Bayesian segmentation via asymptotic partition functions
Lanterman, A.D.; Grenander, U.; Miller, M.I.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume 22, Issue 4, Apr 2000 Page(s):337 - 347
Digital Object Identifier 10.1109/34.845376
Summary: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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