Non-heuristic reduction of the graph in graph-cut optimization

During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut

A Non-Heuristic Reduction Method For Graph Cut Optimization

Graph cuts optimization is now well established for their efficiency but remains limited to the minimization of some Markov Random Fields (MRF) over a small number of variables due to the large memory requirement for storing the graphs. An existing strategy to reduce the graph size consists in testing every node and to create the node satisfying a given local condition. The remaining nodes are typically located in a thin band around the object to segment. However, there does not exists any theoretical guarantee that this strategy permits to construct a global minimizer of the MRF. In this paper, we propose a local test similar to already existing test for reducing these graphs. A large part of this paper consists in proving that any node satisfying this new test can be safely removed from the non-reduced graph without modifying its max-flow value. The constructed solution is therefore guanranteed to be a global minimizer of the MRF. Afterwards, we present numerical experiments for segmenting grayscale and color images which confirm this property while globally having memory gains similar to ones obtained with the previous existing local test

Geometry Analysis of Superconducting Cables For The Optimization of Global Performances

International audienceSuperconducting cables have now become a mature technology for energy transport, high-field magnets (MRI, LHC) and fusion applications (ToreSupra, and eventually ITER and DEMO). The superconductors are extremely brittle and suffer from electrical damages brought by mechanical strain induced by electromagnetic field that they generate. An optimal wiring architecture, obtained by simulation, can limit these damages. However, the simulation is a complex process and needs validation. This validation is performed on real 3D samples by the means of image processing. Within this objective, this paper is, to our best knowledge, the first one to present a method to segment the samples of three types of cables as well as a shape and geometry analysis. Preliminary results are encouraging and intended to be later compared to the simulation results

Reduced graphs for min-cut/max-flow approaches in image segmentation

International audienceIn few years, min-cut/max-flow approach has become a leading method for solving a wide range of problems in computer vision. However, min-cut/max-flow approaches involve the construction of huge graphs which sometimes do not fit in memory. Currently, most of the max-flow algorithms are impracticable to solve such large scale problems. In this paper, we introduce a new strategy for reducing exactly graphs in the image segmentation context. During the creation of the graph, we test if the node is really useful to the max-flow computation. Numerical experiments validate the relevance of this technique to segment large scale images

Fast and Memory Efficient Segmentation of Lung Tumors Using Graph Cuts

12In medical imaging, segmenting accurately lung tumors stay a quite challenging task when touching directly with healthy tissues. In this paper, we address the problem of extracting interactively these tumors with graph cuts. The originality of this work consists in (1) reducing input graphs to reduce resource consumption when segmenting large volume data and (2) introducing a novel energy formulation to inhibit the propagation of the object seeds. We detail our strategy to achieve relevant segmentations of lung tumors and compare our results to hand made segmentations provided by an expert. Comprehensive experiments show how our method can get solutions near from ground truth in a fast and memory efficient way

Numerical study of an optimization problem for mosaic active imaging

5International audienceIn this paper, we focus on the restoration of an image in mosaic active imaging. This emerging imaging technique consists in acquiring a mosaic of images (laser shots) by focusing a laser beam on a small portion of the target object and subsequently moving it to scan the whole field of view. To restore the whole image from such a mosaic, a prior work proposed a simplified forward model describing the acquisition process. It also provides a prior on the acquisition parameters. Together with a prior on the distribution of images, this leads to a MAP estimate alternating between the estimation of the restored image and the estimation of these parameters. The novelty of the current paper is twofold: (i) We provide a numerical study and argue that faster convergence can be achieved for estimating the acquisition parameters; (ii) we show that the results from this earlier work are improved when the laser shots are acquired according to a more compact pattern

Bayesian image restoration for mosaic active imaging

International audienceIn this paper, we focus on the restoration of images acquired with a new active imaging concept. This new instrument generates a mosaic of active imaging acquisitions. We first describe a simplified forward model of this so-called ''mosaic active imaging''. We also assume a prior on the distribution of images, using the \ac{TV}, and deduce a restoration algorithm. This algorithm iterates one step for the estimation of the restored image and one step for the estimation of the acquisition parameters. We then provide the details useful to the implementation of these two steps. In particular, we show that the image estimation can be performed with graph-cuts. This allows a fast resolution of this image estimation step. Finally, we detail numerical experiments showing that acquisitions made with a mosaic active imaging device can be restored even under severe noise levels, with few acquisitions

