Advertisement

International Journal of Computer Vision

, Volume 92, Issue 2, pp 192–210 | Cite as

Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement

  • Fethallah BenmansourEmail author
  • Laurent D. Cohen
Article

Abstract

We present a new interactive method for tubular structure extraction. The main application and motivation for this work is vessel tracking in 2D and 3D images. The basic tools are minimal paths solved using the fast marching algorithm. This allows interactive tools for the physician by clicking on a small number of points in order to obtain a minimal path between two points or a set of paths in the case of a tree structure. Our method is based on a variant of the minimal path method that models the vessel as a centerline and surface. This is done by adding one dimension for the local radius around the centerline. The crucial step of our method is the definition of the local metrics to minimize. We have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric. The designed metric is well oriented along the direction of the vessel, admits higher velocity on the centerline, and provides a good estimate of the vessel radius. Based on the optimally oriented flux this measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel. We obtain promising results on noisy synthetic and real 2D and 3D images and we present a clinical validation.

Keywords

Vessel segmentation Minimal path method Fast marching algorithm Anisotropy Enhancement Multi-scale 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benmansour, F. (2009). Minimal path method applied to medical imaging: tubular structure and surface segmentation using multi-scaled anisotropy and recursive keypoints detection. Ph.D. Thesis, Université Paris Dauphine. Google Scholar
  2. Benmansour, F., & Cohen, L.D. (2009). Tubular anisotropy segmentation. In SSVM (pp. 14–25). Google Scholar
  3. Bornemann, F., & Rasch, C. (2006). Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle. Computing and Visualization in Science, 9(2). Google Scholar
  4. Caselles, V., Kimmel, R., & Sapiro, G. (1995). Geodesic active contours. In IEEE international conference in computer vision (ICCV’95) (pp. 694–699). Google Scholar
  5. Caselles, V., Kimmel, R., & Sapiro, G. (1997). Geodesic active contours. International Journal of Computer Vision, 22, 61–79. zbMATHCrossRefGoogle Scholar
  6. Chan, T. F., & Vese, L. A. (2001). Active contours without edges. IEEE Transactions on Image Processing, 10(2), 266–277. zbMATHCrossRefGoogle Scholar
  7. Chern, S.-S. (1996). Finsler geometry is just Riemannian geometry without the quadratic restriction. Notices of the American Mathematical Society, 43, 959–963. MathSciNetzbMATHGoogle Scholar
  8. Chopp, D. L. (2001). Replacing iterative algorithms with single-pass algorithms. Proceedings of the National Academy of Science of the USA, 98(20), 10992–10993. CrossRefGoogle Scholar
  9. Cohen, L. D., & Deschamps, T. (2007). Segmentation of 3D tubular objects with adaptive front propagation and minimal tree extraction for 3D medical imaging. Computer Methods in Biomechanics and Biomedical Engineering, 10(4), 289–305. CrossRefGoogle Scholar
  10. Cohen, L. D., & Kimmel, R. (1997). Global minimum for active contour models: a minimal path approach. International Journal of Computer Vision, 24, 57–78. CrossRefGoogle Scholar
  11. Davatzikos, C. A., & Prince, J. L. (1995). An active contour model for mapping the cortex. IEEE Transactions on Medical Imaging, 14(1), 65–80. CrossRefGoogle Scholar
  12. Deschamps, T., & Cohen, L. D. (2001). Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Image Analysis, 5, 281–299. CrossRefGoogle Scholar
  13. Deschamps, T., & Cohen, L. D. (2002). Fast extraction of tubular and tree 3D surfaces with front propagation methods. In IEEE international conference on pattern recognition (ICPR’02) (pp. 731–734). Google Scholar
  14. Descoteaux, M., Collins, L., & Siddiqi, K. (2008). A geometric flow for segmenting vasculature in proton-density weighted MRI. Medical Image Analysis, 12(4), 497–513. CrossRefGoogle Scholar
  15. Dijkstra, E. W. (1959). A note on two problems in connection with graphs. Numerische Mathematic, 1, 269–271. MathSciNetzbMATHCrossRefGoogle Scholar
  16. Evans, C. L. (1998). Partial differential equations. Providence: American Mathematical Society. zbMATHGoogle Scholar
  17. Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998). Multiscale vessel enhancement filtering. In Lecture notes in computer science (Vol. 1496, pp. 130–137). Berlin: Springer. Google Scholar
  18. Freeman, W. T., & Adelson, E. H. (1991). The design and use of steerable filters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(9), 891–906. CrossRefGoogle Scholar
