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A geometric multigrid approach to solving the 2D inhomogeneous Laplace equation with internal Dirichlet boundary conditions

A geometric multigrid approach to solving the 2D inhomogeneo...

引用

IEEE International Conference on Image Processing

作者： L. Grady T. Tasdizen R. Whitaker Department of Imaging and Visualization Siemens AG Corporate Research and Development Princeton NJ USA Scientific Computing and Imaging Institute Salt Lake UT USA

The inhomogeneous Laplace (Poisson) equation with internal Dirichlet boundary conditions has recently appeared in several applications to image processing and analysis. Although these approaches have demonstrated quality results, the computational burden of solution demands an efficient solver. Design of an efficient multigrid solver is difficult for these problems due to unpredictable inhomogeneity in the equation coefficients and internal Dirichlet conditions with arbitrary location and value. We present a geometric multigrid approach to solving these systems designed around weighted prolongation/restriction operators and an appropriate system coarsening. This approach is compared against a modified incomplete Cholesky conjugate gradient solver for a range of image sizes. We note that this approach applies equally well to the anisotropic diffusion problem and offers an alternative method to the classic multigrid approach of Acton (1998).

关键词： Laplace equations Boundary conditions Poisson equations Image segmentation Pixel Image processing Anisotropic magnetoresistance visualization Educational institutions Buildings

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Maximizing adaptivity in hierarchical topological models

Maximizing adaptivity in hierarchical topological models

引用

International Conference on Shape Modeling and Applications

作者： P.-T. Bremer V. Pascucci B. Hamann Department of Computer Science University of Illinois Urbana-Champaign USA Lawrence Livermore National Laboratory Center for Applied Scientific Computing USA Institute for Data Analysis and Visualization Department of Computer Science University of California Davis USA

We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Following concepts of Morse theory, a Morse-Smale complex (and therefore a function's topology) can be simplified by successively canceling pairs of critical points. We demonstrate how cancellations can be effectively encoded to produce a highly adaptive topology-based multi-resolution representation of a given function. Contrary to the approach, we avoid encoding the complete complex in a traditional mesh hierarchy. Instead, the information is split into a new structure we call a cancellation forest and a traditional dependency graph. The combination of this new structure with a traditional mesh hierarchy proofs to be significantly more flexible than the one previously reported. In particular, we can create hierarchies that are guaranteed to be of logarithmic height.

关键词： Topology Data visualization Data analysis Computer science Encoding Level set Shape scientific computing Laboratories Transfer functions

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Reversible N-bit to N-bit integer haar-like transforms

Reversible N-bit to N-bit integer haar-like transforms

引用

Proceedings of the Seventh IASTED International Conference on Computer Graphics and Imaging

作者： Senecal, Joshua G. Duchaineau, Mark A. Joy, Kenneth I. Inst. for Sci. Computing Research L-419 PO Box 808 Livermore CA 94551 United States Ctr. for Appl. Scientific Computing Lawrence Livermore Natl. Laboratory L-561 PO Box 808 Livermore CA 94551 United States Inst. Data Anal. and Visualization Computer Science Department University of California Davis One Shields Ave. Davis CA 95616 United States

We introduce TLHaar, an n-bit to n-bit reversible trans-form similar to the S-transform, TLHaar uses lookup tables that approximate the S-transform, but reorder the co-efficients so they fit into n bits. TLHaar is suited for loss-less compression in fixed-width channels, such as digital video channels and graphics hardware frame buffers. Tests indicate that when the incoming image data has lines or hard edges TLHaar coefficients compress better than S-transform coefficients. For other types of image data TL-Haar coefficients compress up to 2.5% worse than those of the S-transform, depending on the data and the compression method used.

关键词： Image compression

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SCIRun/BioPSE: integrated problem solving environment for bioelectric field problems and visualization

SCIRun/BioPSE: integrated problem solving environment for bi...

引用

IEEE International Symposium on Biomedical Imaging

作者： R.S. MacLeod O.M. Weinstein J. Davison de St Germain D.H. Brooks C.R. Johnson S.G. Parker Scientific Computing and Imaging Institute University of Utah Salt Lake UT USA Department of Electrical and Computer Engineering Northeastern University Boston MA USA Center for Bioelectric Field Modeling Simulation and Visualization NIH/NCRR

SCIRun is a general purpose problem solving environment that seeks to integrate the steps of preparing, executing, and visualizing simulations of physical and biological systems. The implementation of SCIRun is by means of an interactive dataflow network consisting of modules and data pipes exposed as a visual programming language. SCIRun also contains specific modules for bioelectric field simulations and visualizations and the combination of SCIRun with this package is known as BioPSE (***/software/biopse). This software has been in the public domain since 2000 and in that time we have developed strategies for software development, engineering, testing, documentation, and training. We have also continued to expand the scope of the SCIRun/BioPSE package not only through our own codes but by constructing bridges to other systems, both open source and proprietary. We have also created a repository for relevant sample networks and datasets with the aim of allowing diverse groups to test and evaluate algorithms using identical data and to share their results with the community for comparison of performance and accuracy. We present here a summary of the software system and describe specific experiences and conclusions with regard to creating and managing a large open source software project carried out within a university setting.

