Asymptotic global confidence regions for 3-D parametric shape estimation in inverse problems

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This paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in R-3. Unlike conventional pixel-based image reconstruction approaches, our problem is reconstruction of the shape of binary or homogeneous objects. The fundamental uncertainty of such estimation problems can be represented by global confidence regions, which facilitate geometric inference and optimization of the imaging system. Compared to our previous work on global confidence region analysis for curves [two-dimensional (2-D) shapes], computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2-D variable. We derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional Gaussian random field, which can, in turn, be evaluated using the tube formula due to Sun. Simulation results demonstrate the tightness of the resulting bound and the usefulness of the three-dimensional global confidence region approach.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2006-10
Language
English
Article Type
Article
Keywords

CRAMER-RAO BOUNDS; EXCURSION SETS; RANDOM-FIELDS; MAXIMA; TUBES

Citation

IEEE TRANSACTIONS ON IMAGE PROCESSING, v.15, pp.2904 - 2919

ISSN
1057-7149
DOI
10.1109/TIP.2006.877524
URI
http://hdl.handle.net/10203/91044
Appears in Collection
BiS-Journal Papers(저널논문)
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