Advertisement

Pde-Based Three Dimensional Path Planning For Virtual Endoscopy

  • M. Sabry Hassouna
  • Aly A. Farag
  • Robert Falk
Part of the Topics in Biomedical Engineering. International Book Series book series (ITBE)

Three-dimensional medial curves (MC) are an essential component of any virtual endoscopy (VE) system, because they serve as flight paths for a virtual camera to navigate the human organ and to examine its internal views. In this chapter, we propose a novel framework for inferring stable continuous flight paths for tubular structures using partial differential equations (PDEs). The method works in two passes. In the first pass, the overall topology of the organ is analyzed and its important topological nodes identified. In the second pass, the organ’s flight paths are computed by tracking them starting from each identified topological node. The proposed framework is robust, fully automatic, computationally efficient, and computes medial curves that are centered, connected, thin, and less sensitive to boundary noise. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several synthetic 3D phantoms and clinical datasets.

Keywords

Color Version Cluster Graph Virtual Colonoscopy Virtual Camera Virtual Endoscopy 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baert AL, Sartor K. 2001. Virtual endoscopy and related 3D techniques. Berlin: Springer.Google Scholar
  2. 2.
    Buthiau D, Khayat D. 2003. Virtual endoscopy. Berlin: Springer.Google Scholar
  3. 3.
    Y Zhou, Toga AW. 1999. Efficient skeletonization of volumetric objects. IEEE Trans Visualiz Comput Graphics 5(3):196-209.CrossRefGoogle Scholar
  4. 4.
    Bitter I, Kaufman AE, Sato M. 2001. Penalized-distance volumetric skeleton algorithm. IEEE Trans Visualiz Comput Graphics 7(3):195-206.CrossRefGoogle Scholar
  5. 5.
    Ma CM, Sonka M. 1996. A fully parallel 3d thinning algorithm and its applications. Comput Vision Image Understand 64:420-433.CrossRefGoogle Scholar
  6. 6.
    Svensson S, Nystr öm I, Sanniti di Baja G. 2002. Curve skeletonization of surface-like objects in 3d images guided by voxel classification. Pattern Recognit Lett, 23(12):1419-1426.MATHCrossRefGoogle Scholar
  7. 7.
    Deschamps T. 2001. Curve and shape extraction with minimal path and level-sets techniques: applications to 3D medical imaging. PhD dissertation, Universit é Paris, IX Dauphine.Google Scholar
  8. 8.
    Bouix S, Siddiqi K, Tannenbaum A. 2003. Flux driven fly throughs. In Proceedings of the IEEE computer society conference on computer vision and pattern recognition, pp. 449-454. Washing-ton, DC: IEEE Computer Society.Google Scholar
  9. 9.
    Hassouna MS, Farag AA. 2005. PDE-based three-dimensional path planning for virtual en-doscopy. In: Information processing in medical imaging: 19th international conference, IPMI 2005, pp. 529-540. Lecture Notes in Computer Science, Vol. 3565. Berlin: Springer.Google Scholar
  10. 10.
    Hassouna MS, Farag AA, Falk R. 2005. Differential fly-throughs (DFT): a general framework for computing flight paths. In Medical image computing and computer-assisted intervention: MICCAI 2005: 8th international conference, pp. 26-29. Berlin: Springer.Google Scholar
  11. 11.
    Ma CM. 1995. A fully parallel thinning algorithm for generating medial faces. Pattern Recognit Lett 16:83-87.CrossRefGoogle Scholar
  12. 12.
    Tsao YF, Fu KS. 1981. A parallel thinning algorithm for 3d pictures. Comput Graphics Image Process 17:315-331.CrossRefGoogle Scholar
  13. 13.
    Saha PK, Majumder DD. 1997. Topology and shape preserving parallel thinning for 3d digital images: a new approach. In Proceedings of the 9th international conference on image analysis and processing, Vol. 1, pp. 575-581. Lecture Notes in Computer Science, Vol. 1310. Berlin: Springer.Google Scholar
  14. 14.
    Palagyi K, Kuba A. 1997. A parallel 12-subiteration 3d thinning algorithm to extract medial lines. In Proceedings of the 7th international conference on computer analysis of images and patterns, pp. 400-407. Lecture Notes in Computer Science, Vol. 1296. Berlin: Springer.CrossRefGoogle Scholar
  15. 15.
    Lohou C, Bertrand G. 2004. A 3d 12-subiteration thinning algorithm based on p-simple points. Discr Appl Math 139(1-3):171-195.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Manzanera A, Bernard TM, Pr êteux F, Longuet B. 1999. A unified mathematical framework for a compact and fully parallel n-d skeletonization procedure. Proc SPIE, 3811:57-68.CrossRefGoogle Scholar
