Skip to main content
SpringerLink
Log in

A Unified Tensor Level Set Method for Image Segmentation

  • Chapter
Book cover Multimedia Analysis, Processing and Communications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 346))

Summary

This paper presents a new unified level set model for multiple regional image segmentation. This model builds a unified tensor representation for comprehensively depicting each pixel in the image to be segmented, by which the image aligns itself with a tensor field composed of the elements in form of high order tensor. Then the multi-phase level set functions are evolved in this tensor field by introducing a new weighted distance function. When the evolution converges, the tensor field is partitioned, and meanwhile the image is segmented. The proposed model has following main advantages. Firstly, the unified tensor representation integrates the information from Gaussian smoothed image, which results the model is robust against noise, especially the salt and pepper noise. Secondly, the local geometric features involved into the unified representation increase the weight of boundaries in energy functional, which makes the model more easily to detect the edges in the image and obtain better performance on non-homogenous images. Thirdly, the model offers a general formula for energy functional which can deal with the data type varying from scalar to vector then to tensor, and this formula also unifies single and multi-phase level set methods. We applied the proposed method to synthetic, medical and natural images respectively and obtained promising performance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 299.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adalsteinsson, D., Sethian, J.A.: A fast level set method for propagating interfaces. J. Computational Physics 118(2), 269–277 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chopp, D.L.: Computing minimal surfaces via level set curvature flow. J. Computational Physics 106(1), 77–91 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Processing 10(2), 266–277 (2001)

    Article  MATH  Google Scholar 

  4. Chan, T.F., Sandberg, B.Y., Vese, L.A.: Active contours without edges for vector-valued images. J. Visual Communication and Image Representation 11(2), 130–141 (2000)

    Article  Google Scholar 

  5. Chesnaud, C., Refregier, P., Boulet, V.: Statistical region snake-based segmentation adapted to different noise models. IEEE Trans. Pattern Analysis and Machine Intelligence 21(11), 1145–1157 (1999)

    Article  Google Scholar 

  6. Cohen, L.D.: On active contour models and balloons. CVGIP: Image Understanding 53(2), 211–218 (1991)

    Article  MATH  Google Scholar 

  7. Daugman, J.G.: Two-dimensional spectral analysis of cortical receptive field profiles. Vision Research 20(10), 847–856 (1980)

    Article  Google Scholar 

  8. Daugman, J.G.: Uncertainty relation for resolution in space, spatial frequency and orientation optimized by two-dimensional visual cortical filters. J. Optical Soc. Am. 2(7), 1160–1169 (1985)

    Article  Google Scholar 

  9. Han, X., Xu, C., Prince, J.L.: A topology preserving level set method for geometric deformable models. IEEE Trans. Pattern Analysis and Machine Intelligence 25(6), 755–768 (2003)

    Article  Google Scholar 

  10. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int’l J. Computer Vision 1(4), 321–331 (1988)

    Article  Google Scholar 

  11. Lee, T.S.: Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Analysis and Machine Intelligence 18(10), 959–971 (2003)

    Google Scholar 

  12. Li, C., Xu, C., Gui, C., Fox, M.D.: Level set evolution without reinitialization: a new variational formulation. In: IEEE Conf. Computer Vision Pattern Recognition, vol. 1, pp. 430–436 (2005)

    Google Scholar 

  13. Li, X., et al.: Discriminant locally linear embedding with high-order tensor data. IEEE Trans. on Systems, Man, and Cybernetics, Part B 38(2), 342–352 (2008)

    Article  Google Scholar 

  14. Lie, J., Lysaker, M., Tai, X.: A Binary Level Set Model and Some Applications to Mumford-Shah Image Segmentation. IEEE Trans. Image Process. 15(5), 1171–1181 (2006)

    Article  Google Scholar 

  15. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Applied Mathematics 42(5), 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mumford, D., Shah, J.: Boundary detection by minimizing functionals. In: Proc. IEEE Conf. Computer Vision Pattern Recognition, pp. 22–26 (1985)

    Google Scholar 

  17. Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: a level set approach. IEEE Trans. Pattern Analysis and Machine Intelligence 17(2), 158–175 (1995)

    Article  Google Scholar 

  18. Marcelja, S.: Mathematical description of the responses of simple cortical cells. J. Optical Soc. Am. 70(11), 1297–1300 (1980)

    Article  MathSciNet  Google Scholar 

  19. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation. J. Computational Physics 79(1), 12–49 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  20. Osher, S., Fedkiw, R.: Level Set Methods and Dynamics Implicit Surfaces. Springer, Heidelberg (2003)

    Google Scholar 

  21. Park, S.W., Savvides, M.: A computationally efficient tensor framework without requiring mode factorization. IEEE Trans. on Systems, Man, and Cybernetics, Part B 37(5), 1156–1166 (2007)