Une méthode de réduction exacte pour la segmentation par graph cuts

8 pagesLes graph cuts sont désormais un standard au sein de la communauté de la vision par ordinateur. Néanmoins, leur grande consommation mémoire reste un problème majeur : les graphes sous-jacents contiennent des milliards de noeuds et davantage d'arcs. Excepté quelques méthodes [14, 10, 5] exactes, les heuristiques présentes dans la littérature ne permettent d'obtenir qu'une solution approchée [12, 8]. Dans un premier temps, nous présentons une nouvelle stratégie pour réduire exactement ces graphes : le graphe est construit en ajoutant les noeuds qui satisfont localement une condition donnée et correspond à une bande étroite autour des contours de l'objet à segmenter. Les expériences présentées pour segmenter des images en niveaux de gris et en couleur mettent en évidence une faible consommation mémoire tout en garantissant une faible distance sur les segmentations. Nous présentons aussi une application de cette méthode pour segmenter des tumeurs dans des images scanner

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.

Réduction de graphes et application à la segmentation de tumeurs pulmonaires

In this thesis, we first present a new band-based strategy for reducing the graphs involved in binary graph cut segmentation. This is done by locally testing if a node is really useful to the maximum flow computation in these graphs. Like previous band-based methods, the remaining nodes are typically located in narrow bands surrounding the object edges to segment. In a first time, we propose an heuristic condition to decide if a node can be added to the reduced graph which can be computed in constant time (except for image borders). When the amount of regularization is large, extra parameters are embedded into this test for both further reducing the graphs and removing segments due to noise in the segmentations. When the amount of regularization is of moderate level, the time required by this algorithm is even compensated by the maximum flow time on the reduced graph. In this situation, we experimentally show that this algorithm drastically reduce the memory usage of standard graph cuts while keeping a low pixel error on segmentations. In a second time, we describe another test with a slightly higher computational cost. We prove that each node satisfying this test can be safely removed without modifying the maximum flow value. Numerical experiments exhibit similar performance than the heuristic test. In a second part, we present an application of this reduction technique devoted to the semi-interactive segmentation of lung tumors in 3D CT images. The novelty of this work is to embed a prior on the object seeds location and control their propagation thanks to a Fast Marching algorithm based on the image gradient. Qualitative and quantitative results against provided ground truths exhibit an accurate delineation of tumors with a Dice coefficient greater than 80\% in average.Dans cette thèse, nous présentons d'abord une nouvelle stratégie à base de bandes pour réduire les graphes impliqués dans la segmentation binaire par graph cuts. Ceci est effectué en testant localement si un noeud est réellement utile au calcul du flot maximum dans ces graphes. À l'instar des méthodes antérieures à base de bandes, les noeuds restants sont typiquement localisés dans des bandes étroites autour des contours de l'objet à segmenter. Dans un premier temps, nous proposons un test heuristique pour décider si un noeud peut être ajouté au graphe réduit qui peut être calculée en temps constant (excepté pour les bords de l'image). Lorsque le degré de régularisation est élevé, des paramètres supplémentaires sont intégrés à ce test pour à la fois réduire davantage les graphes et supprimer les zones dues au bruit dans les segmentations. Lorsque le degré de régularisation est moindre, le temps requis par cet algorithme est même compensé par le temps de calcul du flot maximum sur le graphe réduit. Dans cette situation, nous montrons expérimentalement que cet algorithme réduit significativement la consommation mémoire des graph cuts standard tout en conservant une erreur quasi nulle sur les segmentations. Dans un second temps, nous décrivons un autre test avec un coût computationnel légèrement supérieur. Nous démontrons que chaque noeud vérifiant ce test peut être retiré sans altérer la valeur du flot maximum. Des expériences numériques permettent d'exhiber des performances équivalentes au test heuristique. Dans une seconde partie, nous présentons une application de cette technique de réduction à la segmentation semi-interactive de tumeurs pulmonaires dans des images CT 3D. L'originalité de ce travail consiste à intégrer un a priori sur la localisation des graines objet et contrôler leur propagation grâce à un algorithme de Fast Marching basé sur le gradient de l'image. Les résultats quantitatifs et qualitatifs comparés aux vérités terrains fournies montrent une délimitation précise des tumeurs avec un coefficient de Dice supérieur à 80\% en moyenne