Convergence of Entropic Schemes for Optimal Transport and Gradient Flows

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach has recently been used successfully to solve optimal transport related problems in several applied fields such as imaging sciences, machine learning and social sciences. The main reason for this success is that, in contrast to linear programming solvers, the resulting algorithms are highly parallelizable and take advantage of the geometry of the computational grid (e.g. an image or a triangulated mesh). The first contribution of this article is the proof of the $\Gamma$-convergence of the entropic regularized optimal transport problem towards the Monge-Kantorovich problem for the squared Euclidean norm cost function. This implies in particular the convergence of the optimal entropic regularized transport plan towards an optimal transport plan as the entropy vanishes. Optimal transport distances are also useful to define gradient flows as a limit of implicit Euler steps according to the transportation distance. Our second contribution is a proof that implicit steps according to the entropic regularized distance converge towards the original gradient flow when both the step size and the entropic penalty vanish (in some controlled way)

A propos d'interactions qui permettent d'analyser une vidéo

National audienceWith a massive amount of new images and videos being produced every day, understanding visual content becomes a major issue in today's research. Can users be part of this process which is usually adressed by computer vision mechanisms ? We try in this paper to answer this question. We present here a method to analyze users' behaviour when viewing interactive videos (zoomable video) to detect regions of interest (ROI). We do not analyze spatio-temporal properties of the video but only traces of users' interactions, to detect the Region of Interest. We aim at investigating in future work the different ways of combining those two methods.Face à la production massive actuelle d'images et de vidéos numériques, la compréhension automatique de contenus visuels est un enjeu majeur. Quel peut-être le rôle des utilisateurs dans ce processus d'analyse qui s'appuie, aussi, sur des mécanismes de vision artificielle ? Telle est la question centrale soulevée dans cet article. L'approche suivie ici consiste à analyser le comportement des utilisateurs lorsqu'ils visionnent des vidéos interactives (zoomables) pour détecter des régions d'intérêt (ROI). La détection de ROI s'opère ici par analyse des usages (crowdsourcing) et non par analyse des propriétés spatio-temporelles du contenu de la vidéo. Notre objectif dans des travaux futurs est de montrer la complémentarité de ces deux méthodes et d'en étudier les modalités

A Video Timeline with Bookmarks and Prefetch State for Faster Video Browsing

International audienceReducing seek latency by predicting what the users will access is important for user experience, particularly during video browsing, where users seek frequently to skim through a video. Much existing research strived to predict user access pattern more accurately to improve the prefetching hit rate. This paper proposed a different approach whereby the prefetch hit rate is improved by biasing the users to seek to prefetched content with higher probability, through changing the video player user interface. Through a user study, we demonstrated that our player interface can lead to up to 4$\times$ more seeks to bookmarked segments and reduce seek latency by 40\%, compared to a video player interface commonly used today. The user study also showed that the user experience and the understanding of the video content when browsing is not compromised by the changes in seek behavior.

A Γ\Gamma-Convergence Result for the Upper Bound Limit Analysis of Plates

Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have proposed to use various finite elements discretizations. We provide in this paper a mathematical analysis which ensures the convergence of the finite element method, even with finite elements with discontinuous derivatives such as the quadratic 6 node Lagrange triangles and the cubic Hermite triangles. More precisely, we prove the $\Gamma$-convergence of the discretized problems towards the continuous limit analysis problem. Numerical results illustrate the relevance of this analysis for the yield design of both homogeneous and non-homogeneous materials

Food safety objectives and management of the risk of staphylococcal food poisoning from cream-filled baked goods

