Volumetric Segmentation Using Shape Models In The Level Set Framework

  • Fuxing Yang
  • Jasjit S. Suri
  • Milan Sonka
Part of the Topics in Biomedical Engineering. International Book Series book series (ITBE)

It is an arduous task to extract the structural detail in medical images because of noisy or partial volume effects, or incomplete information. However, expert-identified segmentation results are often available, and most of the structures to be extracted have a similar shape from one subject to another. Then to model the family of shapes and restricting the new structure to be extracted within the class is of particular interest. Generally, active shape models are used to implement this framework. However, the definition of the image term is the most challenging factor in such an approach. The level set methods define a powerful optimization framework via an implicit description of different shapes in various dimensional spaces. This advantage can help recover objects of interest by the propagation of curves or surfaces. The properties of the level set methods support complex topologies, considered in higher dimensions, are implicit, intrinsic, and parameter free. In this chapter, we give a review of the level set method and show the usage of the shape models for segmentation of objects in 2D and 3D in a level set framework via regional information.


Active Contour SHAPE Model Active Contour Model Active Appearance Model Active Shape Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8 References

  1. 1.
    Suri JS, Liu K, Singh S, Laxminarayan S, Zeng X, Reden L. 2002. Shape recovery algorithms using level sets in 2-d/3-d medical imagery: a state-of-the-art review. IEEE Trans Inform Technol Biomed 6:8-28.CrossRefGoogle Scholar
  2. 2.
    Angenent S, Chopp D, Ilmanen T. 1995. On the singularities of cones evolving by mean cur- vature. Commun Partial Differ Eq 20:1937-1958.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Chopp DL. 1993. Computing minimal surfaces via level set curvature flow. J Comput Phys 106:77-91.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Sethian JA. 1990. Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws. J Differ Geom 31:131-161.MATHMathSciNetGoogle Scholar
  5. 5.
    Sethian JA, Malladi R. 1996. An O(N log N ) algorithm for shape modeling. Proc Natl Acad Sci USA 93:9389-9392.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Sethian JA. 1995. Algorithms for tracking interfaces in CFD and material science. Annu Rev Comput Fluid Mech 12:125-138.Google Scholar
  7. 7.
    Sussman M, Smereka P, Osher SJ. 1994. A level set method for computing solutions to incom- pressible two-phase flow. J Comput Phys 114:146-159.MATHCrossRefGoogle Scholar
  8. 8.
    Rhee C, Talbot L, Sethian JA. 1995. Dynamical study of a premixed V-flame. J Fluid Mech 300:87-115.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Sethian JA, Strain JD. 1992. Crystal growth and dentritic solidification. J Comput Phys 98:231- 253.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Adalsteinsson D, Sethian JA. 1995. A unified level set approach to etching, deposition and lithography, I: algorithms and two-dimensional simulations. J Comput Phys 120:128-144.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Breen DE, Whitaker RT. 2001. A level-set approach for the metamorphosis of solid models. IEEE Trans Visualiz Comput Graphics 7:173-192.CrossRefGoogle Scholar
  12. 12.
    Mansouri AR, Konrad J. 1999. Motion segmentation with level sets. IEEE Trans Image Process 12(2):201-220.CrossRefGoogle Scholar
  13. 13.
    Paragios N, Deriche R. 2000. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans Pattern Anal Machine Intell 22(3):266-280.CrossRefGoogle Scholar
  14. 14.
    Kornprobst P, Deriche R, Aubert G. 1999. Image sequence analysis via partial differential equations. J Math Imaging Vision 11:5-26.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Faugeras O, Keriven R. 1998. Variational principles, surface evolution, PDEs, level set methods and the stereo problem. IEEE Trans Image Process 7:336-344.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kimmel R. 1995. Tracking level sets by level sets: a method for solving the shape from shading problem. Comput Vision Image Understand 62:47-58.CrossRefGoogle Scholar
  17. 17.
