Skip to main content

Framelet-Based Algorithm for Segmentation of Tubular Structures

  • Conference paper
Book cover Scale Space and Variational Methods in Computer Vision (SSVM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6667))

Abstract

Framelets have been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation that depend on the partial differential equation modeling. In this paper, we apply the framelet-based approach to identify tube-like structures such as blood vessels in medical images. Our method iteratively refines a region that encloses the possible boundary or surface of the vessels. In each iteration, we apply the framelet-based algorithm to denoise and smooth the possible boundary and sharpen the region. Numerical experiments of real 2D/3D images demonstrate that the proposed method is very efficient and outperforms other existing methods.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Arivazhagan, S., Ganesan, L.: Texture segmentation using wavelet transform. Pattern Recognition Letters 24, 3197–3203 (2003)

    Article  MATH  Google Scholar 

  2. Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J., Osher, S.: Fast global minimization of the active contour/snake model. J. Math. Imaging Vision 28, 151–167 (2007)

    Article  MathSciNet  Google Scholar 

  3. Cai, J.F., Chan, R.H., Shen, L.X., Shen, Z.W.: Simultaneously inpainting in image and transformed domains. Numer. Math. 112, 509–533 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cai, J.F., Chan, R.H., Shen, Z.W.: A framelet-based image inpainting algorithm. Appl. Comput. Harmon. Anal. 24, 131–149 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cai, J.F., Osher, S., Shen, Z.W.: Split Bregman methods and frame based image restoration. Multiscale Modeling and Simulation 8, 337–369 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Candès, E., Demanet, L., Donoho, D., Ying, L.: Fast discrete curvelet transforms. Multiscale Modeling and Simulation 5, 861–899 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chan, R.H., Setzer, S., Steidl, G.: Inpainting by flexible Haar-wavelet shrinkage. SIAM J. Imaging Sci. 1, 273–293 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chan, R.H., Chan, T.F., Shen, L.X., Shen, Z.W.: Wavelet algorithms for high-resolution image reconstruction. SIAM J. Sci. Comput. 24, 1408–1432 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chan, T.F., Esedoglu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. Technical Report 54, UCLA (2004)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  11. Daubechies, I.: Ten lectures on wavelets. Lecture Notes, vol. CBMS-NSF(61). SIAM, Philadelphia (1992)

    Book  MATH  Google Scholar 

  12. Do, M.N., Vetterli, M.: The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14, 2091–2106 (2004)

    Article  Google Scholar 

  13. Dong, B., Chien, A., Shen, Z.W.: Frame based segmentation for medical images. Technical Report 22, UCLA (2010)

    Google Scholar 

  14. Dong, B., Shen, Z.W.: MRA based wavelet frames and applications. IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing, Park City Mathematics Institute (2010)

    Google Scholar 

  15. Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inform. Theory 41, 613–627 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  16. Franchini, E., Morigi, S., Sgallari, F.: Segmentation of 3D tubular structures by a PDE-based anisotropic diffusion model. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, J.-L., Mørken, K., Schumaker, L.L. (eds.) MMCS 2008. LNCS, vol. 5862, pp. 224–241. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Franchini, E., Morigi, S., Sgallari, F.: Composed segmentation of tubular structures by an anisotropic PDE model. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 75–86. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Gooya, A., Liao, H., et al.: A variational method for geometric regularization of vascular segmentation in medical images. IEEE Trans. Image Process. 17, 1295–1312 (2008)

    Article  MathSciNet  Google Scholar 

  19. Gonzales, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice Hall, Englewood Cliffs (2008)

    Google Scholar 

  20. Hassan, H., Farag, A.A.: Cerebrovascular segmentation for MRA data using levels set. International Congress Series, vol. 1256, pp. 246–252 (2003)

    Google Scholar 

  21. Kirbas, C., Quek, F.: A review of vessel extraction techniques and algorithms. ACM Computing Surveys 36, 81–121 (2004)

    Article  Google Scholar 

  22. Ron, A., Shen, Z.W.: Affine Systems in L2(Rd): The Analysis of the Analysis Operator. J. Funct. Anal. 148, 408–447 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  23. Sandberg, B., Chan, T.F.: A logic framework for active contours on multi-channel images. J. Vis. Commun. Image R. 16, 333–358 (2005)

    Article  Google Scholar 

  24. Scherl, H., et al.: Semi automatic level set segmentation and stenosis quantification of internal carotid artery in 3D CTA data sets. Medical Image Analysis 11, 21–34 (2007)

    Article  Google Scholar 

  25. Unser, M.: Texture classification and segmentation using wavelet frames. IEEE Trans. Image Process. 4, 1549–1560 (1995)

    Article  Google Scholar 

  26. Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cai, X., Chan, R.H., Morigi, S., Sgallari, F. (2012). Framelet-Based Algorithm for Segmentation of Tubular Structures. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24785-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24784-2

  • Online ISBN: 978-3-642-24785-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics