Asymptotic global confidence regions in parametric shape estimation problems

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We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramer-Rao bounds are used to define an asymptotic confidence region, centered around the true boundary. Computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem, because the estimate is a two-dimensional nonstationary random process. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to asymptotic confidence regions Formed around the estimated boundaries, lower-bounding the probability that the entire true boundary lies within the confidence region. The results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities. These asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences, Numerical simulations suggest that the new bounds are quite tight.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2000-08
Language
English
Article Type
Article
Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.46, no.5, pp.1881 - 1895

ISSN
0018-9448
URI
http://hdl.handle.net/10203/69959
Appears in Collection
AI-Journal Papers(저널논문)
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