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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. 337347, April, 2000.  
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@article{ 10.1109/34.845376, author = {Aaron D. Lanterman and Ulf Grenander and Michael I. Miller}, title = {Bayesian Segmentation via Asymptotic Partition Functions}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {22}, number = {4}, issn = {01628828}, year = {2000}, pages = {337347}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.845376}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Bayesian Segmentation via Asymptotic Partition Functions IS  4 SN  01628828 SP337 EP347 EPD  337347 A1  Aaron D. Lanterman, A1  Ulf Grenander, A1  Michael I. Miller, PY  2000 KW  Gaussian Markov random fields KW  texture segmentation KW  stochastic difference equations. VL  22 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
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 lognormalizer converges to the integral of the logspectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operatorinduced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximumlikelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actinmyocin complexes in electron micrographs and clutter in forwardlooking 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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