E. D. López–Espinoza*¹, L. Altamirano–Robles²

¹ Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, Del. Coyoacan, México, D.F., CP 04510. *E–mail: danae@atmosfera.unam.mx

² Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla Puebla, México, CP 72840.

ABSTRACT

In Markov random field (MRF) models, parameters such as internal and external reference fields are used. In this paper, the influence of these parameters in the segmentation quality is analyzed, and it is shown that, for image segmentation, a MRF model with a priori energy function defined by means of non–homogeneous internal and external field has better segmentation quality than a MRF model defined only by a homogeneous internal reference field. An analysis of the MRF models in terms of segmentation quality, computational time and tests of statistical significance is done. Significance tests showed that the segmentations obtained with MRF model defined by means of non–homogeneous reference fields are significant at levels of 85% and 75%.

Keywords: Image segmentation, unsupervised segmentation, Markov random field, non–homogeneous random field.

RESUMEN

En modelos de Campos Aleatorios de Markov (MRF) se emplean parámetros como el campo de referencia interno y externo. En este artículo, analizamos su influencia en la calidad de la segmentación final, y mostramos que, para segmentación de imágenes, un modelo MRF con una función de energía definida mediante un campo de referencia interno y uno externo no homogéneos, obtiene mejores calidades de segmentación que un modelo MRF definido a través de un solo campo de referencia interno homogéneo. El análisis de los modelos MRF es realizado en términos de la calidad de segmentación, tiempo computacional y pruebas de significancia estadística. Las pruebas de significancia mostraron que los resultados de segmentación obtenidos con el modelo MRF definido a través de campos de referencia no homogéneos son significativos en un nivel del 85% y 75%.

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References

[1] Akram A. Moustafa and Z. A. Alqadi, Reconstructed color image segmentation, Proceedings of the World Congress on Engineering and Computer Science WCECS'09, ISBN:978–988–18210–2–7, Vol IM282––1285, October 20–22, 2009, San Francisco, USA.         [ Links ]

[2] S. Z. Li., Markov Random Field Modeling in Computer Vision, Chapter 1–http://www.cbsr.ia.ac.cn/users/szli/MRF_Book/book.html, (accessed March 2010).         [ Links ]

[3] Z. Kato and T–Chuen Pong, A Markov random field image segmentation model for color textured images, Image and Vision Computing, 24:1103––1114, January 2006.         [ Links ]

[4] Z. Kato, T–Chuen Pong, and J. Chung–M. Lee. Color image segmentation and parameter estimation in a Markovian framework. Pattern Recognition Letters, 22:309––321,2001.         [ Links ]

[5] S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721–741,1984.         [ Links ]

[6] G.Poggio and A. R. Averbuch, Image segmentation by tree–structured Markov random field, IEEE Signal Processing Lett., pages 155––157, July 1999.         [ Links ]

[7] C. D'Elia, G. Poggi, and G. Scarpa, A tree–structured Markov random field model for Bayesian image segmentation, IEEE Trans. on Image Proc., 12 (10):1259––1273, October 2003.         [ Links ]

[8] G. Poggi, G. Scarpa, and J. Zerubia, Supervised segmentation of remote–sensing images based on a tree–structured MRF model, IEEE Transaction on Geoscience and Remote Sensing, 43(8):1901––1911, August 2005.         [ Links ]

[9] G. Cuozzo, Dapos, C. Elia, and V. Puzzolo, A method based on tree–structured Markov random field for forest area classification, IEEE International Geoscience and Remote Sensing Symposium, 2:2352––2354, 2004.         [ Links ]

[10] B. Aiazzi, L. Alparone, S. Baronti, G. Cuozzo, C. D'Elia, and G. Schirinzi. SAR image segmentation through information theoretic heterogeneity feature and tree–structured Markov random fields. Proc. IEEE International Geoscience and Remote Sensing Symposium, 4:2803––2806, 2005.         [ Links ]

[11] X. Zheng F. Li, J. Peng, Object–based and semantic image segmentation using MRF. EURASIP Journal on Applied Signal Processing, 6:883––840, 2004.         [ Links ]

[12] M. Haindl G. Scarpa, Unsupervised texture segmentation by spectral–spatial–independent clustering, 18th International Conference on Pattern Recognition ICPR, 2:151––154, 2006.         [ Links ]

[13] I. Kovtun. Texture segmentation of images on the basis of Markov random fields, Tech. rep.: TUD–FI03, 05 2003, Department of Image Processing and Recognition, International Research and Training Centre for Information Technologies and Systems, Dresden Technical University, Kiev, Ukraine.         [ Links ]

[14] Z. Kato, Bayesian color image segmentation using Reversible Jump Markov Chain Monte Carlo, Research Report PNA–R9902, Centrum voor Wiskunde en Informatica, 1999.         [ Links ]

[15] E. D. López–Espinoza and L. Altamirano–Robles, A method based on tree–structured Markov random field and a texture energy function for classification of remote sensing images, Workshop on Computational Advances in Processing Remote Sensing Imagery CASI2008, part of the 5th International Conference CCE08, IEEE Catalog Number: CFP08827 –CDR, ISBN: 978–1–42442499–3.         [ Links ]

[16] E. D. López–Espinoza and L. Altamirano–Robles, Segmentación Markoviana usando modelos de textura, Reporte técnico No. CCC–09–002, Coordinación de Ciencias Computacionales, INAOE, Mayo 2009.         [ Links ]

[17] B. Porat J. M. Francos, A.Z. Meiri. A unified texture model based on a 2–d wold like decomposition. IEEE Transactions on Signal Processing, 41:2665––2678, 1993.         [ Links ]

[18] R. Picard, C. Graczyk, S. Mann, J. Wachman, L. Picard, and L. Campbell, MIT VisTex texture database, Vision and Modeling Group of the MIT Media Laboratory, Cambridge, Massachusetts, http://vismod.media.mit.edu/vismod/imagery/VisionTexture/vistex.html (accessed March 2010).         [ Links ]

[19] P. Carbonetto, Corel photography set, Department of Human Genetics University of Chicago, http://www.cs.ubc.ca/~pcarbo/#data, (accessed March 2010).         [ Links ]

[20] M. Berthod, Z. Kato, S. Yu, and Josiane Zerubia, Bayesian Image Classification Using Markov Random Fields. Image and Vision Computing, 14:285––295, 1996.         [ Links ]

[21] S. Mohammad Shahrokhy, Visual and statistical quality assessment and improvement of remotely sensed images, In Geo–Imagery Bridging Continents, XXth ISPRS Congress, Vol. XXXV, ISSN 1682–1750, Istanbul, Turkey p. 104––108, July 2004.         [ Links ]

[22] J. Torres and S. O. Infante, Wavelet analysis for the elimination of striping noise in satellite images, Society of Photo–Optical Instrumentation Engineers, 40:1309–1314, 2001.         [ Links ]

[23] B. Tsai, T. Kojima, N. Kosaka, T. Akiyama, Forest type classification using data fusion of multispectral and panchromatic high–resolution satellite imageries, Geoscience and Remote Sensing Symposium, IGARSS apos;05 Proceedings, IEEE International, 4:12980–2983, 2005.         [ Links ]

[24] E. D. López–Espinoza and L. Altamirano–Robles, Deterministic component of 2–d Wold decomposition for geometry and texture descriptors discovery, Lecture Notes in Computer Science, Progress in Pattern Recognition, Image Analysis and Applications, 4756/2008:241––250, 2007.         [ Links ]

[25] G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods, Springer–Verlag, Second edition, New York, Part 6:268, 2006.         [ Links ]