    Kimmel R, Bruckstein AM. 1995. Global shape from shading. Comput Vision Image Understand 62:360-369.CrossRefGoogle Scholar
  18. 18.
    Sapiro G, Kimmel R, Shaked D, Kimia BB, Bruckstein AM. 1997. Implementing continuous-scale morphology via curve evolution. Pattern Recognit 26:1363-1372.CrossRefGoogle Scholar
  19. 19.
    Sochen N, Kimmel R, Malladi R. 1998. A geometrical framework for low level vision. IEEE Trans Image Process 7:310-318.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Sapiro G, 1997. Color snakes. Comput Vision Image Understand 68:247-253.CrossRefGoogle Scholar
  21. 21.
    Caselles V, Kimmel R, Sapiro G, Sbert C. 1996. Three dimensional object modeling via minimal surfaces. In Proceedings of the European conference on computer vision (ECCV), pp. 97-106. New York: Springer.Google Scholar
  22. 22.
    Kimmel R, Amir A, Bruckstein AM. 1995. Finding shortest paths on surfaces using level sets propagation. IEEE Trans Pattern Anal Machine Intell 17:635-640.CrossRefGoogle Scholar
  23. 23.
    DeCarlo D, Gallier J. 1996. Topological evolution of surfaces. In Proceedings of the graphics interface 1996 conference, pp. 194-203. Ed WA Davis, RM Bartels. Mississauga, Ontario: Canadian Human-Computer Communications Society.Google Scholar
  24. 24.
    Telea A. 2004. An image inpainting technique based on the fast marching method. Graphics Tools 9:23-24.Google Scholar
  25. 25.
    Suri JS. 2001. Two dimensional fast mr brain segmentation using a region-based level set approach. Int J Eng Med Biol 20(4):84-95.CrossRefMathSciNetGoogle Scholar
  26. 26.
    Malladi R, Sethian JA. 1998. A real-time algorithm for medical shape recovery. In Proceedings of the international conference on computer vision (ICCV’98), pp. 304-310. Washington, DC: IEEE Computer Society.Google Scholar
  27. 27.
    Hermosillo G, Faugeras O, Gomes J. 1999. Unfolding the cerebral cortex using level set meth- ods. In Proceedings of the second international conference on scale-space theories in computer vision. Lecture notes in computer science, Vol. 1682, pp. 58-69. New York: Springer.Google Scholar
  28. 28.
    Sarti A, Ortiz C, Lockett S, Malladi R. 1996. A unified geometric model for 3d confocal image analysis in cytology. In Proceedings of the international symposium on computer graphics, image processing, and vision (SIBGRAPI’98), pp. 69-76. Washington, DC: IEEE Computer Society.Google Scholar
  29. 29.
    Niessen WJ, ter Haar Romeny BM, Viergever MA. 1998. Geodesic deformable models for medical image analysis. IEEE Trans Med Imaging 17:634-641.CrossRefGoogle Scholar
  30. 30.
    Gomes J, Faugeras O. 2000. Level sets and distance functions. In Proceedings of the European conference on computer vision (ECCV), pp. 588-602. New York: Springer.Google Scholar
  31. 31.
    Suri JS. 2000. Leaking prevention in fast level sets using fuzzy models: an application in MR brain. In Proceedings of the International Conference on information technology applications in biomedicine, pp. 220-226. Washington, DC: IEEE Computer Society.Google Scholar
  32. 32.
    Zeng X, Staib LH, Schultz RT, Duncan JS. 1999. Segmentation and measurement of the cortex from 3d mr images using coupledsurfaces propagation. IEEE Trans Med Imaging 18:927-937.CrossRefGoogle Scholar
  33. 33.
    Angelini E, Otsuka R, Homma S, Laine A. 2004. Comparison of ventricular geometry for two real time 3D ultrasound machines with a three dimensional level set. In Proceedings of the IEEE international symposium on biomedical imaging (ISBI), Vol. 1, pp. 1323-1326. Washington, DC: IEEE Computer Society.Google Scholar
  34. 34.
