Abstract
We describe segmentation based on textures using the label and image model of D. Gemanet al., “Boundary Detection by Constrained Optimization,”IEEE Trans. Pattern Analysis and Machine Intelligence, 12(7):609–628, July 1990. We replace their maximuma posteriori estimation criterion with a Bayesian estimator that minimizes the sum of the pixel misclassification probabilities. The new estimation goal allows the use of a different computational algorithm, which is deterministic rather than random, based on approximating lattices by trees. An example demonstrating an accurate segmentation of a collage of Brodatz textures is included.
Similar content being viewed by others
References
Julian Besag. On the statistical analysis of dirty pictures.J. Royal Stat. Soc. B, 48:259–302, 1986.
Donald Geman, Stuart Geman, Christine Graffigne, and Ping Dong. Boundary detection by constrained optimization.IEEE Trans. PAMI, 12(7):609–627, July 1990.
Stuart Geman and Donald Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images.IEEE Trans. PAMI, 6(6):721–741, November 1984.
Christine Graffigne.Experiments in Texture Analysis and Segmentation. PhD thesis, Brown University, Providence, RI, May 1987.
J. Marroquin, S. Mitter, and T. Poggio. Probabilistic solution of ill—posed problems in computational vision.J. Am. Stat. Assoc., 82(397):76–89, 1987.
J. M. Ortega and W. C. Rheinboldt.Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, Inc., San Diego, 1970.
William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling.Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press, Cambridge, 2 edition, 1992.
Chi-hsin Wu.Deterministic Parallelizable Solutions for Bayesian Markov Random Field Estimation Problems. PhD thesis, Purdue University, West Lafayette, IN, USA, May 1994.
Chi-hsin Wu and Peter C. Doerschuk. Tree approximations to Markov random fields.IEEE Trans. PAMI, 17(4):391–402, April 1995.
Author information
Authors and Affiliations
Additional information
This work was supported by the Purdue Research Foundation, a Whirlpool Faculty Fellowship, U. S. National Science Foundation grant MIP-9110919, and the School of Electrical Engineering, Purdue University.
Rights and permissions
About this article
Cite this article
Wu, CH., Doerschuk, P.C. Texture-based segmentation using markov random field models and approximate Bayesian estimators based on trees. J Math Imaging Vis 5, 277–286 (1995). https://doi.org/10.1007/BF01250284
Issue Date:
DOI: https://doi.org/10.1007/BF01250284