Abstract
This paper explores the use of the Learning Automata (LA) algorithm to compute threshold selection for image segmentation as it is a critical preprocessing step for image analysis, pattern recognition and computer vision. LA is a heuristic method which is able to solve complex optimization problems with interesting results in parameter estimation. Despite other techniques commonly seek through the parameter map, LA explores in the probability space providing appropriate convergence properties and robustness. The segmentation task is therefore considered as an optimization problem and the LA is used to generate the image multi-threshold separation. In this approach, one 1-D histogram of a given image is approximated through a Gaussian mixture model whose parameters are calculated using the LA algorithm. Each Gaussian function approximating the histogram represents a pixel class and therefore a threshold point. The method shows fast convergence avoiding the typical sensitivity to initial conditions such as the Expectation- Maximization (EM) algorithm or the complex time-consuming computations commonly found in gradient methods. Experimental results demonstrate the algorithm’s ability to perform automatic multi-threshold selection and show interesting advantages as it is compared to other algorithms solving the same task.
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Abak, T., Baris, U., Sankur, B.: The performance of thresholding algorithms for optical character recognition. In: Proceedings of International Conference on Document Analytical Recognition, pp. 697–700 (1997)
Kamel M., Zhao A.: Extraction of binary character/graphics images from grayscale document images. Graph Models Image Process. 55(3), 203–217 (1993)
Trier O.D., Jain A.K.: Goal-directed evaluation of binarization methods. IEEE Trans. Pattern Anal. Mach. Intell. 17(12), 1191–1201 (1995)
Bhanu B.: Automatic target recognition: state of the art survey. IEEE Trans. Aerosp. Electron. Syst. 22, 364–379 (1986)
Sezgin, M., Sankur, B.: Comparison of thresholding methods for non-destructive testing applications. In: IEEE International Conference on Image Processing, pp. 764–767 (2001)
Sezgin M., Tasaltin R.: A new dichotomization technique to multilevel thresholding devoted to inspection applications. Pattern Recognit. Lett. 21(2), 151–161 (2000)
Guo R., Pandit S.M.: Automatic threshold selection based on histogram modes and discriminant criterion. Mach. Vis. Appl. 10, 331–338 (1998)
Pal N.R., Pal S.K.: A review on image segmentation techniques. Pattern Recognit. 26, 1277–1294 (1993)
Shaoo P.K., Soltani S., Wong A.K.C., Chen Y.C: Survey: a survey of thresholding techniques. Comput. Vis. Graph. Image Process. 41, 233–260 (1988)
Snyder W., Bilbro G., Logenthiran A., Rajala S.: Optimal thresholding: a new approach. Pattern Recognit. Lett. 11, 803–810 (1990)
Chen S., Wang M.: Seeking multi-thresholds directly from support vectors for image segmentation. Neurocomputing 67(4), 335–344 (2005)
Chih-Chih L.: A novel image segmentation approach based on particle swarm optimization. IEICE Trans. Fundam. 89(1), 324–327 (2006)
Böhning D., Seidel W.: Recent developments in mixture models. Comput. Stat. Data Anal. 41, 349–357 (2003)
Gupta L., Sortrakul T.: A Gaussian-mixture-based image segmentation algorithm. Pattern Recognit. 31(3), 315–325 (1998)
Dempster A.P., Laird A.P., Rubin D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39(1), 1–38 (1977)
Zhang Z., Chen C., Sun J., Chan L.: EM algorithms for Gaussian mixtures with split-and-merge operation. Pattern Recognit. 36, 1973–1983 (2003)
Park H., Amari S., Fukumizu K.: Adaptive natural gradient learning algorithms for various stochastic models. Neural Netw. 13, 755–764 (2000)
Redner R.A., Walker H.F.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26((2), 195–239 (1984)
Park H., Ozeki T.: Singularity and slow Convergence of the EM algorithm for Gaussian mixtures. Neural Process Lett. 29, 45–59 (2009)
Ma J., Xu L., Jordan M.I.: Asymptotic convergence rate of the EMalgorithm for Gaussian mixtures. Neural Comput. 12, 2881–2907 (2000)
Xu L., Jordan M.I.: On convergence properties for the EM algorithm. Neural Comput. 8, 129–151 (1996)
Xu L., Jordan M.I.: On corvengence of the EM algorithm for Gaussian mixtures. Neural Comput. 8(1), 129–151 (1996)
Olsson R., Petersen K., Lehn-Schiøler T.: State-space models: from the EM algorithm to a gradient approach. Neural Comput. 19(4), 1097–1111 (2008)
Narendra K.S., Thathachar M.A.L.: Learning Automata: An Introduction. Prentice-Hall, London (1989)
Najim K., Poznyak A.S: Learning Automata—Theory and Applications. Pergamon Press, Oxford (1994)
Seyed-Hamid Z.: Learning automata based classifier. Pattern Recognit. Lett. 29, 40–48 (2008)
Zeng X., Zhou J., Vasseur C.: A strategy for controlling non-linear systems using a learning automaton. Automatica 36, 1517–1524 (2000)
Howell M., Gordon T.: Continuous action reinforcement learning automata and their application to adaptive digital filter design. Eng. Appl. Artif. Intell. 14, 549–561 (2001)
Wu Q.H.: Learning coordinated control of power systems using inter-connected learning automata. Int. J. Electr. Power Energy Syst. 17, 91–99 (1995)
Thathachar M.A.L., Sastry P.S.: Varieties of learning automata: an overview. IEEE Trans. Systems. Man Cybernet. Part B Cybernet. 32, 711–722 (2002)
Zeng X., Liu Z.: A learning automaton based algorithm for optimization of continuous complex function. Inf. Sci. 174, 165–175 (2005)
Beygi H., Meybodi M.R.: A new action-set learning automaton for function optimization. Int. J. Franklin Inst. 343, 27–47 (2006)
Frost, G.P.: Stochastic optimization of vehicle suspension control systems via learning automata. Ph.D. Thesis, Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough (1998)
Howell M.N., Frost G.P., Gordon T.J., Wu Q.H.: Continuous action reinforcement learning applied to vehicle suspension control. Mechatronics 7(3), 263–276 (1997)
Howell M.N., Best M.C.: On-line PID tuning for engine idle-speed control using continuous action reinforcement learning automata. Control Eng. Pract. 8, 147–154 (2000)
Kashki, M., Abdel-Magid Y., Abido, M.: A reinforcement learning automata optimization approach for optimum tuning of PID controller in AVR system. In: Huang, D.-S., et al. (eds.) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence, ICIC 2008, LNAI 5227, pp. 684–692 (2008)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Addison Wesley, Reading (1992)
Baştürk A., Günay E.: Efficient edge detection in digital images using a cellular neural network optimized by differential evolution algorithm. Expert Syst. Appl. 36(8), 2645–2650 (2009)
Lai C.-C., Tseng D.-C.: An optimal L-filter for reducing blocking artifacts using genetic algorithms. Signal Process. 81(7), 1525–1535 (2001)
Tseng D.-C., Lai C.-C.: A genetic algorithm for MRF-based segmentation of multispectral textured images. Pattern Recognit. Lett. 20(14), 1499–1510 (1999)
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Cuevas, E., Zaldivar, D. & Pérez-Cisneros, M. Seeking multi-thresholds for image segmentation with Learning Automata. Machine Vision and Applications 22, 805–818 (2011). https://doi.org/10.1007/s00138-010-0249-0
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DOI: https://doi.org/10.1007/s00138-010-0249-0