    Lin N, Yu W, Duncan JS. 2003. Combinative multi-scale level set framework for echocardio- graphic image segmentation. Med Image Anal 7:529-537.CrossRefGoogle Scholar
  35. 35.
    Baillard C, Hellier P, Barillot C. 2000. Segmentation of 3-d brain structures using level sets. Internal Publication of IRISA, Rennes Cedex, France.Google Scholar
  36. 36.
    Leventon ME, Grimson WL, Faugeras O. 2000. Statistical shape influence in geodesic active contours. In Proceedings of the IEEE conference on computer vision and pattern recognition, Vol. 1, pp. 316-323. Washington, DC: IEEE Computer Society.Google Scholar
  37. 37.
    Tsai A, Yezzi A, Wells W, Tempany C, Tucker D, Fan A, Grimson WE, Willsky A. 2003. A shape-based approach to the segmentation of medical imagery using level sets. IEEE Trans Med Imaging 22:137-154.CrossRefGoogle Scholar
  38. 38.
    Rousson M, Paragios N, Deriche R. 2004. Implicit active shape models for 3d segmentation in MRI imaging. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI), pp. 209-216. New York: Springer.Google Scholar
  39. 39.
    Sethian JA. 1999. Level set methods and fast marching methods evolving interfaces in com- putational geometry, fluid mechanics, computer vision, and materials science. Cambridge: Cambridge UP.Google Scholar
  40. 40.
    Osher S, Paragios N. 2003. Geometric level set methods in imaging vision and graphics. New York: Springer.MATHGoogle Scholar
  41. 41.
    Osher S, Sethian JA. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation. Comput Phys 79:12-49.MATHCrossRefMathSciNetGoogle Scholar
  42. 42.
    Adalsteinsson D, Sethian JA. 1995. A fast level set method for propagating interfaces. J Comput Phys 118:269-277.MATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Mori K, Hasegawa J, Toriwaki J, Anno H, Katada K. 1996. Recognition of Bronchus in three dimensional x-ray ct images with applications to virtualized bronchoscopy system. In Pro- ceedings of the IEEE international conference on pattern recognition (ICPR’96), pp. 528-532. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  44. 44.
    Walker NE, Olszewski ME, Wahle A, Nixon E, Sieren JP, Yang F, Hoffman EA, Rossen JD, Sonka M. 2005. Measurement of coronary vasoreactivity in sheep using 64-slice multidetector computed tomography and 3-d segmentation. Computer-assisted radiology and surgery (CARS 2005): proceedings of the 19th international congress and exhibition. Amsterdam: Elsevier.Google Scholar
  45. 45.
    Cohen LD, Cohen RK. 1997. Global minimum for active contour models: a minimal path approach. Comput Vision 24:57-78.CrossRefGoogle Scholar
  46. 46.
    Lin Q. 2003. Enhancement, extraction, and visualization of 3d volume data. PhD dissertation, Department of Electrical Engineering, Linkoping University, Sweden.Google Scholar
  47. 47.
    Kass M, Witkin A, Terzopoulos D. 1988. Snakes: active contour models. Int J Comput Vision 1:321-331.CrossRefGoogle Scholar
  48. 48.
    Caselles V, Catte F, Coll T, Dibos F. 1993. A geometric model for active contours in image processing. Numer Math 66:1-31.MATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Malladi R, Sethian JA, Vemuri BC. 1994. Evolutionary fronts for topology-independent shape modeling and recovery. In Proceedings of the third European conference on computer vision (ECCV’1994). Lecture notes in computer science, Vol. 800, pp. 3-13.Google Scholar
  50. 50.
    Yang F, Mackey MA, Ianzini F, Gallardo G, Sonka M. 2005. Cell segmentation, tracking, and mitosis detection using temporal context. in Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI). New York: Springer. In press.Google Scholar
  51. 51.
