Abstract
The estimation of parameters in the Autobinomial model is an important task for characterizing the content of an image and generating synthetic textures. This paper compares the performance of three estimation methods of the model: coding, maximum pseudo-likelihood and conditional least squares, under textures with different levels of additive contamination, using a feature similarity image index, via Monte Carlo studies. This novel framework quantifies the similarity between the original texture and its texture regenerated by each method. Differences in performance were tested with a Repeated Measures ANOVA model design. Simulation results show that the Conditional Least Squares method is associated with the highest value of the similarity image measure in contaminated textures, while Coding and Maximum Pseudo-Likelihood methods have a comparable behavior and there is no clear pattern whether to prefer one over the other. An application for landscape classification using real Landsat images with different spatial resolutions is described.
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References
Agresti A (1996) An introduction to categorical data analysis. Wiley, New York
Anderson JR, Hardy EE, Roach JT, Witmer RE (1976) A land use and land cover classification system for use with remote sensor data. U.S. Government Printing Office, USA
Besag J (1974) Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc Ser B 36:192–236
Besag J (1975) Statistical analysis of non-lattice data. J R Stat Soc Ser D (The Statistician) 24(3):179–195
Besag J, Moran PA (1975) On the estimation of spatial interaction in Gaussian lattice processes. Biometrika 62(3):555–562
Besag J (1977) Efficiency of pseudo likelihood estimation for simple Gaussian fields. Biometrika 64(3):616–618
Besag J (1986) On the statistical analysis of dirty pictures. J R Stat Soc B–48:259–302
Borges CF (1999) On the estimation of Markov random field parameters. IEEE Trans Pattern Anal Mach Intel 21(3):216–224
Cariou C, Chehdi K (2008) Unsupervised texture segmentation/classification using 2-D autoregressive modeling and the stochastic expectation-maximization algorithm. Pattern Recogn Lett 29(7):905–917
Cross GR, Jain AK (1983) Markov random field texture models. IEEE Trans Pattern Anal Mach Intell 5(1):25–39
Datcu M, Seidel K, Walessa M (1998) Spatial information retrieval from remote-sensing images. I. Information theoretical perspective. IEEE Trans Geosci Remote Sens 36(5):1431–1445
Derin H, Elliott H (1978) Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans Pattern Anal Mach Intel PAMI–9(1):39–55
Elfadel I, Picard R (1994) Gibbs random fields, cooccurrences, and texture modeling. IEEE Trans Pattern Anal Mach Intel 16(1):24–37
Fox AJ (1972) Outliers in time series. J R Stat Soc 34:350–363
Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–741
Gleich D (2012) Markov random field models for non-quadratic regularization of complex SAR images. IEEE J Select Top Appl Earth Observ Remote Sens 5(3):952–961
Greenhouse S, Geisser S (1959) On methods in the analysis of profile data. Psychometrika 24(2):95–112
Gürelli MI, Onural L (1994) On a parameter estimation method for Gibbs–Markov random fields. IEEE Trans Pattern Anal Mach Intell 16(4):424–430
Hassner M, Sklansky J (1980) The use of Markov random fields as models of texture. Comput Graph Image Process 12(4):357–370
Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109
Hebar M, Gleich D, Cucej Z (2009) Autobinomial model for SAR image despeckling and information extraction. IEEE Trans Geosci Remote Sens 47(8):2818–2835
Huynh H, Feldt LS (1976) Estimation at the box correction for degrees of freedom for sample data in randomised block and split-plot designs. J Educ Stat 1(1):69–82
Johansson JO (2001) Parameter-estimation in the auto-binomial model using the coding and pseudo-likelihood method approached with simulated annealing and numerical optimization. Pattern Recogn Lett 22(11):1233–1246
Kaneko H, Yodogawa E (1982) A Markov random field application to texture classification. In: Proceedings of conference on pattern recognition and image processing, IEEE Computer Society, Los Vegas, NE pp 221–225
Kutner MH, Nachtsheim CJ, Neter J, Li W (2005) Applied linear statistical models, 5th edn. McGraw Hill, New York
Landis JR, Koch GG (1977) The measurement of observer agreement for categorical data. Biometrics 33(1):159–174
Lele SR, Ord JK (1986) Conditional least squares estimation for spatial processes: some asymptotics results. Tech Report No. 1986–65. Pennsylvania State University Department Statistics
Mauchly JW (1940) Significance test for sphericity of a normal \(n\)-variate distribution. Ann Math Stat 11(2):204–209
Molina DE, Datcu M, Gleich D (2009) Cramer-Rao bound-based evaluation of texture extraction from SAR images. In: 16th international conference on systems, signals and image processing, pp 1–4
Molina DE, Gleich D, Datcu M (2012) Evaluation of Bayesian despeckling and texture extraction methods based on Gauss–Markov and auto-binomial Gibbs random fields: application to terraSAR-X data. IEEE Trans Geosci Remote Sens 50(5):2001–2025
Reulke R, Lippok A (2008) Markov random fields (MRF)-based texture segmentation for road detection. ISPRS Beijing, pp 615–620
Schröder M, Seidel S, Datcu M (1997) Gibbs random field models for image content characterization. In: IEEE international geoscience and remote sensing symposium (IGARSS97), pp 258–260
Schröder M, Rehrauer H, Seidel K, Datcu M (1998) Spatial information retrieval from remote sensing images: part B. Gibbs Markov random fields. IEEE Trans Geosci Remote Sens 36:1446–1455
Vallejos RO, García-Donato G (2006) Bayesian analysis of contaminated quarter plane moving average models. J Stat Comput Simul 76(2):131–147
Winkler G (1995) Image analysis, random fields and dynamic Monte Carlo methods: a mathematical introduction, 3rd edn. Springer, Berlin
Zhang L, Zhang L, Moun X, Zhang D (2011) FSIM: a feature similarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386
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This paper has been partially supported by SGCyT-UNS and SeCyT-UNC. The imagery used in the application section was kindly provided by CONAE, Argentina. The authors want to thank the Editor, Associate Editor and the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.
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Pistonesi, S., Martinez, J. & Ojeda, S.M. A sensibility study of the autobinomial model estimation methods based on a feature similarity index. Comput Stat 31, 1327–1357 (2016). https://doi.org/10.1007/s00180-015-0634-2
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DOI: https://doi.org/10.1007/s00180-015-0634-2