Colour Image Segmentation with Integrated Left Truncated Bivariate Gaussian Mixture Model and Hierarchical Clustering

  • G. V. S. Rajkumar
  • K. Srinivasa Rao
  • P. Srinivasa Rao
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 199)


Image segmentation plays a dominant role in image analysis and image retrievals. Much work has been reported in literature regarding image segmentation based on Gaussian mixture model (GMM). The main drawback of GMM is regarding the assumption that each image region is characterized by Gaussian component, in which the feature vector is mesokurtic and having infinite range. But in colour images the feature vector is represented by Hue and Saturation which are non- negative and may not be symmetrically distributed. Hence the image segmentation can not be accurate unless the non-negative nature of the feature vector is included. In this paper an image segmentation method is developed and analyzed with the assumption that the bivariate feature vector consisting of Hue and Saturation of each pixel follows a left truncated bivariate Gaussian mixture model. In this method the number of components (Image regions) are determined by Hierarchical clustering. The segmentation algorithm is proposed under Bayesian frame with maximum likelihood. The experimentation with six images taken from Berkeley dataset reveals that the proposed image segmentation method outperforms the existing image segmentation method with GMM and finite left truncated bivariate Gaussian mixture model with K-means.


Image Segmentation Bivariate Gaussian Mixture model Image Quality Metrics Hierarchical clustering EM- algorithm 


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  1. 1.
    Muthen, B.: Moments of the censored and truncated bivariate normal distribution. British Journal of Mathematical and Statistical Psychology (43), 131–143 (1990)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Eskicioglu, M.A., Fisher, P.S.: Image Quality Measures and their Performance. IEEE Transactions on Communications 43(12) (1995)Google Scholar
  3. 3.
    Haralick, Shapiro: Survey: Image segmentation Techniques. In: Proc. of Int. Conf. CVGIP 1985, vol. 29, pp. 100–132 (1985)Google Scholar
  4. 4.
    Johnson, S.C.: A Tutorial on Clustering Algorithms (1967),
  5. 5.
    Kato, Z., Pong, T.C.: A markov random field image segmentation model using combined color and texture features. In: Proc. of Int. Conf. on Computer Analysis of Images and Patterns, pp. 547–551 (2001)Google Scholar
  6. 6.
    Kato, Z., Pong, T.-C., Qiang, S.G.: Unsupervised segmentation of color textured images using a multilayer MRF model. In: Proc. of Intl. Conf. on Image Processing, vol. 1, pp. 961–964 (2003)Google Scholar
  7. 7.
    Kato, Z., Pong, T.-C.: A Markov random field image segmentation model for color textured images. Image and Computing Vision 24(10), 1103–1114 (2006)CrossRefGoogle Scholar
  8. 8.
    Lucchese, L., Mitra, S.K.: Color image segmentation: A state-of art survey. Proc. of Indian National Science Academy (INSA-A) 67-A, 207–221 (2001)Google Scholar
  9. 9.
    Paulinas, M., Usinskas, A.: A survey of genenetic algorithms applications for image enhancement and segmentation. Information Technology and Control 36(3), 278–284 (2007)Google Scholar
  10. 10.
    Sojodishijani, O., Rostami, V., Ramli, A.R.: Real Time Colour Image Segmentation with Non-Symmetric Gaussian Membership Functions. In: Proc. of 5th Int. Conf. on Computer Graphics, Imaging and Visualisation, pp. 165–170 (2008)Google Scholar
  11. 11.
    Pal, S.K., Pal, N.R.: A Review on Image Segmentation Techniques. Pattern Recognition 26(9), 1277–1294 (1993)Google Scholar
  12. 12.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing. A text book from Pearson education, India (2001)Google Scholar
  13. 13.
    Farnoosh, R., Yari, G., Zarpak, B.: Image Segmentation using Gaussian Mixture Models. IUST International Journal of Engineering Science 19(1), 29–32 (2008)Google Scholar
  14. 14.
    Rajkumar, G.V.S., Srinivasa Rao, K., Srinivasa Rao, P.: Studies on Colour Image Segmentation method based on finite left truncated bivariate Gaussian mixture model with K-Means. Global Journal of Computer Science and Technology X1(XVIII), 21–30 (2011)Google Scholar
  15. 15.
    Randen, Husoy, J.: Filtering for texture classification: A comparative study. IEEE Trans. on Pattern Analysis and Machine Intelligence 21(4), 291–310 (1999)CrossRefGoogle Scholar
  16. 16.
    Raut, S., Raghuvanshi, M., Dharaskar, R., Raut, A.: Image Segmentation- A state-of-Art Survey for Prediction. In: Proc. of Int. Conf. on Advanced Computer Control, pp. 420–424 (2009)Google Scholar
  17. 17.
    Shivani, G., Manika, P., Shukhendu, D.: Unsupervised segmentation of texture images using a combination of gab or and wavelet features. In: Proceedings of the 4th Indian Conference on Computer Vision, Graphics & Image Processing, pp. 370–375 (2004)Google Scholar
  18. 18.
    Bhattacharyya, S.: A Brief Survey of Color Image Preprocessing and Segmentation Techniques. Journal of Pattern Recognition Research, 120–129 (2011)Google Scholar
  19. 19.
    Sujaritha, M., Annadurai, S.: Color Image segmentation using Adaptive Spatial Gaussian Mixture Model. International Journal of Signal processing 6(1), 28–32 (2010)Google Scholar
  20. 20.
    Wu, Y., et al.: Unsupervised Color Image Segmentation Based on Gaussian Mixture Models. In: Proceedings of 2003 Joint Conference At The 4th International Conference on Information, Communication and Signal Processing, vol. 1, pp. 541–544 (2003)Google Scholar
  21. 21.
    Fei, Z., Guo, J., Wan, P., Yang, W.: Fast automatic image segmentation based on Bayesian decision-making theory. In: Proc. of Int. Conf. on Information and Automation, pp. 184–188 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • G. V. S. Rajkumar
    • 1
  • K. Srinivasa Rao
    • 2
  • P. Srinivasa Rao
    • 3
  1. 1.Department of Information TechnologyGITAM UniversityVisakhapatnamIndia
  2. 2.Department of StatisticsAndhra UniversityVisakhapatnamIndia
  3. 3.Department of Computer Science and Systems EngineeringAndhra UniversityVisakhapatnamIndia

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