Abstract
We propose a new model for probabilistic image segmentation with spatial coherence through a Markov Random Field prior. Our model is based on a generalized information measure between discrete probability distribution (β-Measure). This model generalizes the quadratic Markov measure field models (QMMF). In our proposal, the entropy control is achieved trough the likelihood energy. This entropy control mechanism makes appropriate our method for being used in tasks that require of the simultaneous estimation of the segmentation and the model parameters.
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Kaus, M.R., Warfield, S.K., Nabavi, A., Black, P.M., Jolesz, F.A., Kikinis, R.: Automated Segmentation of MR Images of Brain Tumors. Radiology 218, 586–591 (2001)
Rivera, M., Ocegueda, O., Marroquín, J.L.: Entropy-controlled quadratic markov measure field models for efficient image segmentation. IEEE Transactions on Image Processing 16, 3047–3057 (2007)
Hower, D., Singh, V., Johnson, S.: Label set perturbation for mrf based neuroimaging segmentation. In: IEEE International Conference on Computer Vision ICCV 2009, pp. 849–856 (2009)
Chamorro-Martinez, J., Sanchez, D., Prados-Suarez, B.: A Fuzzy Colour Image Segmentation Applied to Robot Vision. In: Advances in Soft Computing Engineering, Design and Manufacturing. Springer, Heidelberg (2002)
Mishra, A., Aloimonos, Y.: Active segmentation for robots. In: International Conference on Intelligent Robots and Systems (2009)
Dalmau, O., Rivera, M., Mayorga, P.P.: Computing the alpha-channel with probabilistic segmentation for image colorization. In: IEEE Proc. Workshop in Interactive Computer Vision (ICV 2007), pp. 1–7 (2007)
Dalmau, O., Rivera, M., Alarcon, T.: Bayesian Scheme for Interactive Colourization, Recolourization and Image/Video Editing. To Appear in Computer Graphics Forum (2010)
Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problem. Commun. Pure Appl. Math., 577–685 (1989)
Hewer, G.A., Kenney, C., Manjunath, B.S.: Variational image segmentation using boundary functions. IEEE Transactions on Image Processing 7, 1269–1282 (1998)
Weiss, Y.: Segmentation using eigenvectors: A unifying view. In: ICCV, vol. (2), pp. 975–982 (1999)
Ahmed, M.N., Yamany, S.M., Mohamed, N., Farag, A.A., Moriarty, T.: A modified fuzzy c-means algorithm for bias field estimation and segmentation of mri data. IEEE Trans. Med. Imaging 21(3), 193–199 (2002)
Chuang, K.S., Tzeng, H.L., Chen, S., Wu, J., Chen, T.J.: Fuzzy c-means clustering with spatial information for image segmentation. Computerized Medical Imaging and Graphics 30, 9–15 (2006)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Boykov, Y., Jolly, M.P.: Interactive organ segmentation using graph cuts. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 276–286. Springer, Heidelberg (2000)
Marroquin, J.L., Velazco, F., Rivera, M., Nakamura, M.: Gauss-markov measure field models for low-level vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 337–348 (2001)
Marroquin, J.L., Arce, E., Botello, S.: Hidden Markov measure field models for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 1380–1387 (2003)
Dalmau, O., Rivera, M.: A general bayesian markov random field model for probabilistic image segmentation. In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol. 5852, pp. 149–161. Springer, Heidelberg (2009)
Cha, S.H.: Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions. International Journal of Mathematical Models and Methods in Applied Sciences 1, 300–307 (2007)
Bezdek, J.C., Coray, C., Gunderson, R., Watson, J.: Detection and characterization of cluster substructure i. linear structure: Fuzzy c-lines. SIAM Journal on Applied Mathematics 40(2), 339–357 (1981)
Bezdek, J.C., Coray, C., Gunderson, R., Watson, J.: Detection and characterization of cluster substructure ii. fuzzy c- varieties and convex combinations thereof. SIAM Journal on Applied Mathematics 40(2), 358–372 (1981)
Taneja, I.J., Gupta, H.: On generalized measures of relative information and inaccuracy. Applications of Mathematics 23, 317–333 (1978)
Grady, L., Schiwietz, T., Aharon, S., Westermann, R.: Random Walks for interactive organ segmentation in two and three dimensions: Implementation and validation. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 773–780. Springer, Heidelberg (2005)
Grady, L.: Multilabel random walker image segmentation using prior models. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CVPR, vol. 1, pp. 763–770. IEEE, Los Alamitos (June 2005)
Kerridge, D.: Inaccuracy and inference. Journal of the Royal Statistical, Series B, 184–194 (1961)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operation Research (2000)
Geman, D., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. Pattern Anal. Mach. Intell. 14(3), 367–383 (1992)
Black, M., Rangarajan, A.: On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Int’l J. Computer Vision 19(1), 57–92 (1996)
Rivera, M., Dalmau, O., Tago, J.: Image segmentation by convex quadratic programming. In: ICPR, pp. 1–5. IEEE, Los Alamitos (2008)
Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)
Juan, O., Keriven, R.: Trimap segmentation for fast and user-friendly alpha matting. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds.) VLSM 2005. LNCS, vol. 3752, pp. 186–197. Springer, Heidelberg (2005)
Neal, R.M., Hinton, G.E.: A view of the EM algorithm that justifies incremental, sparse, and other variants. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 355–368. Kluwer Academic Publishers, Boston (1998)
Marroquín, J.L., Santana, E.A., Botello, S.: Hidden Markov measure field models for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 1380–1387 (2003)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical recipes in C: the art of scientific computing, 2nd edn. Cambridge University Press, New York (1992)
Vogel, C.R., Oman, M.E.: Iterative methods for total variation denoising. SIAM J. Sci. Comput. 17, 227–238 (1996)
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Dalmau, O., Rivera, M. (2010). Beta-Measure for Probabilistic Segmentation. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds) Advances in Artificial Intelligence. MICAI 2010. Lecture Notes in Computer Science(), vol 6437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16761-4_28
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DOI: https://doi.org/10.1007/978-3-642-16761-4_28
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