Abstract
Level set method and Gaussian Mixture model (GMM) are two very valuable tools for natural image segmentation. The former aims to acquire good geometrical continuity of segmentation boundaries, while the latter focuses on analyzing statistical properties of image feature data. Some studies on the integration between them have been reported due to their complementarity in the last 10 years. However, these studies generally supposed that the image-featured data density distribution of every segmented domain is independent with each other and can be separately approximated by Gaussian model or GMM, which conflicts with the fundamental idea of GMM clustering-based image segmentation. To remedy this problem, we give a new insight at image segmentation objective under the combined framework between Bayesian theory and GMM density approximation. Thereby, a novel level set image segmentation method integrated with GMM (GMMLS) is proposed. Then, the theoretical analysis on GMMLS is given, in which some valuable results are demonstrated. At last, several types of natural image segmentation experiments are reported and the corresponding results indicate that GMMLS can obtain better or at least equivalent performance compared with existing relevant methods in almost all cases.
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Pala Nikhil R., Pala Sankar K.: A review on image segmentation techniques. Pattern Recognit. 26(9), 1277–1294 (1993)
Cai W., Chen S., Zhang D.: Fast and robust fuzzy C-means clustering algorithms incorporating local information for image segmentation. Pattern Recognit. 40(3), 825–838 (2007)
Xia Y., Wang T., Zhao R. et al.: Image segmentation by clustering of spatial patterns. Pattern Recognit. Lett. 28(12), 1548–1555 (2007)
Chaudhury K., Ramakrishnan K.: Stability and convergence of the level set method in computer vision. Pattern Recognit. Lett. 28(7), 884–893 (2007)
Cremers D., Rousson M., Deriche R.: A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int. J. Comput. Vis. 72(2), 195–215 (2007)
Chan, T., Vese, L.: Image segmentation using level sets and the piecewise constant Mumford–Shah model. Tech. Rep. 0014. Comput. Appl. Math. Group (2000)
Ray, N., Acton, S.T.: Image segmentation by level set with clustering. In: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, pp. 495–498. Pacific Grove, CA, USA (2000)
Gibou, F., Fedkiw, R.: A fast hybrid K-means level set algorithm for segmentation. In: 4th Annual Hawaii International Conference on Statistics and Mathematics, pp. 281–291 (2005)
Karypis G., Han E., Kumar V.: Chameleon: hierarchical clustering using dynamic modeling. Computer 32(8), 68–75 (1999)
Sumengen B., Manjunath B.: Graph partitioning active contours (GPAC) for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 28(4), 509–521 (2006)
Jenssen R., Erdogmus D., Hild Ii K.E. et al.: Information cut for clustering using a gradient descent approach. Pattern Recognit. 40(3), 796–806 (2007)
Boykov Y., Funka-Lea G.: Graph cuts and efficient ND image segmentation. Int. J. Comput. Vis. 70(2), 109–131 (2006)
Bilmes J.: A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. Int. Comput. Sci. Inst. 4, 1–13 (1998)
Redner R., Walker H.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26(2), 195–239 (1984)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Presented at the first international conference on computer vision, London, pp. 259–268 (1987)
Cheng J., Foo S.: Dynamic directional gradient vector flow for snakes. IEEE Trans. Image Process. 15(6), 1563–1571 (2006)
Kass M., Witkin A., Terzopoulos D.: Snakes: active contour models. Int. J. Comput. Vis. 1(4), 31–331 (1988)
Rousson, M.: Cues Integrations and Front Evolutions in Image Segmentation. Universite de Nice-Sophia Antipolis, Nice, France (2004)
Mumford, D., Shah, J.: Boundary detection by minimizing functionals. In: Proceedings of IEEE Conference Computer Vision and Pattern Recognition, pp. 22–26 (1985)
Mumford D., Shah J.: Optimal approximation by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 2(5), 577–685 (1989)
Kim J., Fisher J. II, Yezzi A. et al.: A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans. Image Process. 14(10), 1486–1502 (2005)
Zhu S.C., Yuille A.: Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Analysis Mach. Intell. 18(9), 884–900 (1996)
Ben Ayed I., Mitiche A., Belhadj Z.: Polarimetric image segmentation via maximum-likelihood approximation and efficient multiphase level sets. IEEE Trans. Pattern Analysis Mach. Intell. 28(9), 1493–1500 (2006)
Brox, T., Weickert, J.: Level set based image segmentation with multiple regions. In: Lecture Notes in Computer Science, vol. 3175, pp. 415–423, August 2004
Brox T., Weickert J.: Level set segmentation with multiple regions. IEEE Trans. Image Process. 15(10), 3213–3218 (2006)
Chan T., Vese L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)
Xie, Z.P., Wang, S.T.: A new level set method for image segmentation integrated with FCM. Presented at the fourth international conference on fuzzy systems and knowledge discovery 2007, vol. 4, pp. 699–703. Haikou, Hainan, China, August 24–27 2007
Xie Z.P., Wang S.T.: An extended Mumford–Shah model integrated with fuzzy clustering. Acta Electron. Sin. 36(1), 127–132 (2008)
Corso, J.J., Yuille, A., Tu, Z.: Graph-shifts: natural image labeling by dynamic hierarchical computing. Presented at the IEEE conference on computer vision and pattern recognition CVPR 2008, pp. 1–8. Anchorage, AK, USA, June 23–28 2008
Orbanz P., Buhmann J.M.: Nonparametric Bayesian image segmentation. Int. J. Comput. Vis. 77(1), 25–45 (2008)
Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of Eighth International Conference Computer Vision, vol. 2, pp. 416–423. Vancouver, BC, Canada, July 07–14 2001
Shah Shishir K.: Performance modeling and algorithm characterization for robust image segmentation. Int. J. Comput. Vis. 80(1), 92–103 (2008)
Wang S.T., Chung F.L., Xiong F.S.: A novel image thresholding method based on parzen window estimate. Pattern Recognit. 41(1), 117–129 (2008)
Wang S.T., Wang M.: A new detection algorithm (NDA) based on fuzzy cellular neural networks for white blood cell detection. IEEE Trans. Inf. Technol. Biomed. 10(1), 5–10 (2006)
Wang S.T., Fu D., Xu M., Hu D.: Advanced fuzzy cellular neural network: application to CT liver images. Artif. Intell. Med. 39(1), 65–77 (2007)
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Xie, Z., Wang, S. & Hu, D. New insight at level set & Gaussian mixture model for natural image segmentation. SIViP 7, 521–536 (2013). https://doi.org/10.1007/s11760-011-0254-4
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DOI: https://doi.org/10.1007/s11760-011-0254-4