Uncertainty in Geometric Computations

1. Front Matter

   Pages i-xviii

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2. Affine Intervals in a CSG Geometric Modeller

   • Adrian Bowyer, Ralph Martin, Huahao Shou, Irina Voiculescu

   Pages 1-14

3. Fast and Reliable Plotting of Implicit Curves

   • Katja Buehler

   Pages 15-28

4. Data Assimilation with Sequential Gaussian Processes

   • Lehel Csato, Dan Cornford, Manfred Opper

   Pages 29-39

5. Conformal Geometry, Euclidean Space and Geometric Algebra

   • Chris Doran, Anthony Lasenby, Joan Lasenby

   Pages 41-58

6. Towards the Robust Intersection of Implicit Quadrics

   • Laurent Dupont, Sylvain Lazard, Sylvain Petitjean, Daniel Lazard

   Pages 59-68

7. Computational Geometry and Uncertainty

   • A. R. Forrest

   Pages 69-77

8. Geometric Uncertainty in Solid Modeling

   • Pierre J. Malraison, William A. Denker

   Pages 79-89

9. Reliable Geometric Computations with Algebraic Primitives and Predicates

   • Mark Foskey, Dinesh Manocha, Tim Culver, John Keyser, Shankar Krishnan

   Pages 91-106

10. Feature Localization Error in 3D Computer Vision

    • Daniel D. Morris, Takeo Kanade

    Pages 107-117

11. Bayesian Analysis of Computer Model Outputs

    • Jeremy Oakley, Anthony O’Hagan

    Pages 119-130

12. B

    • T. Poggio, S. Mukherjee, R. Rifkin, A. Raklin, A. Verri

    Pages 131-141

13. Affine Arithmetic and Bernstein Hull Methods for Algebraic Curve Drawing

    • Huahao Shou, Ralph Martin, Guojin Wang, Irina Voiculescu, Adrian Bowyer

    Pages 143-154

14. Local Polynomial Metrics for K Nearest Neighbor Classifiers

    • Robert R. Snapp

    Pages 155-164

15. Visualisation of Incomplete Data Using Class Information Constraints

    • Yi Sun, Peter Tino, Ian Nabney

    Pages 165-173

16. Towards Videorealistic Synthetic Visual Speech

    • Barry Theobald, J. Andrew Bangham, Silko Kruse, Gavin Cawley, Iain Matthews

    Pages 175-184

17. Properties of the Companion Matrix Resultant for Bernstein Polynomials

    • Joab R. Winkler

    Pages 185-198

18. Computation with a Number of Neurons

    • Si Wu, Danmei Chen

    Pages 199-207

19. Back Matter

    Pages 209-210

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This book contains the proceedings of the workshop Uncertainty in Geomet­ ric Computations that was held in Sheffield, England, July 5-6, 2001. A total of 59 delegates from 5 countries in Europe, North America and Asia attended the workshop. The workshop provided a forum for the discussion of com­ putational methods for quantifying, representing and assessing the effects of uncertainty in geometric computations. It was organised around lectures by invited speakers, and presentations in poster form from participants. Computer simulations and modelling are used frequently in science and engi­ neering, in applications ranging from the understanding of natural and artificial phenomena, to the design, test and manufacturing stages of production. This widespread use necessarily implies that detailed knowledge of the limitations of computer simulations is required. In particular, the usefulness of a computer simulation is directly dependent on the user's knowledge of the uncertainty in the simulation. Although an understanding of the phenomena being modelled is an important requirement of a good computer simulation, the model will be plagued by deficiencies if the errors and uncertainties in it are not consid­ ered when the results are analysed. The applications of computer modelling are large and diverse, but the workshop focussed on the management of un­ certainty in three areas : Geometric modelling, computer vision, and computer graphics.

• 3D
• Analysis
• Video
• algorithms
• ants
• computational geometry
• computer graphics
• computer simulation
• computer vision
• geometric modelling
• management
• model
• modeling
• simulation
• visualization

• University of Sheffield, UK

  Joab Winkler, Mahesan Niranjan

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