Sur le choix de méthode de segmentation statistique d'images
On the Choice of Statistical Image Segmentation Method
OPEN ACCESS
In this paper we deal with the statistical grey-level segmentation, without any reference to texture . These methods can be divided in two families : local methods and global ones . Local methods classify each pixel, using tools of Bayesian classification, from the information contained in its neighbourhood of a small size . Global methods are based on hidden Markov models and allow one to apply Bayesian techniques taking into account the entire information available . Adding a previous model parameter estimation step, which is a mixture estimation, all these methods can be rendered automated, or unsupervised . On the one hand, results obtained with unsupervised methods differ little from results obtained with true parameter based methods . On the other hand, for a given segmentation method, the choice of the parameter estimation method has little influence on the final result . However, the general behaviour of local and global methods are different. Although global methods can give excellent results when data are well suited to the underlying model, in other situations local methods can ensure clearly better performance. The aim of the present work is to propose a method for choosing between local and global methods . The choice we propose is automated, i .e . , independent from any human intervention and only depending on the image to be segmented . We deduce the choice from two factors: class image homogeneity and spatial correlation of the noise . The good behaviour of our algorithm is validated with simulations and real-world image segmentation results.
Résumé
Nous traitons dans cet article du problème de la segmentation d'images à partir de niveaux de gris et sans prise en compte de la notion de texture . Les méthodes statistiques de telle segmentation peuvent être divisées en deux familles : méthodes locales , où l'on classe chaque pixel à partir de l'information contenue dans son voisinage de petite taille, et méthodes globales, qui font appel aux modélisations markoviennes et permettent d'effectuer des classifications bayésiennes en tenant compte de toute l'information disponible. Toutes les méthodes peuvent être rendues automatiques, ou non supervisées, en leur adjoignant une méthode d'estimation de mélanges . Des études antérieures ont montré que le choix de la méthode d'estimation a, dans le cas gaussien, peu d'influence sur le résultat final . Cependant, les comportements généraux des méthodes locales et globales sont très différents et aucune famille n'est supérieure à l'autre dans toutes les situations . Nous proposons dans cet article un algorithme de choix automatique, à savoir fonctionnant sans intervention humaine et à partir de la seule image à segmenter, entre les méthodes locales et les méthodes globales . Le choix de l'algorithme est fait à partir de l'homogénéité de l'image des classes et de la corrélation spatiale du bruit. La pertinence des choix est montrée via simulations et segmentations des images réelles.
Statistical image segmentation, Markov Fields, Markov Chains
Mots clés
Segmentation statistique d'images, champs de Markov, chaînes de Markov
[BeP95] B . Benmiloud, W. Pieczynski, Estimation des paramètres dans les chaînes de Markov cachées et segmentation d'images, Traitement du Signal, Vol. 12 , No . 5, pp.433-454, 1995 .
[Bes86] J. Besag, On the statistical analysis of dirty pictures, Journal of the Royal Statistical Society, Series B, 48, pp . 259-302, 1986.
[BoL94] J . M. Boucher and P. Lena, Unsupervised Bayesian classification, application to the forest of Paimpont (Brittany), Photo Interprétation, Vol . 32, No. 1994/4, 199511-2, 1995, pp . 79-81 .
[BPM93] B . Braathen, W. Pieczynski, P. Masson, Global and local methods of unsupervised Bayesian segmentation of images, Machine Graphics & Vision , Vol . 2, No . 1, pp . 39-52, 1993 .
[BCD83] M . Broniatowski, G. Celeux, J . Diebolt, Reconnaissance de mélanges de densités par un algorithme d'apprentissageprobabiliste, Data Analysis an Informatics 3, E . Diday (Ed .), North Holland, Amsterdam, 1983 .
[CPH97] H. Caillol, W. Pieczynski, and A. Hillon, Estimation of Fuzzy Gaussian Mixture and Unsupervised Statistical Image Segmentation, IEEE Transactions on Image Processing, Vol . 6, No . 3, pp . 425-440, 1997 .
[CeD86] G. Celeux, J. Diebolt, L'algorithme SEM : un algorithme d'apprentissage probabiliste pour la reconnaissance de mélanges de densités, Revue de Statistique Appliqueé, Vol. 34, No. 2, pp . 35-52, 1986 .
[Cha89] B . Chalmond, An iterative Gibbsian technique for reconstruction of mary images, Pattern Recognition, Vol . 22, No . 6, pp . 747-761, 1989 .
[ChJ93] R . Chellapa, A . Jain Ed., Markov Random Fields, Theory and Application, Academic Press, San Diego, 1993 .
[DMP97] Y. Delignon, A . Marzouki, W. Pieczynski, Estimation of Generalized Mixture and Its Application in Image Segmentation, IEEE Transactions on Image Processing, Vol . 6, No. 10, pp . 1364-1375, 1997.
