Image Segmentation Using Quadtree-Based Similarity Graph and Normalized Cut

  • Marco Antonio Garcia de Carvalho
  • Anselmo Castelo Branco Ferreira
  • André Luis Costa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6419)


The graph cuts in image segmentation have been widely used in recent years because it regards the problem of image partitioning as a graph partitioning issue, a well-known problem in graph theory. The normalized cut approach uses spectral graph properties of the image representative graph to bipartite it into two or more balanced subgraphs, achieving in some cases good results when applying this approach to image segmentation. In this work, we discuss the normalized cut approach and propose a Quadtree based similarity graph as the input graph in order to segment images. This representation allow us to reduce the cardinality of the similarity graph. Comparisons to the results obtained by other graph similarity representation were also done in sampled images.


image segmentation quadtree graph partitioning spectral graph 


  1. 1.
    Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8(6), 679–698 (1986)CrossRefGoogle Scholar
  2. 2.
    Carvalho, M.A.G., Ferreira, A.C.B., Pinto, T.W., Cesar Jr., R.M.: Image segmentation using watershed and normalized cuts. In: Proc. of 22th Conference on Graphics, Patterns and Images (SIBGRAPI). Rio de Janeiro, Brazil (2009)Google Scholar
  3. 3.
    Chung, F.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence (1997)zbMATHGoogle Scholar
  4. 4.
    Consularo, L.A., Cesar Jr., R.M.: Quadtree-based inexact graph matching for image analysis. In: Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI 2005), Natal - Brazil, pp. 205–212 (2005)Google Scholar
  5. 5.
    Cour, T., Bénézit, F., Shi, J.: Spectral segmentation with multiscale graph decomposition. In: Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition - CVPR 2005, vol. 2, pp. 1124–1131 (2005)Google Scholar
  6. 6.
    Fiedler, M.A.: Property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory. Czech Math Journal 25(100), 619–633 (1975)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Malik, J.: Visual grouping and object recognition. In: Proc. of 11th International Conference on Image Analysis and Processing, pp. 612–621 (2001)Google Scholar
  8. 8.
    Malik, J., Belongie, S., Shi, J., Leung, T.: Textons, contours and regions: cue integration in image segmentation. In: Proc. of IEEE International Conference on Computer Vision, Corfu, Greece, pp. 918–925 (1999)Google Scholar
  9. 9.
    Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proc. of 8th Int’l Conf. Computer Vision, vol. 2, pp. 416–423 (July 2001)Google Scholar
  10. 10.
    Monteiro, F.C., Campilho, A.: Watershed framework to region-based image segmentation. In: Proc. of IEEE 19th International Conference on Pattern Recognition - ICPR, pp. 1–4 (2008)Google Scholar
  11. 11.
    Samet, H.: The quadtree and related hierarchical structures. ACM Computing Surveys 16(2), 187–261 (1984)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-22(8), 888–905 (2000)Google Scholar
  13. 13.
    Soundararajan, P., Sarkar, S.: Analysis of mincut, average cut and normalized cut measures. In: Workshop on Perceptual Organization in Computer Vision (2001)Google Scholar
  14. 14.
    Spielman, D.: Spectral graph theory and its applications. In: Proc. of 48th Annual IEEE Symposium on Foudations of Computer Science, pp. 29–38 (2007)Google Scholar
  15. 15.
    Sun, F., He, J.P.: A normalized cuts based image segmentation method. In: Proc. of II International Conference on Information and Computer Science, pp. 333–336 (2009)Google Scholar
  16. 16.
    Tolliver, D.A., Miller, G.L.: Graph partitioning by spectral rounding: Applications in image segmentation and clustering. In: Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition - CVPR 2006, vol. 1, pp. 1053–1060 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marco Antonio Garcia de Carvalho
    • 1
  • Anselmo Castelo Branco Ferreira
    • 1
  • André Luis Costa
    • 1
  1. 1.School of Technology - FTState University of Campinas - UNICAMP Rua Paschoal MarmoBrazil

Personalised recommendations