Type
Conference PaperKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionComputer Science Program
Visual Computing Center (VCC)
Date
2012-11-01Permanent link to this record
http://hdl.handle.net/10754/575790
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We 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.Citation
Hadwiger, 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:10.1145/2366145.2366152Journal
ACM Transactions on GraphicsConference/Event name
Proceedings of ACM SIGGRAPH Asia 2012ae974a485f413a2113503eed53cd6c53
10.1145/2366145.2366152
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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.