Uncertainty in Geometric Computations

by Winkler, Joab; Niranjan, Mahesan

• ISBN13: 9780792373094
• ISBN10: 079237309X
• Format: Hardcover
• Copyright: 2002-09-01
• Publisher: Kluwer Academic Pub

Summary

Computer simulations and modelling are used frequently in science and engineering, 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 a 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. Typical limitations of computer simulations include uncertainty in the data, parameter uncertainty, errors in the initial data, modelling errors, unmodelled phenomena, reduced order models, and approximations and numerical errors. Although an improvement in the physical understanding of the phenomena being modelled is an important requirement of a good computer simulation, the simulation will be plagued by deficiencies if the limitations listed above are not considered when analyzing its results. Since uncertainties can never be completely eliminated, they must be quantified and their propagation through the computations must be considered. The uses of computer modelling are diverse, and one particular application, the effect of uncertainty in geometric computations, is considered in this book. In particular, geometric computations occur extensively in geometric modelling, computer vision, computer graphics and pattern recognition. Uncertainty in Geometric Computations contains the proceedings of a workshop that was held in Sheffield, United Kingdom, in which the management and assessment of uncertainty in geometric computations was considered. The theme that unites these four subject areas is the requirement to perform computations on real geometric data, which (i) may have errors, for example, the tolerance of a coordinate measuring machine that is used in reverse engineering, and/or (ii) is incomplete because of occlusion, which may occur in computer vision, for example, a face recognition system. These characteristics of real geometric data impose tight constraints on the methods and algorithms that are used for their processing and interrogation, and this workshop provided a forum for their discussion. One of the novel features of the workshop was the wide background of the audience and invited speakers &e applied mathematicians, computer scientists and engineers &e and this provided a forum for the establishment of new collaborative links between mathematicians and engineers, thereby emphasizing the interdisciplinary nature of the many outstanding problems.

Table of Contents

Contributors and Participants	vii
Preface	xvii
Affine Intervals in a CSG Geometric Modeller	1	(14)
Adrian Bowyer
Ralph Martin
Huahao Shou
Irina Voiculescu
Fast and Reliable Plotting of Implicit Curves	15	(14)
Katja Buehler
Data Assimilation with Sequential Gaussian Processes	29	(12)
Lehel Csato
Dan Cornford
Manfred Opper
Conformal Geometry, Euclidean Space and Geometric Algebra	41	(18)
Chris Doran
Anthony Lasenby
Joan Lasenby
Towards the Robust Intersection of Implicit Quadrics	59	(10)
Laurent Dupont
Sylvain Lazard
Sylvain Petitjean
Daniel Lazard
Computational Geometry and Uncertainty	69	(10)
A.R. Forrest
Geometric Uncertainty in Solid Modeling	79	(12)
Pierre J. Malraison
William A. Denker
Reliable Geometric Computations with Algebraic Primitives and Predicates	91	(16)
Mark Foskey
Dinesh Manocha
Tim Culver
John Keyser
Shankar Krishnan
Feature Localization Error in 3D Computer Vision	107	(12)
Daniel D. Morris
Takeo Kanade
Bayesian Analysis of Computer Model Outputs	119	(12)
Jeremy Oakley
Anthony O'Hagan
b	131	(12)
T. Poggio
S. Mukherjee
R. Rifkin
A. Raklin
A. Verri
Affine Arithmetic and Bernstein Hull Methods for Algebraic Curve Drawing	143	(12)
Huahao Shou
Ralph Martin
Guojin Wang
Irina Voiculescu
Adrian Bowyer
Local Polynomial Metrics for k Nearest Neighbor Classifiers	155	(10)
Robert R. Snapp
Visualisation of Incomplete Data Using Class Information Constraints	165	(10)
Yi Sun
Peter Tino
Ian Nabney
Towards Videorealistic Synthetic Visual Speech	175	(10)
Barry Theobald
J. Andrew Bangham
Silko Kruse
Gavin Cawley
Iain Matthews
Properties of the Companion Matrix Resultant for Bernstein Polynomials	185	(14)
Joab R. Winkler
Computation with a Number of Neurons	199	(10)
Si Wu, Danmei Chen
Index	209