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Bayesian Segmentation via Asymptotic Partition Functions (2000)
| Citations: | 4 - 0 self |
BibTeX
@MISC{Lanterman00bayesiansegmentation,
author = {Aaron D. Lanterman and Ulf Gren and Michael I. Miller and Senior Member},
title = {Bayesian Segmentation via Asymptotic Partition Functions},
year = {2000}
}
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Abstract
Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic di#erence equations determined by finitely supported, stationary, linear di#erence operators, adjusted to be non-stationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the di#erential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-m...
Keyphrases
bayesian segmentation asymptotic partition function gaussian random field log-normalizer converges partition function field amount random field linear di erence operator variable orientation matrix analysis technique texture parameter stochastic di erence equation asymptotic maximum-likelihood underlying shape increase directional model partial derivative mixture isotropic model asymptotic approximation
