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Robert G. Aykroyd, "Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 533539, May, 1998.  
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@article{ 10.1109/34.682182, author = {Robert G. Aykroyd}, title = {Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {20}, number = {5}, issn = {01628828}, year = {1998}, pages = {533539}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.682182}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields IS  5 SN  01628828 SP533 EP539 EPD  533539 A1  Robert G. Aykroyd, PY  1998 KW  Adaptive smoothing KW  compound GaussMarkov random fields KW  coupled random fields KW  doubly stochastic random fields KW  Markov random fields KW  MetropolisHastings algorithm. VL  20 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described using a second random field. The coupled Markov random fields are used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation is based. All model parameters are estimated, in a fully Bayesian setting, using the MetropolisHastings algorithm. The full posterior estimation procedures are illustrated and compared using various artificial examples. For these examples the inhomogeneous model performs very favorably when compared to the homogeneous model, allowing differential degrees of smoothing and varying local textures.
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