关键词： Biopsy Problem-solving Bioelectric phenomena Data visualization Biological system modeling Packaging Biological systems Computer languages Software packages Programming

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An improved N-bit to N-bit reversible Haar-like transform

An improved N-bit to N-bit reversible Haar-like transform

引用

Pacific Conference on Computer Graphics and Applications

作者： J.G. Senecal P. Lindstrom M.A. Duchaineau K.I. Joy Inst. for Sci. Comput. Res. Lawrence Livermore Nat. Lab. CA USA Center for Applied Scientific Computing Lawrence Livemore National Laboratory USA Institute for Data Analysis and Visualization Computer Science Department University of California Davis USA

We introduce the piecewise-linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and is therefore uniquely usable with both lossy and lossless methods (e.g. image compression). PLHaar has both integer and continuous (i.e. non-discrete) forms. By keeping the coefficients to n bits PLHaar is particularly suited for use in hardware environments where channel width is limited, such as digital video channels and graphics hardware.

关键词： Wavelet transforms Continuous wavelet transforms Hardware Dynamic range Image coding scientific computing Image reconstruction Laboratories Data analysis Data visualization

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Double exponential smoothing: An alternative to Kalman filter-based predictive tracking

Double exponential smoothing: An alternative to Kalman filte...

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9th EUROGRAPHICS Workshop on Virtual Environments, EGVE 2003

作者： LaViola Jr., Joseph J. Brown University Technology Center for Advanced Scientific Computing and Visualization PO Box 1910 Providence RI 02912 United States

ISBN: (纸本)1581136862

We present novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing. These algorithms, when compared against Kalman and extended Kalman filter-based predictors with derivative free measurement models, run approximately 135 times faster with equivalent prediction performance and simpler implementations. This paper describes these algorithms in detail along with the Kalman and extended Kalman Filter predictors tested against. In addition, we describe the details of a predictor experiment and present empirical results supporting the validity of our claims that these predictors are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors. © 2003 The Eurographics Association.

关键词： Extended Kalman filters

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A testbed for studying and choosing predictive tracking algorithms in virtual environments

A testbed for studying and choosing predictive tracking algo...

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9th EUROGRAPHICS Workshop on Virtual Environments, EGVE 2003

作者： LaViola Jr., Joseph J. Brown University Technology Center for Advanced Scientific Computing and Visualization PO Box 1910 Providence RI 02912 United States

ISBN: (纸本)1581136862

We present a testbed for comparing predictive tracking algorithms that allows virtual environment system developers to make better choices about which predictors to use in their environments and aids researchers in determining how predictors work across various virtual environment configurations. Our testbed saves the virtual environment developer and researcher both time and effort with the important task of reducing dynamic tracking error and masking latency. The testbed consists of three components: a prediction algorithm library, a motion data repository, and a graphical testing application which provides users with the ability to test different predictive tracking algorithms across a variety of user motion sequences. The testbed provides enough generality for testing across different algorithmic and system parameters such as sampling rate, prediction time, and noise variance. The paper describes the contents of the predictor library and how to extend it, the types of motion data sets collected thus far, the motion data preparation methodology, and the graphical testing application's functionality and architecture. A simple testing scenario showing output from the testbed is also presented. © 2003 The Eurographics Association.

关键词： Testbeds

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A testbed for studying and choosing predictive tracking algorithms in virtual environments 03

A testbed for studying and choosing predictive tracking algo...

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Proceedings of the workshop on Virtual environments 2003

作者： Joseph J. LaViola Brown University Technology Center for Advanced Scientific Computing and Visualization Providence RI

ISBN: (纸本)9781581136869

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Double exponential smoothing: an alternative to Kalman filter-based predictive tracking 03

Double exponential smoothing: an alternative to Kalman filte...

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Proceedings of the workshop on Virtual environments 2003

作者： Joseph J. LaViola Brown University Technology Center for Advanced Scientific Computing and Visualization Providence RI

ISBN: (纸本)9781581136869

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An experiment comparing double exponential smoothing and Kalman filter-based predictive tracking algorithms

An experiment comparing double exponential smoothing and Kal...

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IEEE Annual International Symposium Virtual Reality

作者： J.J. LaViola Advanced Scientific Computing and Visualization Brown University Technology Center Providence RI USA

We present an experiment comparing double exponential smoothing and Kalman filter-based predictive tracking algorithms with derivative free measurement models. Our results show that the double exponential smoothers run approximately 135 times faster with equivalent prediction performance. The paper briefly describes the algorithms used in the experiment and discusses the results.

关键词： Smoothing methods Kalman filters Prediction algorithms Equations Vectors Predictive models Quaternions Interpolation scientific computing visualization

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