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A multiphase segmentation method based on binary segmentation method for Gaussian noisy image

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Abstract

In this paper, a new multiphase segmentation method is proposed, in which a binary segmentation method is used in an iterative process. At each time of iteration, the region of pixels with darker mean value of intensity is separated from other regions. This segmentation is done by means of intensity function, eigenvector of Hessian matrix, and Curvelet. Proper extraction of the pixels around and on the ridge in the Gaussian noisy image and simultaneous denoizing and segmentation are the advantages of the present method. Experimental results are provided for showing the efficiency of our method.

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Notes

  1. Tight-Frame-based Algorithm.

  2. TFA with Eigenvector.

  3. Segmentation Accuracy.

  4. Peak Signal to Noise Ratio.

References

  1. Cai, X., Chan, R., Morigi, S., Sgallari, F.: Vessel segmentation in medical imaging using a tight-frame based algorithm. SIAM J. Imaging 6(1), 464–486 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Li, Fang, Ng, Michael K., Zeng, Tie Yong, Shen, Chunli: A multiphase image segmentation method based on fuzzy region competition SIAM. J. Imaging 3(3), 277–299 (2010)

    MathSciNet  MATH  Google Scholar 

  3. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vision 1, 61–79 (1997)

    Article  MATH  Google Scholar 

  4. Kass, M., Witkin, A., Tetzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vision 1, 321–331 (1988)

    Article  Google Scholar 

  5. MacQueen, J. B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability 1. University of California Press. pp. 281-297 (1967)

  6. Forgy, E.W.: Cluster analysis of multivariate data: efficiency versus interpretability of classifications. Int. J. Comput. Vision 21, 768–769 (1965)

    Google Scholar 

  7. Hartigan, J.A.: Clustering Algorithms. John Wiley & Sons, Inc, New York City (1975)

    MATH  Google Scholar 

  8. Hartigan, J.A., Wong, M.A.: Algorithm AS 136: a K-means clustering algorithm. Int. J. Comput. Vision 28(1), 100–108 (1979)

    MATH  Google Scholar 

  9. Mumford, D., Shah, J.: Boundary detection by minimizing functionals. In: Ullman, S., Richards, W. (eds.) Image Understanding, pp. 19–43. Springer, Berlin (1989)

    Google Scholar 

  10. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Int. J. Comput. Vis. 42, 577–685 (1989)

    MathSciNet  MATH  Google Scholar 

  11. Bar, L., Chan, T.F., Chung, G., Jung, M., Kiryati, N., Mohieddine, R., Sochen, N., Vese, L.A.: Mumford and Shah model and its applications to image segmentation and image restoration. Handbook of Mathemathical Methods in Imaging, pp. 1095–1157. Springer, Berlin (2011)

  12. Cai, X., Chan, R., Zeng, T.: A Two-stage image segmentation method using a convex variant of the MumfordShah Model and thresholding SIAM. Int. J. Comput. Vision 6(1), 368–390 (2013)

    MATH  Google Scholar 

  13. Bezdek, J.C., Ehrlich, R., Full, W.: Fcm: the fuzzyc-means clustering algorithm. Int. J. Comput. Vision 10(2–3), 191–203 (1984)

    Google Scholar 

  14. He, Y., Hussaini, M., Ma, J., Shafei, B., Steidl, G.: A new fuzzy c-means method with total variation regularization for segmentation of images with noisy and incomplete data. Int. J. Comput. Vision 45, 3463–3471 (2012)

    MATH  Google Scholar 

  15. Aghazadeh, N., Cigaroudy, L Sharafyan.: A multistep segmentation algorithm for vessel extraction in medical imaging. (2014) arXiv:1412.8656 [cs.CV]

  16. Aghazadeh, N., Akbarifard, F., Cigaroudy, L.Sharafya: A restoration-segmentation algorithm based on flexible Arnoldi–Tikhonov method and curvelet denoising. Int. J. Comput. Vision 10(5), 935–942 (2016)

    Google Scholar 

  17. Cengizler, C., Guven, M., Avci, M.: A fluid dynamics-based deformable model for segmentation of cervical cell images. Int. J. Comput. Vision 8(1), 2132 (2014)

    Google Scholar 

  18. Jain, R., Kasturi, R., Schunck, B.G.: Machine Vision. McGrow-Hill, New York City (1995)

    Google Scholar 

  19. Sivakumar, R.: Denoising of computer tomography images using curvelet transform. ARPN J. Eng. Appl. Sci. 2(1), 21–26 (2007)

    Google Scholar 

  20. Candes, E., Demanet, L., Donoho, D., Ying, L.: Fast discrete curvelet transforms. Int. J. Comput. Vision 5(3), 861899 (2006)

    MathSciNet  MATH  Google Scholar 

  21. Florack, L.M.J.: Image structure, Dodrecht. Kluwer Academic, The Netherland (1997)

    Book  Google Scholar 

  22. X. Cai, R. Chan, M. Nikolova, S. Member, IEEE, and T. Zeng :A Three-stage approach for segmenting degraded color images: smoothing, lifting and thresholding (SLaT) (2015) arXiv:1506.00060v1 [cs.CV]

  23. Chan, R., Yang, H., Zeng, T.: A two-stage image segmentation method for blurry images with poisson or multiplicative gamma noise SIAM. Int. J. Comput. Vision 7(1), 98127 (2014)

    MATH  Google Scholar 

  24. Li, F., Ng, M., Zeng, T., Shen, C.: A multiphase image segmentation method based on fuzzy region competition. Int. J. Comput. Vision 3(2), 277299 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Pock, T., Cremers, D., Chambolle, A., Bischof, H.:A convex relaxation approach for computing minimal partitions, In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), pp. 810817 (2009)

  26. Storath, M., Weinmann, A.: Fast partitioning of vector-valued images. Int. J. Comput. Vision 7(3), 1826–1852 (2014)

    MathSciNet  MATH  Google Scholar 

  27. Cai, J.F., Jib, H., Shenb, Z., Yea, G.B.: Data-driven tightframe construction and image denoising. Int. J. Comput. Vision 37, 89–105 (2014)

  28. Dong, B., Chien, A., Shen, Z.: Frame based segmentation for medical image. Int. J. Comput. Vision 32(4), 1724–1739 (2010)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Image Processing Laboratory, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Ladan Sharafyan Cigaroudy & Nasser Aghazadeh

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  1. Ladan Sharafyan Cigaroudy
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  2. Nasser Aghazadeh
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Correspondence to Nasser Aghazadeh.

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Cigaroudy, L.S., Aghazadeh, N. A multiphase segmentation method based on binary segmentation method for Gaussian noisy image. SIViP 11, 825–831 (2017). https://doi.org/10.1007/s11760-016-1028-9

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  • DOI: https://doi.org/10.1007/s11760-016-1028-9

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