Edge detection using topological gradients: a scale-space approach

International audienceWe provide in this paper a link between two methods of edge detection: edge detection using scale-space analysis, and edge detection using topological asymptotic analysis. More precisely, we show that the topological gradient associated with an image u is given by a combination of the gradients of two smoothed versions of the image u at two different scales, namely φ⋆u and (φ⋆φ)⋆u, where φ is the fundamental so- lution of the elliptic restoration equation. In the same setting we propose a new edge detector based on the maximization of the variance of the image. Then we generalize our approach to Gaussian kernels considering a topological asymptotic analysis of the parabolic heat equation. A numerical comparison of these detectors together with the Canny edge detector is presented

Devoirs à domicile différenciés :: comment les instaurer et quelle en est la perception d’enseignants jurassiens ?

Ce travail de mémoire est basé sur la thématique des devoirs à domicile. En effet, il s’agit d’un thème très important, qui fait débat depuis plusieurs années maintenant, car beaucoup de personnes s’interrogent sur leur finalité. À cet effet, je me suis intéressée à une pratique très peu connue, qui est celle des devoirs à domicile différenciés. En effet, même si la différenciation est une pratique très actuelle dans les écoles jurassiennes, elle n’est pas présente lors de la distribution des devoirs à domicile. Afin de répondre aux diverses interrogations ayant trait à cette thématique, j’ai introduit cette pratique dans une classe de 4ème année, afin d’en observer les effets. Par conséquent, il a fallu réfléchir à toutes les modalités à mettre en place pour que cette manière de fonctionner puisse être avantageuse pour les élèves. Au terme de cette expérimentation, j’ai comparé mes résultats avec les avis de deux enseignantes, travaillant dans le même degré

TOPOLOGICAL ASYMPTOTIC ANALYSIS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS

International audienceTopological asymptotic expansions for quasilinear elliptic equations have not been studied yet. Such questions arise from the need to apply topological asymptotic methods in shape optimization to nonlinear elasticity equations as in imaging to detect sets with codimensions ≥ 2 (e.g. points in 2D or segments in 3D). Our main contribution is to provide topological asymptotic expansions for a class of quasilinear elliptic equations, perturbed in non-empty subdomains. The obtained topological gradient can be split into a classical linear term and a new term which accounts for the non linearity of the equation. With respect to topological asymptotic analysis, moving from linear equations onto quasilinear ones requires to heavily revise the implemented methods and tools. By comparison with the steps carried out to obtain such expansions with the Laplace equation, the core issue for a quasilinear equation lies in the ability to defi ne the variation of the direct state at scale 1 in R^N . Accordingly we build dedicated weighted quotient Sobolev spaces, which semi-norms encompass both the L^p norm and the L^2 norm of the gradient in R^N. Then we consider an appropriate class of quasilinear elliptic equations, to ensure that the problem de ning the direct state at scale 1 enjoys a combined p and 2 ellipticity property. The needed asymptotic behavior of the solution of the nonlinear interface problem in R^N is then proven. An appropriate duality scheme is set up between the direct and adjoint states at each stage of approximation

Toolkit for simulated commissioning of storage-ring light sources and application to the advanced light source upgrade accumulator

We present a new accelerator toolbox (AT)-based toolkit for simulating the commissioning of light-source storage rings. The toolkit provides a framework for supporting high-level scripts to represent with realism the various procedures (e.g., orbit and optics correction, beam-based alignment, etc.) encountered during commissioning and is designed to mirror as closely as possible the reality as seen from the control room. Emphasis is placed on the inclusion of a comprehensive set of error sources and faithful modeling of beam diagnostics. The toolkit capabilities are demonstrated in an application to the recent design and commissioning studies of the Advanced Light Source Upgrade (ALS-U) Accumulator Ring, a short-time successful commissioning of which will be critical to the overall ALS-U project success

Effects of carbonate on the electrolytic removal of ammonia and urea from urine with thermally prepared IrO2 electrodes

Recent studies have shown that electrolysis can be an efficient process for nitrogen removal from urine. These studies have been conducted with urea solutions or fresh urine, but urine collected in NoMix toilets and urinals has a substantially different composition, because bacteria hydrolyse urea quickly to ammonia and carbonate. In this study, we compared electrochemical removal of nitrogen from synthetic solutions of fresh and stored urine using IrO2 anodes. We could show that in fresh urine both ammonia and urea are efficiently eliminated, mainly through chlorine-mediated oxidation. However, in stored urine the presence of carbonate, arising from urea hydrolysis, leads to an inhibition of ammonia oxidation. We suggest two parallel mechanisms to explain this effect: the competition between chloride and carbonate oxidation at the anode and the competition between chlorate formation, enhanced by the buffering effect of carbonate, and ammonia oxidation for the consumption of active chlorine in the bulk. However, further experiments are needed to support the latter mechanism. In conclusion, this study highlights the negative consequences of the presence of carbonate in urine solutions, but also in other wastewaters, when subjected to an electrolytic treatment on IrO2 in alkaline medi