The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

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Remote Sensing And Image Interpretation

In the real world, a realistic setting for computer vision or multimedia recognition problems is that we have some classes containing lots of training data and many classes contain a small amount of training data. Therefore, how to use frequent classes to help learning rare classes for which it is harder to collect the training data is an open question. Learning with Shared Information is an emerging topic in machine learning, computer vision and multimedia analysis. There are different level of components that can be shared during concept modeling and machine learning stages, such as sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, etc. Regarding the specific methods, multi-task learning, transfer learning and deep learning can be seen as using different strategies to share information. These learning with shared information methods are very effective in solving real-world large-scale problems. This special issue aims at gathering the recent advances in learning with shared information methods and their applications in computer vision and multimedia analysis. Both state-of-the-art works, as well as literature reviews, are welcome for submission. Papers addressing interesting real-world computer vision and multimedia applications are especially encouraged. Topics of interest include, but are not limited to:  • Multi-task learning or transfer learning for large-scale computer vision and multimedia analysis • Deep learning for large-scale computer vision and multimedia analysis • Multi-modal approach for large-scale computer vision and multimedia analysis • Different sharing strategies, e.g., sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, • Real-world computer vision and multimedia applications based on learning with shared information, e.g., event detection, object recognition, object detection, action recognition, human head pose estimation, object tracking, location-based services, semantic indexing. • New datasets and metrics to evaluate the benefit of the proposed sharing ability for the specific computer vision or multimedia problem. • Survey papers regarding the topic of learning with shared information.  Authors who are unsure whether their planned submission is in scope may contact the guest editors prior to the submission deadline with an abstract, in order to receive feedback.

IEEE transactions on pattern analysis and machine intelligence

In this paper we introduce a novel method to detect and localize abnormal behaviors in crowd videos using Social Force model. For this purpose, a grid of particles is placed over the image and it is advected with the space-time average of optical flow. By treating the moving particles as individuals, their interaction forces are estimated using social force model. The interaction force is then mapped into the image plane to obtain Force Flow for every pixel in every frame. Randomly selected spatio-temporal volumes of Force Flow are used to model the normal behavior of the crowd. We classify frames as normal and abnormal by using a bag of words approach. The regions of anomalies in the abnormal frames are localized using interaction forces. The experiments are conducted on a publicly available dataset from University of Minnesota for escape panic scenarios and a challenging dataset of crowd videos taken from the web. The experiments show that the proposed method captures the dynamics of the crowd behavior successfully. In addition, we have shown that the social force approach outperforms similar approaches based on pure optical flow.

Abnormal crowd behavior detection using social force model

In this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from computer vision, originally designed for quasi-rigid motions with stable salient features, are not well adapted in this context. We thus investigate a dedicated minimization-based motion estimator. The cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics, which is compatible with large displacements. This term is associated with an original second-order div-curl regularization which prevents the washing out of the salient vorticity and divergence structures. The performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images. In addition, we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence.

/pdf/dense-estimation-of-fluid-flows-2c4woyl92v.pdf

Dense estimation of fluid flows

We present in this paper a novel approach dedicated to the measurement of velocity in fluid experimental flows through image sequences. Unlike most of the methods based on particle image velocimetry (PIV) approaches used in that context, the proposed technique is an extension of “optical-flow” schemes used in the computer vision community, which includes a specific enhancement for fluid mechanics applications. The method we propose enables to provide accurate dense motion fields. It includes an image based integrated version of the continuity equation. This model is associated to a regularization functional, which preserve divergence and vorticity blobs of the motion field. The method was applied on synthetic images and on real experiments carried out to allow a thorough comparison with a state-of-the-art PIV method in conditions of strong local free shear.

Fluid experimental flow estimation based on an optical-flow scheme. Experiments in fluids

We present in this paper a novel approach dedicated to the measurement of velocity in fluid experimental flows through image sequences. Unlike most of the methods based on particle image velocimetry (PIV) approaches used in that context, the proposed technique is an extension of ‘‘optical-flow'' schemes used in the computer vision community, which includes a specific enhancement for fluid mechanics applications. The method we propose enables to provide accurate densemotion fields. It includes an image based integrated version of the continuity equation. This model is associated to a regularization functional, which preserve divergence and vorticity blobs of the motion field. The method was applied on synthetic images and on real experiments carried out to allow a thorough comparison with a state-of-the-art PIV method in conditions of strong local free shear.

Fluid experimental flow estimation based on an Optical-flow scheme

Monitoring with high resolution land cover and especially of urban areas is a key task that is more and more required in a number of applications (urban planning, health monitoring, ecology, etc.). At the moment, some operational products, such as the “Copernicus High Resolution Imperviousness Layer”, are available to assess this information, but the frequency of updates is still limited despite the fact that more and more very high resolution data are acquired. In particular, the recent launch of the Sentinel-2A satellite in June 2015 makes available data with a minimum spatial resolution of 10 m, 13 spectral bands, wide acquisition coverage and short time revisits, which opens a large scale of new applications. In this work, we propose to exploit the benefit of Sentinel-2 images to monitor urban areas and to update Copernicus Land services, in particular the High Resolution Layer imperviousness. The approach relies on independent image classification (using already available Landsat images and new Sentinel-2 images) that are fused using the Dempster–Shafer theory. Experiments are performed on two urban areas: a large European city, Prague, in the Czech Republic, and a mid-sized one, Rennes, in France. Results, validated with a Kappa index over 0.9, illustrate the great interest of Sentinel-2 in operational projects, such as Copernicus products, and since such an approach can be conducted on very large areas, such as the European or global scale. Though classification and data fusion are not new, our process is original in the way it optimally combines uncertainties issued from classifications to generate more confident and precise imperviousness maps. The choice of imperviousness comes from the fact that it is a typical application where research meets the needs of an operational production. Moreover, the methodology presented in this paper can be used in any other land cover classification task using regular acquisitions issued, for example, from Sentinel-2.

Monitoring Urban Areas with Sentinel-2A Data: Application to the Update of the Copernicus High Resolution Layer Imperviousness Degree

The aim of this study was to assess the ability of optical images, SAR (Synthetic Aperture Radar) images and the combination of both types of data to discriminate between grasslands and crops in agricultural areas where cloud cover is very high most of the time, which restricts the use of visible and near-infrared satellite data. We compared the performances of variables extracted from four optical and five SAR satellite images with high/very high spatial resolutions acquired during the growing season. A vegetation index, namely the NDVI (Normalized Difference Vegetation Index), and two biophysical variables, the LAI (Leaf Area Index) and the fCOVER (fraction of Vegetation Cover) were computed using optical time series and polarization (HH, VV, HV, VH). The polarization ratio and polarimetric decomposition (Freeman–Durden and Cloude–Pottier) were calculated using SAR time series. Then, variables derived from optical, SAR and both types of remotely-sensed data were successively classified using the Support Vector Machine (SVM) technique. The results show that the classification accuracy of SAR variables is higher than those using optical data (0.98 compared to 0.81). They also highlight that the combination of optical and SAR time series data is of prime interest to discriminate grasslands from crops, allowing an improved classification accuracy.

Thomas Corpetti

Papers

Dense estimation of fluid flows

Fluid experimental flow estimation based on an optical-flow scheme. Experiments in fluids

Fluid experimental flow estimation based on an Optical-flow scheme

Monitoring Urban Areas with Sentinel-2A Data: Application to the Update of the Copernicus High Resolution Layer Imperviousness Degree

Combined Use of Multi-Temporal Optical and Radar Satellite Images for Grassland Monitoring