[DLR77] M .M . Dempster, N .M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Series B, 39, pp. 1-38, 1977 .
[DuJ89] R .C . Dubes, A.K. Jain, Random field models in image analysis, Journal of Applied Statistics, Vol. 16, No . 2, pp . 131-164, 1989 .
[GeG84] S . Geman, G. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on PAMI, Vol. 6, No. 6 , pp . 721-741, 1984 .
[GGG90] S . Geman, D. Geman, C . Graffigne, et P. Dong, Boundary detection by constrained optimization, IEEE Transactions on PAMI, Vol. 12, No. 7, pp . 609-627, 1990 .
[GiP97] N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on PAMI, Vol. 19, No . 5, pp . 465-475, 1997 .
[Guy93] X. Guyon, Champs aléatoires sur un réseau, Collection Techniques Stochastiques, Masson, Paris, 1993 .
[HaH86] R . Haralick, J . Hyonam, A context classifier, IEEE Transactions on GRS, Vol. GE-24, No. 6, pp. 997-1007, 1986 .
[Hi192] A . Hillion, Les approches statistiques pour la reconnaissance des images de télédétection, Atti della XXXVI Riunione Scientifica, SIS, Vol. 1, pp . 287-297, 1992.
[KeF95] C . Kervrann et E Heitz, A Markov random field model based approach to unsupervised texture segmentation using local and global spatial statistics , IEEE Transactions on Image Processing, Vol . 4, No . 6, pp . 856-862, 1997 .
[LaD89] S . Lakshmanan, H. Derin, Simultaneous parameter estimation and segmentation of Gibbs random fields, IEEE Transactions on PAMI, Vol . 11 , pp . 799-813, 1989 .
[LJC92] Z. Liang, R .J. Jaszczak, R.E. Coleman, Parameter Estimation of Finite Mixture Using the EM Algorithm and Information Criteria with Application to Medical Image Processing, IEEE Transactions on Nuclear Science, No. 4 , Vol . 39, pp. 1126-1133, 1992 .
[MMP87] J. Marroquin, S . Mitter, T Poggio, Probabilistic solution of illposed problems in computational vision, Journal of the American Statistical Association, 82, pp . 76-89, 1987.
[MCP97] M. Mignotte, C . Collet, P. Pérez, et P. Bouthemy, Unsupervised segmentation applied on sonar images, Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science : 1223 , Springer-Verlag, Berlin, pp .491-506, 1997 .
[PeP95] A . Peng, W. Pieczynski, Adaptive Mixture Estimation and Unsupervised Local Bayesian Image Segmentation, Graphical Models and Image Processing, Vol . 57, No . 5, pp. 389-399, 1995 .
[Pie94] W. Pieczynski, Champs de Markov cachés et estimation conditionnelle itérative, Traitement du Signal, Vol . 11, No . 2, pp . 141-153, 1994 .
[QiT89] W. Qian and D.M . Titterington, On the use of Gibbs Markov chain models in the analysis of images based on second-order pairwise interactive distributions, Journal of Applied Statistics, Vol . 16, No . 2, pp . 267-282, 1989 .
[ReW84] R .A . Redner, H .F. Walker, Mixture densities, maximum likelihood and the EM algorithm, SIAM Review, 26, pp . 195-239, 1984.
[Sa196] F. Salzenstein, Modèles Markoviens Flous et Segmentation non Supervisée d'Images, thèse de l'Université Rennes I, 1996 .
[SaP97] F. Salzenstein and W. Pieczynski, Parameter Estimation in Hidden Fuzzy Markov Random Fields and Image Segmentation, Graphical Models and Image Processing, Vol . 59, No . 4, pp. 205-220, 1997 .
[Ska92] W. Skarbek, Generalized Hilbert scan in image printing, Theoretical Foundations of Computer Vision, R . Klette et W. G . Kropetsh Ed., Akademik Verlag, pp . 45-57, 1992.
[Yao89] J .F. Yao, Segmentation bayésienne d'images : comparaisons de méthodes contextuelles et globales, Cahier du Centre d'Etudes et de Recherches, Op .3 0(4), pp. 269-290, 1989.
[You88] L. Younes, Estimation and annealing for Gibbsian fields, Annales de l'Institut Henri Poincaré , 24, pp. 269-294, 1988 .
[You89] L. Younes, Parametric inference for imperfectly observed Gibbsian fields , Probability Theory and Related Fields, 82, pp . 625-645, 1989.
[Zec93] J. Zerubia, and R. Chellapa, Mean field annealing using Compound Gauss-Markov Random Fields for edge detection and image estimation, IEEE Transactions on Neural Networks, 8(4), pp . 703-709, 1993 .