    Lee J. 1983. Digital image noise smoothing and the sigma filter. Comput Vision Graphics Image Process 24:255-269.CrossRefGoogle Scholar
  52. 52.
    Perona P, Malik J. 1990. Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Machine Intell 12(7):629-639.CrossRefGoogle Scholar
  53. 53.
    Osher S, Rudin L. 1990. Feature-oriented image enhancement using shock filters. SIAM J Numer Anal 27:919-940.MATHCrossRefGoogle Scholar
  54. 54.
    Caselles V, Kimmel R, Sapiro G. 1997. Geodesic active contours. Int J Comput Vision 22:61-79.MATHCrossRefGoogle Scholar
  55. 55.
    Cootes TF, Taylor CJ, Cooper DH, Graham J. 1995. Active shape models—their training and application. Comput Vision Image Understand 61:38-59.CrossRefGoogle Scholar
  56. 56.
    Leventon ME, Grimson WL, Faugeras O, Wells III WM. 2000. Level set based segmentation with intensity and curvature priors. In Proceedings of the IEEE workshop on mathematical methods in biomedical image analysis, pp. 1121-1124. Washington, DC: IEEE Computer Society.Google Scholar
  57. 57.
    Mumford D, Shah J. 1989. Optimal approximations by piecewise smooth functions and asso- ciated variational problems. Commun Pure Appl Math 42:577-685.MATHCrossRefMathSciNetGoogle Scholar
  58. 58.
    Chan TF, Vese LA. 2001. Active contours without edges. IEEE Trans Image Process 10:266-277.MATHCrossRefGoogle Scholar
  59. 59.
    Angelini ED, Holmes J, Laine A, Homma S. 2003. Segmentation of RT3D ultrasound with implicit deformable models without gradients. In Proceedings of the third international sym- posium on image and signal processing and analysis, Vol. 2, pp. 711-716. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  60. 60.
    Wang Y, Staib LH. 1998. Boundary finding with correspondence using statistical shape models. Comput Vision Pattern Recognit 22(7):338-345.Google Scholar
  61. 61.
    Mitchell SC, Bosch JG, Lelieveldt BPF, van der Geest RJ, Reiber JHC, Sonka M. 2002. 3-d active appearance models: segmentation of cardiac mr and ultrasound images. IEEE Trans Med Imaging 21(9):1167-1178.CrossRefGoogle Scholar
  62. 62.
    Cootes TF, Edwards GJ, Taylor CJ. 2000. Active appearance models. IEEE Trans Pattern Anal Machine Intell 23:681-685.CrossRefGoogle Scholar
  63. 63.
    Riedmiller M, Braun H. 1993. A direct adaptive method for faster backpropagation learning: the rprop algorithm. In Proceedings of the of the IEEE international conference on neural networks, pp. 586-591. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  64. 64.
    Igel C, Toussaint M, Weishui W. 2004. Rprop using the natural gradient compared to Levenberg- Marquardt optimization. In Trends and applications in constructive approximation. Inter- national Series of Numerical Mathematics, Vol. 151, 259-272. Heidelberg: Birkhuser, Springer-Verlag.CrossRefGoogle Scholar
  65. 65.
    Freedman D, Radke R, Zhang T, Jeong Y, Lovelock D, Chen G. 2005. Model-based segmenta- tion of medical imagery by matching distributions. IEEE Trans Med Imaging 24(3):281-292.CrossRefGoogle Scholar
  66. 66.
    Tsai A, Yezzi A, Willsky AS. 2001. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans Image Process 10:1169-1186.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Fuxing Yang
    • 1
  • Jasjit S. Suri
    • 2
  • Milan Sonka
    • 1
  1. 1.Department of Electrical and Computer EngineeringThe University of IowaIowa CityUSA
  2. 2.Eigen LLCGrass ValleyUSA

Personalised recommendations