Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs

International audienceIn this paper we study numerical approximations of the evolution problem for the nonlocal p-Laplacian operator with homogeneous Neumann boundary conditions on inhomogeneous random conver-gent graph sequences. More precisely, for networks on convergent inhomogeneous random graph sequences (generated first by deterministic and then random node sequences), we establish their continuum limits and provide rate of convergence of solutions for the discrete models to their continuum counterparts as the number of vertices grows. Our bounds reveals the role of the different parameters, and in particular that of p and the geometry/regularity of the data

Automated region of interest retrieval and classification using spectral analysis

Efficient use of whole slide imaging in pathology needs automated region of interest (ROI) retrieval and classification, through the use of image analysis and data sorting tools. One possible method for data sorting uses Spectral Analysis for Dimensionality Reduction. We present some interesting results in the field of histopathology and cytohematology

Une méthodologie de développement d'applications de traitement d'image

Nous proposons une méthodologie de développement d'applications de traitement d'image qui se présente comme un guide complet et rigoureux pour la gestion du cycle de vie entier des applications. Cette méthodologie met en avant des capacités d'aide, de réutilisabilité d'expériences, d'uniformisation des représentations et de communication entre les différents personnes impliquées, par la définition de modèles structurés, de représentations graphiques et de règles de mise en oeuvre de ces modèles à chaque étape du développement. Elle se fonde essentiellement sur le paradigme du pilotage d'une bibliothèque de tâches, avec lequel la conception d'une solution est vue comme un processus d'agglomération de tâches ponctuelles et indépendantes. Le formalisme retenu distingue le cycle d'abstraction, qui considère trois niveaux pour la modélisation d'une solution conceptuelle, plus un niveau pour le programme proprement dit, et le cycle de vie qui préconise quatre phases successives pour la gestion complète de l'application

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

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

Joint co-clustering: co-clustering of genomic and clinical bioimaging data

AbstractFor better understanding the genetic mechanisms underlying clinical observations, and better defining a group of potential candidates for protein-family-inhibiting therapy, it is interesting to determine the correlations between genomic, clinical data and data coming from high resolution and fluorescent microscopy. We introduce a computational method, called joint co-clustering, that can find co-clusters or groups of genes, bioimaging parameters and clinical traits that are believed to be closely related to each other based on the given empirical information. As bioimaging parameters, we quantify the expression of growth factor receptor EGFR/erb-B family in non-small cell lung carcinoma (NSCLC) through a fully-automated computer-aided analysis approach. This immunohistochemical analysis is usually performed by pathologists via visual inspection of tissue samples images. Our fully-automated techniques streamlines this error-prone and time-consuming process, thereby facilitating analysis and diagnosis. Experimental results for several real-life datasets demonstrate the high quantitative precision of our approach. The joint co-clustering method was tested with the receptor EGFR/erb-B family data on non-small cell lung carcinoma (NSCLC) tissue and identified statistically significant co-clusters of genes, receptor protein expression and clinical traits. The validation of our results with the literature suggest that the proposed method can provide biologically meaningful co-clusters of genes and traits and that it is a very promising approach to analyse large-scale biological data and to study multi-factorial genetic pathologies through their genetic alterations

Les graphes comme outil de mise en oeuvre de méthodes de segmentation hiérarchique d'images

La segmentation d'images consiste souvent à extraire des objets afin de les caractériser et d'interpréter les images. Parmi les différentes stratégies utilisées pour arriver à un tel résultat, une des plus prometteuses est la segmentation hiérarchique qui analyse les images selon un degré croissant de résolution. Celle-ci fait alors intervenir des entités reliées entre elles par différentes relations. Par définition, les graphes sont susceptibles de représenter toutes ces relations, plus ou moins explicitées lors des traitements. Afin d'utiliser aisément les graphes lorsque cela est opportun, nous avons développé une bibliothèque d'opérateurs de traitement d'images, incluant une structure générale de graphe permettant de représenter des images 2D et 3D. Cette bibliothèque comporte également des opérateurs de traitement de ces graphes en tant qu'outils de segmentation. Nous présentons ici cette bibliothèque d'opérateurs ainsi qu'une application faisant intervenir les graphes dans la résolution d'un problème de quantification d'images biomédicales