A stochastic evaluation of the contour strength

International audienceIf one considers only local neighborhoods for segmenting an image, one gets contours whose strength is often poorly estimated. A method for reevaluating the contour strength by taking into account non local features is presented: one generates a fixed number of random germs which serve as markers for the watershed segmentation. For each new population of markers, another set of contours is generated. "Important" contours are selected more often. The present paper shows that the probability that a contour is selected can be estimated without performing the effective simulations. Copyright Springer-Verlag 2010. The original publication is available at www.springerlink.com/content/y057x103475301r2

Morphologie mathématique et graphes : application à la segmentation interactive d'images médicales

Medical imaging is one of the most active research topics in image analysis. Analyzing and segmenting medical images in a clinical context remains a challenging task due to the multiplicity of imaging modalities and the variability of the patients characteristics and pathologies. Medical image processing also requires a human supervision for interpretation and validation purposes. The numerous applications and the huge amount of medical image data need complex software that combine high level graphical user interfaces as well as robust and fast interactive image analysis tools. Recent research in image segmentation has highlighted the potential of graph based methods for medical applications. These new tools have generated a great interest in the imaging community. Graph theory is the framework used in this thesis to propose innovative image segmentation tools. The focus of this thesis is both theoretical and practical. On the theoretical level, we study properties of minimal spanning trees, shortest paths trees and minimal cuts and we revisit these notions for image segmentation purposes. It allows us to derive new theoretical links between minimal spanning trees, shortest paths trees and minimal multi-terminal cuts. These results highlight the possibilities and the limitations of each technique for image segmentation problems. In a second step, we propose some theoretical and practical improvements of image segmentation based on graph cuts. This structure is particularly interesting for solving a fairly large variety of energy minimization problems. Our strategy is based on the use of the region adjacency graph produced by the watershed transform from mathematical morphology. The combination of morphological and graph cuts segmentation permits us to speed up and define new classes of energy functions that can be minimized using graph cuts. The use of region graphs gives promising results and can potentially become a leading method for interactive medical image segmentation. The third point of this thesis details some qualitative and quantitative studies of medical image segmentation problems, which is the initial motivation of this work. We show that the developed methods are well suited for various medical image segmentation problems. We study applications to surgery simulation, radiotherapy planning and tumors delineation. We show by a quantitative analysis that the combination of morphological and graph cuts segmentation methods outperforms several recent and state of the art tools. This study shows that our methods can be used in a clinical context. The last point of the thesis revisits and extends some classical graph based image segmentation tools. We revisit the well known watershed transform from the point of view of path optimization and path algebra. We recall existing properties of the watershed transform and propose some clear definitions of the watershed transform on graphs. Finally we also propose new extensions of the minimal graph cut problem for image segmentation purposes. New types of constraints are included in the classical minimal graph cut problem, which bring this standard problem into the linear programming framework. This class of combinatorial optimization problems is particulary interesting for image segmentation purposes since it provides a general framework for various constrained image segmentation problems such as boundary constrained minimal cuts and various geometric constrained minimal cuts. These new methods show great potential for various image segmentation scenarios.La recherche en imagerie médicale est une des disciplines les plus actives du traitement d'images. La segmentation et l'analyse d'images dans un contexte clinique reste un problème majeur de l'imagerie médicale. La multiplicité des modalités d'imagerie, ainsi que les fortes variabilités des structures et pathologies à analyser rendent cette tâche fastidieuse. Dans la plupart des cas, la supervision de spécialistes, tels que des radiologistes, est nécessaire pour valider ou interpréter les résultats obtenus par analyse d'images. L'importante quantité de données, ainsi que les nombreuses applications liées à l'imagerie médicale, nécessitent des outils logiciels de très haut niveau combinant des interfaces graphique complexe avec des algorithmes interactifs rapides. Les récentes recherches en segmentation d'images ont montré l'intérêt des méthodes à base de graphes. L'intérêt suscité dans la communauté scientifique a permis de développer et d'utiliser rapidement ces techniques dans de nombreuses applications. Nous avons étudié les arbres de recouvrement minimaux, les coupes minimales ainsi que les arbres de chemins les plus courts. Notre étude a permis de mettre en lumière des liens entre ces structures a priori très différentes. Nous avons prouvé que les forêts des chemins les plus courts, ainsi que les coupes minimales convergent toutes les deux, en appliquant une transformation spécifique du graphe, vers une structure commune qui n'est autre qu'une forêt de recouvrement minimale. Cette étude nous a aussi permis de souligner les limitations et les possibilités de chacune de ces techniques pour la segmentation d'images. Dans un deuxième temps, nous avons proposé des avancées théoriques et pratiques sur l'utilisation des coupe minimales. Cette structure est particulièrement intéressante pour segmenter des images à partir de minimisation d'énergie. D'une part, nous avons montré que l'utilisation de graphes de régions d'une segmentation morphologique permet d'accélérer les méthodes de segmentation à base de coupe minimales. D'autre part nous avons montré que l'utilisation de graphes de régions permet d'étendre la classe d'énergie pouvant être minimisée par coupe de graphes. Ces techniques ont toutes les caractéristiques pour devenir des méthodes de référence pour la segmentation d'images médicales. Nous avons alors étudié qualitativement et quantitativement nos méthodes de segmentation à travers des applications médicales. Nous avons montré que nos méthodes sont particulièrement adaptées à la détection de tumeurs pour la planification de radiothérapie, ainsi que la création de modèles pour la simulation et la planification de chirurgie cardiaque. Nous avons aussi mené une étude quantitative sur la segmentation de tumeurs du foie. Cette étude montre que nos algorithmes offrent des résultats plus stables et plus précis que de nombreuses techniques de l'état de l'art. Nos outils ont aussi été comparés à des segmentations manuelles de radiologistes, prouvant que nos techniques sont adaptées à être utilisée en routine clinique. Nous avons aussi revisité une méthode classique de segmentation d'images : la ligne de partages des eaux. La contribution de notre travail se situe dans la re-définition claire de cette transformation dans le cas des graphes et des images multi spectrales. Nous avons utilisé les algèbres de chemins pour montrer que la ligne de partages des eaux correspond à des cas particuliers de forêt des chemins les plus courts dans un graphe. Finalement, nous proposons quelques extensions intéressantes du problème des coupes minimales. Ces extensions sont basées sur l'ajout de nouveaux types de contraintes. Nous considérons particulièrement les coupes minimales contraintes à inclure un ensemble prédéfini d'arêtes, ainsi que les coupes minimales contraintes par leur cardinalité et leur aires. Nous montrons comment ces problèmes peuvent être avantageusement utilisé pour la segmentation d'images

