Quantitative speeds of convergence for exposure to food contaminants

In this paper we consider a class of piecewise-deterministic Markov processes (PDMPs) modeling the quantity of a given food contaminant in the body. On the one hand, the amount of contaminant increases with random food intakes and, on the other hand, decreases thanks to the release rate of the body. Our aim is to provide quantitative speeds of convergence to equilibrium for the total variation and Wasserstein distances via coupling methods.Comment: 20 page

Fluctuations of the Empirical Measure of Freezing Markov Chains

In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We are interested in the long time behavior of the empirical measure of this freezing Markov chain. Some recent papers provide almost sure convergence and convergence in distribution in the case of the freezing speed $n^{-\theta}$, with different limits depending on $\theta<1,\theta=1$ or $\theta>1$. Using stochastic approximation techniques, we generalize these results for any freezing speed, and we obtain a better characterization of the limit distribution as well as rates of convergence as well as functional convergence.Comment: 30 page

Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories

In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the standard "Tightness/Identification" argument; our method is unified and based on the notion of pseudotrajectories on the space of probability measures

"A Novel Feature-Based Approach for Indoor Monocular SLAM"

Camera tracking and the construction of a robust and accurate map in unknown environments are still challenging tasks in computer vision and robotic applications. Visual Simultaneous Localization and Mapping (SLAM) along with Augmented Reality (AR) are two important applications, and their performance is entirely dependent on the accuracy of the camera tracking routine. This paper presents a novel feature-based approach for the monocular SLAM problem using a hand-held camera in room-sized workspaces with a maximum scene depth of 4–5 m. In the core of the proposed method, there is a Particle Filter (PF) responsible for the estimation of extrinsic parameters of the camera. In addition, contrary to key-frame based methods, the proposed system tracks the camera frame by frame and constructs a robust and accurate map incrementally. Moreover, the proposed algorithm initially constructs a metric sparse map. To this end, a chessboard pattern with a known cell size has been placed in front of the camera for a few frames. This enables the algorithm to accurately compute the pose of the camera and therefore, the depth of the primary detected natural feature points are easily calculated. Afterwards, camera pose estimation for each new incoming frame is carried out in a framework that is merely working with a set of visible natural landmarks. Moreover, to recover the depth of the newly detected landmarks, a delayed approach based on linear triangulation is used. The proposed method is applied to a realworld VGA quality video (640 × 480 pixels) where the translation error of the camera pose is less than 2 cm on average and the orientation error is less than 3 degrees, which indicates the effectiveness and accuracy of the developed algorithm

Bob Flanagan, quand les performances d’un supermasochist exorcisent la mort

Since the end of the last century, we&rsquo;ve noticed in our western society an uneasiness regarding the mention of death. Whereas some mystical dimension allowed man to give death a meaning, the Hegelian-Nietzschean prophecy of the death of God made this impossible. Indeed, knowing that the promise of a Kingdom of Heaven was not assured any more, man prefered to obscure the death that haunted him. Despite the difficulty to face this ontological condition, we can see that the subject of death is more and more present on the contemporary artistic scene. The body which is central in relation to this problematic becomes for the artist the material through which death exorcizes and declines itself. However, from Body Art achievements to the exhibition of corpses, we can see that the experiment of death only seems possible through the treatment of the body as a martyr. If Body Art protagonists seem to find in it their model to experiment the human being in the limits of their own bodies and thus comprehend death, there are others for whom it&rsquo;s the diagnosed death that is shaping the relationship to their own bodies. That&rsquo;s the case with Bob Flanagan. Doomed since childhood by cystic fibrosis, we will see how this artist, by the detour of borderline achievements with a masochistic tendency and ritualised on a setting of Christianity, will redefine his relationship to the body experience and through this manage to exorcize the idea of an impending death.&nbsp

Étude quantitative de processus de Markov déterministes par morceaux issus de la modélisation

