Université d'Auvergne Clermont1 | CNRS

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Seminars

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28 January 2010
Pierre-Antoine Absil, Université Catholique de Louvain, Belgique

 

This presentation concerns applications of differential geometry in optimization, which arise when the optimization problem can be formulated as finding an optimum of a real-valued cost function defined on a smooth nonlinear search space. In most cases, the nonlinearity of the search space is due either to orthogonality constraints, or to invariance properties in the cost function that need to be factored out in order to obtain a nondegenerate optimization problem. In the recent years, the importance of optimization problems on nonlinear manifolds has stimulated the development of geometric optimization algorithms that exploit the differential structure of the manifold search space. In this talk, we give an overview of geometric optimization algorithms and their applications, with an emphasis on the underlying geometric concepts and on the numerical efficiency of the algorithm implementations.
1 January 2010
Søren Olsen, University of Copenhagen, Danemark

Welding is one of the most important industrial processes. Animportant technique within welding is (Short-Arc) V-Groove welding.Today this is domiDanemarknated by manual work.  The welder uses visionfeedback to move the electrode rod (and wire) to avoid burn through and to achieve a uniform filling; The purpose of the research is to develop a low-cost vision based control system without external illumination; Sub-tasks are seam tracking, and molten pool modelling. These tasks are difficult because the illumination from the arc is very much stronger compared to usual vision and because impurities creates a lot of sparks. During the presentation I will describe and show the problems and our solutions, and I will show preliminary results within seam tracking.

24 November 2009
Martin Groher, Technische Universität München, Allemagne

In modern hospitals, abdominal pathologies are often accessed by advancing a catheter through the human vessel system. A navigation based on X-ray fluoroscopy is common in such scenarios, which allows the treatment to be minimally-invasive. However, due to ambiguities in the projective images, patient motion, and radio transparency of vascular structures, this navigation is not optimal and intervention times, X-ray exposure to patient and physician, as well as the amount of administered contrast agent may increase. In this talk, I will address different issues to bring the navigation process from 2D to 3D in a monocular interventional scenario. This includes the processing of medical imagery to extract vessel structures, a 2D-3D pose estimation to relate pre-interventional images to intra- interventional images, deformable 2D-3D registration having only a single view in order to compensate for non-rigid motion, catheter tracking for breathing motion compensation, and finally robust 2D-to-3D back-projection of tracked instruments

22 October 2009
Jean-Charles Delvenne, Université Catholique de Louvain, Belgique

 

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times.
 
We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales. Finally, we obtain hierarchical segmentation of images, without a priori knowledge.
15 October 2009
Chafik Samir, ISIT, France

I will describe an approach for statistical analysis of shapes of 2D boundaries (closed curves) and 3D objects (surfaces) using ideas from Riemannian geometry. A fundamental tool in this shape analysis is the construction and implementation of geodesic paths between shapes on nonlinear manifolds. We use geodesic paths to accomplish a variety of tasks, including the definition of an intrinsic metric to compare shapes, the computation of intrinsic statistics for a given set of shapes, the estimation of optimal deformations on shape spaces, and the construction of smooth paths fitting a given set of shapes. We demonstrate this approach using three applications: (i) 3D face recognition according to their shapes, (ii) symmetrization of 2D and 3D objects, and (iii) 2D and 3D objects metamorphosis.