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On the Estimation of Markov Random Field Parameters
March 1999 (vol. 21 no. 3)
pp. 216-224
ASCII Text
x 
 
Carlos F. Borges, "On the Estimation of Markov Random Field Parameters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 216-224, March, 1999.
 
 
BibTex
x
 
@article{ 10.1109/34.754587,
author = {Carlos F. Borges},
title = {On the Estimation of Markov Random Field Parameters},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {21},
number = {3},
issn = {0162-8828},
year = {1999},
pages = {216-224},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.754587},
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 - On the Estimation of Markov Random Field Parameters
IS - 3
SN - 0162-8828
SP216
EP224
EPD - 216-224
A1 - Carlos F. Borges,
PY - 1999
KW - Markov random fields
KW - parameter estimation.
VL - 21
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

Abstract—We examine the histogram method proposed in [1] for estimating the parameters associated with a Markov random field. This method relies on the estimation of the local interaction sums from histogram data. We derive an estimator for these quantities that is optimal in a well-defined sense. Furthermore, we show that the final step of the histogram method, the solution of a least-squares problem, can be done substantially faster than one might expect if no equation culling is used. We also examine the use of weighted least-squares and see that this seems to lead to better estimates even with small amounts of data.

[1] 216 H. Derin and H. Elliott, "Modelling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp. 39-55, Jan. 1987.[2] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistical Soc., Series B, vol. 2, 1974.[3] G. Cross and A. Jain, "Markov Random Field Texture Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 1, 1983.[4] M. Gurelli and L. Onural, "On a Parameter Estimation Method for Gibbs-Markov Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 4, Apr. 1994.[5] C. Gauss, "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," Classics in Applied Mathematics, SIAM, 1995.[6] B. Calder, L. Linnett, S. Clarke, and D. Carmichael, "Improvements in Markov Random Field Parameter Estimation," IEE E4 Colloquium on Multiresolution Image Processing.London: IEE, Apr. 1995, no. 1995/077.[7] G. Golub and C. Van Loan, Matrix Computations, third ed. Baltimore: Johns Hopkins Univ. Press, 1996.

Index Terms:
Markov random fields, parameter estimation.
Citation:
Carlos F. Borges, "On the Estimation of Markov Random Field Parameters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 216-224, Mar. 1999, doi:10.1109/34.754587
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