The purpose of this Ph.D. thesis is the study of piecewise deterministic Markov processes, which are often used for modeling many natural phenomena. Precisely, we shall focus on their long time behavior as well as their speed of convergence to equilibrium, whenever they possess a stationary probability measure. Providing sharp quantitative bounds for this speed of convergence is one of the main orientations of this manuscript, which will usually be done through coupling methods. We shall emphasize the link between Markov processes and mathematical fields of research where they may be of interest, such as partial differential equations. The last chapter of this thesis is devoted to the introduction of a unified approach to study the long time behavior of inhomogeneous Markov chains, which can provide functional limit theorems with the help of asymptotic pseudotrajectories.L'objet de cette thèse est d'étudier une certaine classe de processus de Markov, dits déterministes par morceaux, ayant de très nombreuses applications en modélisation. Plus précisément, nous nous intéresserons à leur comportement en temps long et à leur vitesse de convergence à l'équilibre lorsqu'ils admettent une mesure de probabilité stationnaire. L'un des axes principaux de ce manuscrit de thèse est l'obtention de bornes quantitatives fines sur cette vitesse, obtenues principalement à l'aide de méthodes de couplage. Le lien sera régulièrement fait avec d'autres domaines des mathématiques dans lesquels l'étude de ces processus est utile, comme les équations aux dérivées partielles. Le dernier chapitre de cette thèse est consacré à l'introduction d'une approche unifiée fournissant des théorèmes limites fonctionnels pour étudier le comportement en temps long de chaînes de Markov inhomogènes, à l'aide de la notion de pseudo-trajectoire asymptotique

Rolling Shutter Stereo

A huge fraction of cameras used nowadays is based on CMOS sensors with a rolling shutter that exposes the image line by line. For dynamic scenes/cameras this introduces undesired effects like stretch, shear and wobble. It has been shown earlier that rotational shake induced rolling shutter effects in hand-held cell phone capture can be compensated based on an estimate of the camera rotation. In contrast, we analyse the case of significant camera motion, e.g. where a bypassing streetlevel capture vehicle uses a rolling shutter camera in a 3D reconstruction framework. The introduced error is depth dependent and cannot be compensated based on camera motion/rotation alone, invalidating also rectification for stereo camera systems. On top, significant lens distortion as often present in wide angle cameras intertwines with rolling shutter effects as it changes the time at which a certain 3D point is seen. We show that naive 3D reconstructions (assuming global shutter) will deliver biased geometry already for very mild assumptions on vehicle speed and resolution. We then develop rolling shutter dense multiview stereo algorithms that solve for time of exposure and depth at the same time, even in the presence of lens distortion and perform an evaluation on ground truth laser scan models as well as on real street-level data

Crowd Behavior Understanding through SIOF Feature Analysis

Realizing the automated and online detection of crowd anomalies from surveillance CCTVs is a research-intensive and application-demanding task. This research proposes a novel technique for detecting crowd abnormalities through analyzing the spatial and temporal features of the input video signals. This integrated solution defines an image descriptor that reflects the global motion information over time. A non-linear SVM has then been adopted to classify dominant or large-scale crow d abnormal behaviors. The work reported has focused on: 1) online (or near real-time) detection of moving objects through a background subtraction model, namely ViBe; and to identify the saliency information as a spatial feature in addition to the optical flow of the motion foreground as the temporal feature; 2) to combine the extracted spatial and temporal features into a novel SIOF descriptor that encapsulates the global movement characteristic of a crowd; 3) the optimization of a nonlinear support vector machine (SVM) as classifier to detect suspicious crowd behaviors. The test and evaluation of the devised models and techniques have selected the BEHAVE database as the primary experimental data sets. Results against benchmarking models and systems have shown promising advancements in terms of the accuracy and efficiency for detecting crowd anomalies

LONG TIME BEHAVIOR OF MARKOV PROCESSES AND BEYOND

International audienceThis note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as propagation of chaos, coupling, functional inequalities, provide a good picture of the classical methods that furnish quantitative rates of convergence to equilibrium.Cet article présente plusieurs progrés récents dans l'étude du comportement en temps long de certains processus de Markov. Les exemples présentés ci-dessous sont motivés par différentes applications issues de la physique ou de la biologie. Les outils mathématiques employés, propagation du chaos, couplage, inégalités fonctionnelles, couvrent un large spectre des techniques disponibles pour obtenir des comportements en temps long quantitatifs

Visual navigation using a single camera

We assess the usefulness of monocular recursive motion estimation techniques for vehicle navigation in the absence of a model for the environment. For this purpose we extend a recently proposed recursive motion estimator, the Essential filter, to handle scale estimation. We examine experimentally the accuracy with which the motion and position of the vehicle may be computed on an 8000 frame indoors sequence. The issues of sampling time frequency and number of necessary features in the environment are addressed systematically