d'informations a priori.Nous détaillons ensuite une architecture de réseaux de neurones. Son principe consiste à simplifier la tâche du classifieur en divisant le problème à résoudre. L'architecture que nous avons définie permet de simplifier la reconnaissance des données, d'améliorer l'apprentissage, de simplifier la structure des réseaux de neurones utilisés mais principalement d'augmenter le taux de reconnaissance du classifieur. Nous avons illustré ces propriétés par des expérimentations sur différentes bases de données.Enfin, nous présentons l'élaboration d'un système d'aide au screening par le tri informatique cellulaire. Ce système réalise la synthèse des méthodes proposées dans les deux premières parties. Il est totalement autonome et permet la reconnaissance des cellules de façon très fiable (94.5% des cellules anormales et 99% des cellules normales)