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Bayesian Segmentation via Asymptotic Partition Functions
April 2000 (vol. 22 no. 4)
pp. 337-347

Abstract—Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary 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 differential 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-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.

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Index Terms:
Gaussian Markov random fields, texture segmentation, stochastic difference equations.
Citation:
Aaron D. Lanterman, Ulf Grenander, Michael I. Miller, "Bayesian Segmentation via Asymptotic Partition Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 4, pp. 337-347, April 2000, doi:10.1109/34.845376
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