  17. 17.
    Palagyi K, Kuba A. 1999. Directional 3d thinning using 8 subiterations. In Proceedings of the 8th international conference on discrete geometry for computer imagery (DCGI ’99). Lecture Notes in Computer Science, Vol. 1568, pp. 325-336. Berlin: Springer.Google Scholar
  18. 18.
    Gong W, Bertrand G. 1990. A simple parallel 3d thinning algorithm. In Proceedings of 10th International Conference on Pattern Recognition, 1990, pp. 188-190. Washington, DC: IEEE.CrossRefGoogle Scholar
  19. 19.
    Borgefors G. 1986. Distance transformations in digital images. Comput Vision Graphics Image Process 34:344-371.CrossRefGoogle Scholar
  20. 20.
    Adalsteinsson D, Sethian J. 1995. A fast level set method for propagating interfaces. J Comput Phys 118:269-277.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Gagvani N, Silver D. 1999. Parameter-controlled volume thinning. Graphical Models Image Process 61(3):149-164.CrossRefGoogle Scholar
  22. 22.
    Bitter I, Sato M, Bender M, McDonnell KT, Kaufman A, Wan M. 2000. Ceasar: a smooth, accurate and robust centerline extraction algorithm. In Proceedings of the Visualization ’00 conference, pp. 45-52. Washington, DC: IEEE Computer Society.Google Scholar
  23. 23.
    Sato M, Bitter I, Bender MA, Kaufman AE, Nakajima M. 2000. Teasar: Tree-structure-extraction algorithm for accurate and robust skeletons. In Proceedings of the 8th Pacific conference on computer graphics and applications (PG ’00), p. 281. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  24. 24.
    Dijkstra EW. 1959. A note on two problems in connexion with graphs. Num Math 1:269-271.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Paik DS, Beaulieu CF, Jeffrey RB, Rubin GD, Napel S. 1998. Automated path planning for virtual endoscopy. Med Phys 25(5):629-637.CrossRefGoogle Scholar
  26. 26.
    Dimitrov P, Damon JN, Siddiqi K. 2003. Flux invariants for shape. In Proceedings of 2003 IEEE computer society conference on computer vision and pattern recognition (CVPR 2003), pp. 835-841. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  27. 27.
    Pudney C. 1998. Distance-ordered homotopic thinning: a skeletonization algorithm for 3d digital images. Comput Vision Image Understand 72(3):404-413.CrossRefGoogle Scholar
  28. 28.
    Telea A, Vilanova A. 2003. A robust level-set algorithm for centerline extraction. In Proceed-ings of the symposium on visualization (VisSym 2003), pp. 185-194. Aire-la-Ville, Switzerland: Eurographics Association.Google Scholar
  29. 29.
    Deschamps T, Cohen LD. 2001. Fast extraction of minimal paths in 3d images and applications to virtual endoscopy. Med Image Anal 5(4): 281-299.CrossRefGoogle Scholar
  30. 30.
    Chuang J-H, Tsai C-H, Ko M-C. 2000. Skeletonization of three-dimensional object using gener-alized potential field. IEEE Trans Pattern Anal Machine Intell 22(11):1241-1251.CrossRefGoogle Scholar
  31. 31.
    Yuan X, Balasubramanian R, Cornea ND, Silver D. 2005. Computing hierarchical curve-skeletons of 3d objects. The Visual Computer. 21(11):945-955.CrossRefGoogle Scholar
  32. 32.
    Ma W-C, Wu F-C, Ouhyoung M. 2003. Skeleton extraction of 3d objects with radial basis func- tions. In Proceedings of the 2003 international conference on shape modeling and applications (SMI 2003), pp. 207-215, 295. Washington, DC: IEEE Computer Society.Google Scholar
  33. 33.
    Wu F-C, Ma W-C, Liou P-C, Laing R-H, Ouhyoung M. 2003. Skeleton extraction of 3d objects withvisiblerepulsiveforce.InProceedingsofthe Computer Graphics Workshop 2003 (Hua-Lien, Taiwan). Available online: http://www.lems.brown.edu/vision/people/leymarie/Refs/ CompGraphics/Shape/Skel.html.
  34. 34.
    Bellman R, Kalaba R. 1965. Dynamic programming and modern control theory. London: London Mathematical Society Monographs.Google Scholar
  35. 35.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP. 1992. Numerical recipes in C: the art of scientific computing. New York: Cambridge UP.Google Scholar
  36. 36.
    Yatziv L, Bartesaghi A, Sapiro G. 2006.A fast o(n) implementation of the fast marching algorithm. J Comput Phys 212(2):393-399.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • M. Sabry Hassouna
    • 1
  • Aly A. Farag
    • 1
  • Robert Falk
    • 2
  1. 1.Computer Vision and Image Processing LaboratoryUniversity of LouisvilleLouisvilleUSA
  2. 2.Department of Medical ImagingJewish HospitalLouisvilleUSA

Personalised recommendations