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

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

Periodic orbit theory for realistic cluster potentials: The leptodermous expansion

The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic-orbit-expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials and show that it describes the shift of the supershells as the surface of a cluster potential gets softer. As a byproduct of our work, we find that the electronic shell and supershell structure is not affected by a lattice contraction, which might be present in small clusters.Comment: 15 pages RevTex, 11 eps figures, additional information at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/users/koch/Diss

Supershells in Metal Clusters: Self-Consistent Calculations and their Semiclassical Interpretation

To understand the electronic shell- and supershell-structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals a surprisingly simple dependence of the supershells on the jellium density. It is shown how this can be understood in the framework of a periodic-orbit-expansion by analytically extending the well-known semiclassical treatment of a spherical cavity to more realistic potentials.Comment: 4 pages, revtex, 3 eps figures included, for additional information see http://radix2.mpi-stuttgart.mpg.de/koch/Diss

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

'Spillout' effect in gold nanoclusters embedded in c-Al2O3(0001) matrix

Gold nanoclusters are grown by 1.8 MeV Au^\sup{2+} implantation on c-Al\sub{2}O\sub{3}(0001)substrate and subsequent air annealing at temperatures 1273K. Post-annealed samples show plasmon resonance in the optical (561-579 nm) region for average cluster sizes ~1.72-2.4 nm. A redshift of the plasmon peak with decreasing cluster size in the post-annealed samples is assigned to the 'spillout' effect (reduction of electron density) for clusters with ~157-427 number of Au atoms fully embedded in crystalline dielectric matrix with increased polarizability in the embedded system.Comment: 14 Pages (figures included); Accepted in Chem. Phys. Lett (In Press

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