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An improved image graph for semi-automatic segmentation

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Abstract

The problem of semi-automatic segmentation has attracted much interest over the last few years. The Random Walker algorithm [1] has proven to be quite a popular solution to this problem, as it is able to deal with several components and models the image using a convenient graph structure. We propose two improvements to the image graph used by the Random Walker method. First, we propose a new way of computing the edge weights. Traditionally, such weights are based on the similarity between two neighbouring pixels, using their greyscale intensities or colours. We substitute a new definition of weights based on the probability distributions of colours. This definition is much more robust than traditional measures, as it allows for textured objects, and objects that are composed of multiple perceptual components. Second, the traditional graph has a vertex set which is the set of pixels and edges between each pair of neighbouring pixels. We substitute a smaller, irregular graph based on Mean Shift oversegmentation. This new graph is typically several orders of magnitude smaller than the original image graph, which can lead to a major savings in computing time. We show results demonstrating the substantial improvement achieved when using the proposed image graph.

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References

  1. Grady L.: Random walks for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1768–1783 (2006)

    Article  Google Scholar 

  2. Rother, C., Kolmogorov, V., Blake, A.: Grabcut: interactive foreground extraction using iterated graph cuts. In: Proceedings of the International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), pp. 309–314 (2004)

  3. Grady L., Funka-Lea G.: Multi-label image segmentation for medical applications based on graph-theoretic electrical potentials. Lect. Notes Comput. Sci. 3117, 230–245 (2004)

    Article  Google Scholar 

  4. Grady, L.: Multilabel random walker image segmentation using prior models. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 763–770 (2005)

  5. Fukunaga K., Hostetler L.: The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Trans. Inf. Theory 21(1), 32–40 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng Y.: Mean shift, mode seeking, and clustering. IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995)

    Article  Google Scholar 

  7. Comaniciu D., Meer P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24(5), 603–619 (2002)

    Article  Google Scholar 

  8. Mortensen, E.N., Barrett, W.A.: Intelligent scissors for image composition. In: Proceedings of the International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), pp. 191–198 (1995)

  9. Barrett W.A., Mortensen E.N.: Fast, accurate, and reproducible live-wire boundary extraction. Lect. Notes Comput. Sci. 1131, 183–192 (1996)

    Article  Google Scholar 

  10. Mortensen, E.N., Barrett, W.A.: Toboggan-based intelligent scissors with a four-parameter edge model. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. 452–458 (1999)

  11. Gleicher, M.: Image snapping. In: Proceedings of the International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), pp. 183–190 (1995)

  12. Boykov, Y., Jolly, M.-P.: Interactive organ segmentation using graph cuts. In: Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 276–286 (2000)

  13. Boykov, Y., Jolly, M.-P.: Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), vol. 1, pp. 105–112 (2001)

  14. Greig D.M., Porteous B.T., Seheult A.H.: Exact maximum a posteriori estimation for binary images. J. R. Stat. Soc. Ser. B (Methodol.) 51(2), 271–279 (1989)

    Google Scholar 

  15. Li, Y., Sun, J., Tang, C.K., Shum, H.Y.: Lazy snapping. In: Proceedings of the International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), vol. 23, pp. 303–308, (2004)

  16. Lombaert, H., Sun, Y., Grady, L., Xu, C.: A multilevel banded graph cuts method for fast image segmentation. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), vol. 1, pp. 259–265, (2005)

  17. Freedman, D., Zhang, T.: Interactive graph cut based segmentation with shape priors. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 755–762 (2005)

  18. Juan, O., Boykov, Y.: Active graph cuts. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 1023–1029 (2006)

  19. Xu N., Ahuja N., Bansal R.: Object segmentation using graph cuts based active contours. Comput. Vis. Image Underst. 107(3), 210–224 (2007)

    Article  Google Scholar 

  20. Zeng Y., Samaras D., Chen W., Peng Q.: Topology cuts: a novel min-cut/max-flow algorithm for topology preserving segmentation in N–D images. Comput. Vis. Image Underst. 112(1), 81–90 (2008)

