L'équipe A3SI du LIGM (unité mixte de recherche de l'Université Paris Est) organise un atelier doctorants le jeudi 11 mai de 13h00 à 15h00 à ESIEE Paris (amphi 260).
Quatre doctorants exposeront leurs travaux :
Abstract: Euclidean rotations in R^2 are bijective and isometric maps, but they lose generally theseproperties when digitized in discrete spaces. In particular, the topological and geometrical defects of digitized rigid motions on the square grid have been studied. In this context, the main problem is related to the incompatibility between the square grid and rotations; in general, one has to accept either relatively high loss of information or non-exactness of the applied digitized rigid motion. Motivated by these considerations, we study digitized rigid motions on the hexagonal grid. We establish a framework for studying digitized rigid motions in the hexagonal grid---previously proposed for the square grid and known as neighborhood motion maps. This allows us to study non-injective digitized rigid motions on the hexagonal grid and to compare the loss of informationbetween digitized rigid motions defined on the two grids.
Abstract: We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm.
Abstract: Studies on fish embryo models are widely developed in research. They are used in several research field such as drug discovery or environmental toxicology. In this article, we propose an entirely automated assay to detect cardiac arrest in Medaka (Oryzias latipes) based on image analysis. We propose a multi-scale pipeline based on mathematical morphology. Starting from video sequences of entire wells in 24-well plates, we focus on the embryo, detect its heart, and ascertain whether or not the heart is beating based on intensity variation analysis. Our image analysis pipeline only uses commonly available operators. It has a low computational cost, allowing analysis at the same rate as acquisition. From an initial dataset of 3,192 videos, 660 were discarded as unusable (20.7%), 655 of them correctly so (99.25%) and only 5 incorrectly so (0.75%). The 2,532 remaining videos were used for our test. On these, 45 errors were made, leading to a success rate of 98.23%.
Abstract: We investigate the behaviour of incidence relations between points and geometric shapes (i.e., geometric set systems). Using recent advances on 'shallow packings', we develop the theory of Mnets. Those are a combinatorial analogue of Macbeath regions in convex geometry. We obtain asymptotically tight bounds on the size of Mnets for common shapes. Our results on Mnets imply all classical bounds on ε-nets, a staple of computational geometry.