A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This data assimilation scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor to capture temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottom tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs velocity and height of the free surface flow based on noisy measurements of the elevation alone

Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating

Many dating techniques include significant error terms which are not independent between samples to date. This is typically the case in Optically Stimulated Luminescence (OSL) dating where the conversion from characteristic equivalent doses to the corresponding ages using the annual dosimetry data includes error terms that are common to all produced datings. Dealing with these errors is essential to estimate ages from a set of datings whose chronological ordering is known. In this work, we propose and we study a Bayesian model to address this problem. For this purpose, we first consider a multivariate model with multiplicative Gaussian errors in a Bayesian framework.This model relates a set of characteristic equivalent doses to the corresponding ages while taking into account for the systematic and non-systematic errors associated to the dosimetry. It thus offers the opportunity to deal properly with stratigraphic constraints within OSL datings, but also with other datings possessing errors which are independent from systematic errors of OSL (e.g. radiocarbon). Then, we use this model to extend an existing Bayesian model for the assessment of characteristic equivalent doses from Single Aliquot and Regenerative (SAR) dose measurements. The overall Bayesian model leads to the joint estimation of all the variables (which include all the dose-response functions and characteristic equivalent doses) of a sequence of, possibly heterogeneous, datings. We also consider a more generic solution consisting in using directly the age model from a set of characteristic equivalent dose estimates and their associated standard errors. We finally give an example of application on a set of five OSL datings with stratigraphic constraints and observe a good adequacy between the two approaches

An efficient EM-ICP algorithm for non-linear registration of large 3D point sets

International audienc

A new efficient EM-ICP algorithm for non-linear registration of 3D point sets

In this paper, we present a new method for non-linear pairwise registration of point sets. In this method, we consider the points of the first set as the draws of a Gaussian mixture model whose centres are the points of the second set displaced by a deformation. Next we perform {\it maximum a posteriori} estimation of the parameters (which include the unknown transformation) of this model using the expectation-maximisation algorithm. Compared to other methods using the same ''EM-ICP'' paradigm/framework, we propose three key modifications leading to an efficient algorithm allowing for fast registration of large point sets: 1) symmetrisation of the point-to-point correspondences; 2) specification of priors on these correspondences using differential geometry; 3) efficient encoding of deformations using the RKHS theory and the Fourier analysis. The resulting algorithm is efficient and is able to register large data sets. We evaluate the added value of the modifications and compare our method to the state-of-the-art CPD algorithm on synthetic data.Dans cet article, nous présentons une nouvelle méthode pour le recalage non-linéaire de deux nuages de points. Dans cette méthode, nous considérons les points du premier nuage comme la réalisation d'un mélange de gaussiennes dont les centres sont les points du second ensemble déplacés par une déformation. Ensuite, nous estimons cette déformation, sur laquelle nous fixons un a priori, selon le principe du maximum a posteriori en utilisant l'algorithme "expectation-maximisation". Par rapport aux autres méthodes qui utilisent un paradigme similaire, nous proposons de: 1) symétriser le processus de correspondance entre les points des deux nuages, 2) spécifier des a priori sur les correspondances en utilisant des outils de la géométrie différentielle et 3) caractériser la déformation à estimer en utilisant la théorie des espaces de Hilbert à noyaux reproduisants et l'analyse de Fourier. L'algorithme résultant est relativement efficace et permet de recaler des nuages de points de grandes tailles. Enfin, nous évaluons l'impact de ces modifications puis nous comparons notre méthode à une méthode de l'état de l'art

Non-Linear Reduced Modeling by Generalized Kernel-Based Dynamic Mode Decomposition

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches

Multi-center (mono-vendor) longitudinal conventional and quantitative spinal cord MRI in Multiple Sclerosis at 3 Tesla - The EMISEP Study : First results

International audienc

Non-Linear Reduced Modeling by Generalized Kernel-Based Dynamic Mode Decomposition

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches

Non-Linear Reduced Modeling by Generalized Kernel-Based Dynamic Mode Decomposition

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing approximation and computational capabilities, and then solving the associated reduced model problem. More specifically, we propose a new efficient algorithm for data-driven reduced modeling of non-linear dynamics based on linear approximations in a RKHS. This algorithm takes advantage of the closed-form solution of a low-rank constraint optimization problem while exploiting advantageously kernel-based computations. Reduced modeling with this algorithm reveals a gain in approximation accuracy, as shown by numerical simulations, and in complexity with respect to existing approaches