    Article  Google Scholar 

  21. Grady, L., Sinop, A.K.: Fast approximate Random Walker segmentation using eigenvector precomputation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–8 (2008)

  22. Singaraju, D., Grady, L., Vidal, R.: Interactive image segmentation via minimization of quadratic energies on directed graphs. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–8 (2008)

  23. Sinop, A.K., Grady, L.: A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), pp. 1–8 (2007)

  24. Couprie, C., Grady, L., Najman, L., Talbot, H.: Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), pp. 731–738 (2009)

  25. Protiere A., Sapiro G.: Interactive image segmentation via adaptive weighted distances. IEEE Trans. Image Process. 16(4), 1046–1057 (2007)

    Article  MathSciNet  Google Scholar 

  26. Vincent L., Soille P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991)

    Article  Google Scholar 

  27. Duchenne, O., Audibert, J.Y., Keriven, R., Ponce, J., Ségonne, F.: Segmentation by transduction. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–8 (2008)

  28. Silverman B.W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, London (1986)

    MATH  Google Scholar 

  29. Girolami M., He C.: Probability density estimation from optimally condensed data samples. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1253–1264 (2003)

    Article  Google Scholar 

  30. Schanda J.: Colorimetry: Understanding the CIE System. Wiley-Interscience, New York (2007)

    Google Scholar 

  31. Nishizeki T., Chiba N.: Planar Graphs: Theory and Algorithms. Elsevier, Amsterdam (1988)

    MATH  Google Scholar 

  32. Munkres, J.R.: Elements of Algebraic Topology (1984)

  33. Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 664–671 (2003)

  34. Wang, P., Lee, D., Gray, A., Rehg, J.M.: Fast mean shift with accurate and stable convergence. In: Proceedings of the Workshop on Artificial Intelligence and Statistics (AISTATS) (2007)

  35. Freedman, D., Kisilev, P.: Fast Mean Shift by compact density representation. pp. 1818–1825 (2009)

  36. Felzenszwalb P.F., Huttenlocher D.P.: Efficient graph-based image segmentation. Int. J. Comput. Vis. 59(2), 167–181 (2004)

    Article  Google Scholar 

  37. Marcotegui, B., Zanoguera, F., Correia, P., Rosa, R., Marques, F., Mech, R., Wollborn, M.: Video object generation tool allowing friendly user interaction. In: Proceedings of the IEEE International Conference on Image Processing (ICIP), vol. 2, pp. 391–395 (1999)

  38. Random Walker code. http://www.cns.bu.edu/~lgrady/random_walker_matlab_code.zip

  39. Freixenet, J., Munoz, X., Raba, D., Marti, J., Cufi, X.: Yet another survey on image segmentation: Region and boundary information integration. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 408–422 (2002)

  40. Pantofaru, C., Hebert, M.: A comparison of image segmentation algorithms. Technical Report CMU-R1-TR-05-40, The Robotics Institute, Carnegie Mellon University (2005)

  41. 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: Proceedings of IEEE International Conference on Computer Vision (ICCV)

  42. Meila, M.: Comparing clusterings: an axiomatic view. In: Proceedings of the International Conference on Machine Learning (ICML), pp. 577–584 (2005)

  43. Yang A.Y., Wright J., Ma Y., Sastry S.S.: Unsupervised segmentation of natural images via lossy data compression. Comput. Vis. Image Underst. 110(2), 212–225 (2008)

    Article  Google Scholar 

  44. Singaraju, D., Grady, L., Vidal, R.: P-brush: Continuous valued MRFs with normed pairwise distributions for image segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1303–1310 (2009)

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Freedman, D. An improved image graph for semi-automatic segmentation. SIViP 6, 533–545 (2012). https://doi.org/10.1007/s11760-010-0181-9

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  • DOI: https://doi.org/10.1007/s11760-010-0181-9

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