KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Visual Computing Center (VCC)
Permanent link to this recordhttp://hdl.handle.net/10754/575790
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AbstractWe introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters. © 2012 ACM.
CitationHadwiger, M., Sicat, R., Beyer, J., Krüger, J., & Möller, T. (2012). Sparse PDF maps for non-linear multi-resolution image operations. ACM Transactions on Graphics, 31(6), 1–12. doi:10.1145/2366145.2366152
JournalACM Transactions on Graphics
Conference/Event nameProceedings of ACM SIGGRAPH Asia 2012
CollectionsConference Papers; Computer Science Program; Computer Science Program; Visual Computing Center (VCC); Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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A Particle Filter-based Adaptive Inflation Scheme for the Ensemble Kalman FilterAit-El-Fquih, Boujemaa; Hoteit, Ibrahim (Quarterly Journal of the Royal Meteorological Society, Wiley, 2020-01-24) [Article]An adaptive covariance inflation scheme is proposed for the ensemble Kalman filter (EnKF) to mitigate for the loss of ensemble variance. Adaptive inflation methods are mostly based on a Bayesian approach, which considers the inflation factor as a random variable with a given prior probability distribution, and then combines it with the inflation likelihood through Bayes’ rule to obtain its posterior distribution. In this work, we introduce a numerical implementation of this generic Bayesian approach that uses a particle filter (PF) to compute a Monte Carlo approximation of the inflation posterior distribution. To alleviate the sample attrition issue, the proposed PF employs an artificial dynamical model for the inflation factor based on the well-known smoothing-kernel West and Liu model. The positivity constraint on the inflation factor is further imposed through an inverse-Gamma transition density, whose parameters suggest analytical expressions. The resulting PF-EnKF scheme is straightforward to implement, and can use different number of particles in its EnKF and PF components. Numerical experiments are conducted with the Lorenz-96 model to demonstrate the effectiveness of the proposed method under various experimental scenarios.
Particle Kalman Filtering: A Nonlinear Framework for Ensemble Kalman FiltersHoteit, Ibrahim; Luo, Xiaodong; Pham, Dinh-Tuan; Moroz, Irene M. (AIP Publishing, 2010-09-20) [Conference Paper]Optimal nonlinear filtering consists of sequentially determining the conditional probability distribution functions (pdf) of the system state, given the information of the dynamical and measurement processes and the previous measurements. Once the pdfs are obtained, one can determine different estimates, for instance, the minimum variance estimate, or the maximum a posteriori estimate, of the system state. It can be shown that, many filters, including the Kalman filter (KF) and the particle filter (PF), can be derived based on this sequential Bayesian estimation framework. In this contribution, we present a Gaussian mixture-based framework, called the particle Kalman filter (PKF), and discuss how the different EnKF methods can be derived as simplified variants of the PKF. We also discuss approaches to reducing the computational burden of the PKF in order to make it suitable for complex geosciences applications. We use the strongly nonlinear Lorenz-96 model to illustrate the performance of the PKF.
Filtering remotely sensed chlorophyll concentrations in the Red Sea using a space-time covariance model and a Kalman filterDreano, Denis; Mallick, Bani; Hoteit, Ibrahim (Spatial Statistics, Elsevier BV, 2015-04-27) [Article]A statistical model is proposed to filter satellite-derived chlorophyll concentration from the Red Sea, and to predict future chlorophyll concentrations. The seasonal trend is first estimated after filling missing chlorophyll data using an Empirical Orthogonal Function (EOF)-based algorithm (Data Interpolation EOF). The anomalies are then modeled as a stationary Gaussian process. A method proposed by Gneiting (2002) is used to construct positive-definite space-time covariance models for this process. After choosing an appropriate statistical model and identifying its parameters, Kriging is applied in the space-time domain to make a one step ahead prediction of the anomalies. The latter serves as the prediction model of a reduced-order Kalman filter, which is applied to assimilate and predict future chlorophyll concentrations. The proposed method decreases the root mean square (RMS) prediction error by about 11% compared with the seasonal average.