The concept of food safety objectives recently proposed by the International Commission on Microbiological Specifications for Foods (ICMSF) is designed to convert the appropriate level of protection of the consumer health into a sanitary objective applicable to foods. Food safety objectives are hence defined as maximum frequencies and/or concentrations of microbiological hazards in foodstuffs at the time of consumption. This concept is illustrated using a recently published study on the risk of staphylococcal food poisoning from cream-filled baked goods. Although interesting for its educational aspect, this example evades however some technical difficulties hidden behind such an approach. The definition of food safety objectives demonstrates an important progress in the management of food safety, but refinements must be made to properly integrate this concept into risk estimation schemes.Le concept d'objectifs de sécurité des aliments récemment proposé par la Commission internationale pour la définition des caractéristiques microbiologiques des aliments (ICMSF) permet de convertir le niveau approprié de protection de la santé des consommateurs en objectif sanitaire applicable au niveau des aliments. Les objectifs de sécurité des aliments correspondent donc à des fréquences et/ou des concentrations maximales de dangers microbiologiques présents dans des aliments au moment de leur consommation. Cet article illustre ce concept à partir d'un exemple publié récemment concernant le risque d'intoxination staphylococcique liée à la consommation de pâtisseries à la crème. Cet exemple, intéressant par son aspect pédagogique, élude cependant certaines difficultés techniques qui se cachent derrière une telle approche. La définition de ces objectifs de sécurité des aliments constitue donc une évolution notable dans la démarche de gestion de la sécurité sanitaire des aliments mais des réflexions doivent encore être menées afin de l'intégrer correctement dans les démarches d'estimation des risques

Modelling of Listeria monocytogenes growth infoods

Les modèles de microbiologie prévisionnelle permettent de simuler la croissance des populations de Listeria monocytogenes dans les aliments. L’approche progressive avec interactions semble la plus fiable pour simuler ces comportements, mais celle-ci se heurte encore à certaines limites comme l’aspect stochastique de la modélisation de la croissance ou l’intégration de l’effet de traitements induisant des stress bactériens. Malgré cela, l’outil se révèle utile dans la détermination des durées de vie des denrées alimentaires.Predictive modelling allows to simulate the growth of Listeria monocytogenes in foods. The multiplicative type model including interactions between environmental factors seems the more reliable to simulate these growths, but there are still some lacks as the stochastic modelling or the inclusion of the effect of process inducing bacterial injury. In spite of this, the tool is prove to be useful for the calculation of food shelf fifes

Quality Control in Crowdsourced Object Segmentation

International audienceThis paper explores processing techniques to deal with noisy data in crowdsourced object segmentation tasks. We use the data collected with "Click'n'Cut", an online interactive segmentation tool, and we perform several experiments towards improving the segmentation results. First, we introduce different superpixel-based techniques to filter users' traces, and assess their impact on the segmentation result. Second, we present different criteria to detect and discard the traces from potential bad users, resulting in a remarkable increase in performance. Finally, we show a novel superpixel-based segmentation algorithm which does not require any prior filtering and is based on weighting each user's contribution according to his/her level of expertise

Crowdsourced object segmentation with a game

We introduce a new algorithm for image segmentation based on crowdsourcing through a game : Ask'nSeek. The game provides information on the objects of an image, under the form of clicks that are either on the object, or on the background. These logs are then used in order to determine the best segmentation for an object among a set of candidates generated by the state-of-the-art CPMC algorithm. We also introduce a simulator that allows the generation of game logs and therefore gives insight about the number of games needed on an image to perform acceptable segmentation.Peer ReviewedPostprint (published version

Grey Box Implementation of Block Ciphers Preserving the Confidentiality of their Design

In 1997,Patarin and Goubin introduce new asymmetric cryptosystems based on the difficulty of recovering two systems of multivariate polynomials from their composition. We make a different use of this difficult algorithmic problem to obtain a way of representing block ciphers concealing their design but still leaving them executable. We show how to implement our solution with Field Programmable Gate Array. Finally, we give a compact representation of our solution using Binary Decision Diagrams

Protocols and Software for Simplified Educational Video Capture and Editing

Recently, educational videos have become important parts of e-learning systems which have in turn become widely used due to their flexibility. These videos should be of high quality since higher production values lead to superior learning outcomes. However, creating high-quality video is a difficult task for teachers since it needs technical knowledge that includes video recording and timeline usage. Hence, creating educational video production software, that is at the same time easy-to-use and able to produce high-quality educational videos, is very advantageous. In this paper, we developed protocols for an easy-to-use piece of software that enables teachers who have little technological background to produce their own educational videos autonomously. In fact, our contribution is to reduce the complexity of the whole video production process by introducing a preparation step based on micro-teaching and upstream specification. An evaluation of the software with six teachers is performed. This evaluation, based on think-aloud protocol and quantitative measurements, showed that the introduction of the preparation step allowed the participant teachers to produce high-quality educational videos in less than three hours