Minimum spanning tree adaptive image filtering

ISBN : 978-1-4244-5653-6International audienceThe main focus of this paper is related to anisotropic morphological edge preserving filters. We present in this work neighborhood filters defined on the minimal spanning tree (MST) of an image (according to a local dissimilarity measure between adjacent pixels). The designed filters take advantage of the property of the MST to detect and follow the local features of an image. This approach leads to neighborhood filters where the structuring elements adapt their shape to the minimal spanning tree structure and therefore to the local image features. We demonstrate the quality of this method on natural and synthetic images

REGION MERGING VIA GRAPH-CUTS

In this paper, we discuss the use of graph-cuts to merge the regions of the watershed transform optimally. Watershed is a simple, intuitive and efficient way of segmenting an image. Unfortunately it presents a few limitations such as over-segmentation and poor detection of low boundaries. Our segmentation process merges regions of the watershed over-segmentation by minimizing a specific criterion using graph-cuts optimization. Two methods will be introduced in this paper. The first is based on regions histogram and dissimilarity measures between adjacent regions. The second method deals with efficient approximation of minimal surfaces and geodesics. Experimental results show that these techniques can efficiently be used for large images segmentation when a pre-computed low level segmentation is available. We will present these methods in the context of interactive medical image segmentation

Morphology on graphs and minimum spanning trees

ISBN : 978-3-642-03612-5International audienceThis paper revisits the construction of watershed and waterfall hierarchies through a thorough analysis of Boruvka's algorithms for constructing minimum spanning trees of edge weighted graphs. In the case where the watershed of a node weighted graph is to be constructed, we propose a distribution of weights on the edges, so that the waterfall extraction on the edge weighted graph becomes equivalent with the watershed extraction on the node weighted graph

Morphologie mathématique et graphes (application à la segmentation interactive d'images médicales)

PARIS-MINES ParisTech (751062310) / SudocSudocFranceF

Computing approximate geodesics and minimal surfaces using watershed and graph cuts

Geodesics and minimal surfaces are widely used for medical image segmentation. At least two different approaches are used to compute such segmentations. First, geodesic active contours use differential geometry to compute optimal contours minimizing a given Riemannian metric. Second, Boykov and Kolmogorov have proposed a method based on integral geometry to compute similar contours using a graph representation of the image and combinatorial optimization. In this paper we present a technique to compute approximate geodesics and minimal surfaces using a low-level segmentation and graph-cuts optimization. Our approach speeds-up the computation of minimal surfaces when a low-level segmentation is available