    Article  Google Scholar 

  22. Peng, D., Merriman, B., Osher, S., Zhao, H.K., Kang, M.: A PDE based fast local level set method. J. Computational Physics 155(2), 410–438 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  23. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University, Cambridge (1999)

    MATH  Google Scholar 

  24. Smereka, P.: Semi-implicit level set methods for curvature and surface diffusion motion. J. Scientific Computing 19(1-3), 439–456 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sun, J., Tao, D., Papadimitriou, S., Yu, P.S., Faloutsos, C.: Incremental Tensor Analysis:Theory and Applications: Theory and Applications. ACM Trans. Knowl. Disc. from Data 2(3), 11:1-11:37 (2008)

    Google Scholar 

  26. Suri, J.S., Liu, K., Singh, S., Laxminarayan, S.N., Zeng, X., Reden, L.: Shape recovery algorithms using level sets in 2D/3D medical imagery: a state-of-the-art review. IEEE Trans. Information Technology in Biomedicine 6(1), 8–28 (2002)

    Article  Google Scholar 

  27. Sapiro, G.: Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  28. Tao, D., Li, X., Wu, X., Maybank, S.J.: General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans. Pattern Analysis and Machine Intelligence 29(10), 1700–1715 (2007)

    Article  Google Scholar 

  29. Tao, D., Song, M., Li, X., Shen, J., Sun, J., Wu, X., Faloutsos, C., Maybank, S.J.: Bayesian Tensor Approach for 3-D Face Modelling. IEEE Trans. Circuits and Systems for Video Technology 18(10), 1397–1410 (2008)

    Article  Google Scholar 

  30. Tao, D., Li, X., Wu, X., Maybank, J.S.: Tensor Rank One Discriminant Analysis - A Convergent Method for Discriminative Multilinear Subspace Selection. Neurocomputing 71(12), 1866–1882 (2008)

    Article  Google Scholar 

  31. Tao, W., Jin, H., Zhang, Y.: Color image segmentation based on mean shift and normalized cuts. IEEE Trans. on Systems, Man, and Cybernetics, Part B 37(5), 1382–1389 (2007)

    Article  Google Scholar 

  32. Tschumperle, D., Deriche, R.: Diffusion PDEs on vector-valued images. IEEE Signal Processing Magazine 19(5), 16–25 (2002)

    Article  Google Scholar 

  33. Vese, L.A., Chan, T.F.: A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model. Int. J. Comput. Vision 50(3), 271–293 (2002)

    Article  MATH  Google Scholar 

  34. Wang, Z., Vemuri, B.C.: Tensor field segmentation using region based active contour model. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 304–315. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  35. Wang, Z., Vemuri, B.C.: DTI segmentation using an information theoretic tensor dissimilarity measure. IEEE Trans. Medical Imaging 24(10), 1267–1277 (2005)

    Article  Google Scholar 

  36. Xu, C., Prince, J.L.: Snake, shapes, and Gradient vector flow. IEEE Trans. Image Processing 7(3), 359–369 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  37. Zhao, H.K., Chan, T.F., Merrian, B., Osher, S.: A Variational Level Set Approach to Multiphase Motion. J. Comput. phys. 127, 179–195 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  38. Zhang, Y.: Advances in Image and Video Segmentation. In: IRM (2006)

    Google Scholar 

  39. Zenzo, S.D.: A note on the gradient of a multi-image. J. Computer Vision, Graphic, and Image Processing 33(1), 116–125 (1986)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. VIPS Lab, School of Electronic Engineering, Xidian University, Xi’an, 710071, P.R. China

    Xinbo Gao & Bin Wang

  2. School of Computer Engineering, Nanyang Technological University, 50 Nanyang Avenue, Blk N4, 639798, Singapore

    Dacheng Tao

  3. State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, 710119, P.R. China

    Xuelong Li

Authors
  1. Xinbo Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dacheng Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuelong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Engineering , Nanyang Technological University, 639798, Singapore

    Weisi Lin  & Dacheng Tao  & 

  2. Intelligent Systems Laboratory Systems Research Institute , Polish Academy of Sciences, Poland

    Janusz Kacprzyk

  3. Department of Computing , Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Zhu Li

  4. School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, U.K.

    Ebroul Izquierdo

  5. TCL-Thomson Electronics , Santa Clara, California

    Haohong Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gao, X., Wang, B., Tao, D., Li, X. (2011). A Unified Tensor Level Set Method for Image Segmentation. In: Lin, W., Tao, D., Kacprzyk, J., Li, Z., Izquierdo, E., Wang, H. (eds) Multimedia Analysis, Processing and Communications. Studies in Computational Intelligence, vol 346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19551-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19551-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19550-1

  • Online ISBN: 978-3-642-19551-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation