Pde-Based Three Dimensional Path Planning For Virtual Endoscopy
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.
KeywordsColor Version Cluster Graph Virtual Colonoscopy Virtual Camera Virtual Endoscopy
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- 1.Baert AL, Sartor K. 2001. Virtual endoscopy and related 3D techniques. Berlin: Springer.Google Scholar
- 2.Buthiau D, Khayat D. 2003. Virtual endoscopy. Berlin: Springer.Google Scholar
- 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.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.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.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
- 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
- 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
- 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
- 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
- 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.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.Bellman R, Kalaba R. 1965. Dynamic programming and modern control theory. London: London Mathematical Society Monographs.Google Scholar
- 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