Fundamental limits of Bayesian inference: order parameters andphase transitions for road tracking
Yuille, A.L.
Coughlan, J.M.
Smith-Kettlewell Eye Res. Inst., San Francisco, CA ;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Feb 2000
Volume: 22,
Issue: 2
On page(s): 160-173
ISSN: 0162-8828
References Cited: 30
CODEN: ITPIDJ
INSPEC Accession Number: 6540528
Digital Object Identifier: 10.1109/34.825754
Current Version Published: 2002-08-06
Abstract
There is a growing interest in formulating vision problems in
terms of Bayesian inference and, in particular, the maximum a posteriori
(MAP) estimator. In this paper, we consider the special case of
detecting roads from aerial images and demonstrate that analysis of this
ensemble enables us to determine fundamental bounds on the performance
of the MAP estimate. We demonstrate that there is a phase transition at
a critical value of the order parameter; below this phase transition, it
is impossible to detect the road by any algorithm. We derive closely
related order parameters which determine the time and memory complexity
of search and the accuracy of the solution using the n* search strategy.
Our approach can be applied to other vision problems, and we briefly
summarize the results when the model uses the “wrong prior”.
We comment on how our work relates to studies of the complexity of
visual search and the critical behaviour in the computational cost of
solving NP-complete problems
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