  19. Gooya, A., Liao, H., Matsumiya, K., Masamune, K., Masutani, Y., & Dohi, T. (2008a). A variational method for geometric regularization of vascular segmentation in medical images. IEEE Transactions on Image Processing, 17(8), 1295–1312. MathSciNetCrossRefGoogle Scholar
  20. Gooya, A., Dohi, T., Sakuma, I., & Liao, H. (2008b). Anisotropic Haralick edge detection scheme with application to vessel segmentation. In MIAR’08: Proceedings of the 4th international workshop on medical imaging and augmented reality (pp. 430–438). Berlin: Springer. CrossRefGoogle Scholar
  21. Gooya, A., Dohi, T., Sakuma, I., & Liao, H. (2008c). R-PLUS: a Riemannian anisotropic edge detection scheme for vascular segmentation. In MICCAI’08: Proceedings of the 11th international conference on medical image computing and computer-assisted intervention—Part I (pp. 262–269). Berlin: Springer. Google Scholar
  22. Hameeteman, R., Freiman, M., Zuluaga, M. A., Joskowicz, L., Rozie, S., van Gils, M. J., van den Borne, L., Sosna, J., Berman, P., Cohen, N., Douek, P., Sánchez, I., Aissat, M., van der Lugt, A., Krestin, G. P., Niessen, W. J., & van Walsum, T. (2009). Carotid lumen segmentation and stenosis grading challenge. In Workshop in international conference on medical image computing and computer assisted intervention, September 2009. Google Scholar
  23. Hernández Hoyos, M., Serfaty, J. M., Maghiar, A., Mansard, C., Orkisz, M., Magnin, I. E., & Douek, P. (2006). Evaluation of semi-automatic arterial stenosis quantification. International Journal of Computer Assisted Radiology, 1(3), 167–175. CrossRefGoogle Scholar
  24. Holtzman-Gazit, M., Kimmel, R., Peled, N., & Goldsher, D. (2006). Segmentation of thin structures in volumetric medical images. IEEE Transactions on Image Processing, 15, 354–363. CrossRefGoogle Scholar
  25. Tavares, J., & Jorge, R. (2009). In Geodesic methods for shape and surface processing : Vol. 13. Advances in computational vision and medical image processing: methods and applications (pp. 29–56). Berlin: Springer. CrossRefGoogle Scholar
  26. Jacob, M., & Unser, M. (2004). Design of steerable filters for feature detection using Canny-like criteria. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(8), 1007–1019. CrossRefGoogle Scholar
  27. Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., & Benali, H. (2008). Accurate anisotropic fast marching for diffusion-based geodesic tractography. International Journal of Biomedical Imaging, 2008(1), 1–12. CrossRefGoogle Scholar
  28. Kimmel, R., & Bruckstein, A. (2003). Regularized Laplacian zero crossings as optimal edge integrators. International Journal of Computer Vision, 53, 225–243. CrossRefGoogle Scholar
  29. Kirbas, C., & Quek, F. K. H. (2004). A review of vessel extraction techniques and algorithms. ACM Computing Surveys, 36, 81–121. CrossRefGoogle Scholar
  30. Konukoglu, E., Sermesant, M., Clatz, O., Peyrat, J.-M., Delingette, H., & Ayache, N. (2007). A recursive anisotropic fast marching approach to reaction diffusion equation: application to tumor growth modeling. In Lecture notes in computer science : Vol. 4584. Proceedings of the 20th international conference on information processing in medical imaging (IPMI’07) (pp. 686–699). Berlin: Springer. Google Scholar
  31. Krissian, K. (2002). Flux-based anisotropic diffusion applied to enhancement of 3-D angiogram. IEEE Transactions on Medical Imaging, 21(11), 1440–1442. CrossRefGoogle Scholar
  32. Krissian, K., Malandain, G., & Ayache, N. (1997). Directional anisotropic diffusion applied to segmentation of vessels in 3D images. In SCALE-SPACE’97: Proceedings of the first international conference on scale-space theory in computer vision, London, UK (pp. 345–348). Berlin: Springer. Google Scholar
  33. Law, W. K., & Chung, A. C. S. (2006). Segmentation of vessels using weighted local variances and an active contour model. In CVPRW ’06: Proceedings of the 2006 conference on computer vision and pattern recognition workshop, Washington, DC, USA (p. 83). Los Alamitos: IEEE Computer Society. CrossRefGoogle Scholar
  34. Law, M. W. K., & Chung, A. C. S. (2007). Weighted local variance-based edge detection and its application to vascular segmentation in magnetic resonance angiography. IEEE Transactions on Medical Imaging, 26(9), 1224–1241. CrossRefGoogle Scholar
  35. Law, M. W., & Chung, A. C. (2008). Three dimensional curvilinear structure detection using optimally oriented flux. In ECCV’08: Proceedings of the 10th European con computer vision, Berlin, Heidelberg (pp. 368–382). Berlin: Springer. Google Scholar
  36. Lenglet, C., Prados, E., Pons, J.-P., Deriche, R. & Faugeras, O. (2009). Brain connectivity mapping using Riemannian geometry, control theory and PDEs. SIAM Journal on Imaging Sciences (SIIMS), 2(2), 285–322. MathSciNetzbMATHCrossRefGoogle Scholar
  37. Lesage, D., Angelini, E. D., Bloch, I., & Funka-Lea, G. (2009a). Bayesian maximal paths for coronary artery segmentation from 3d ct angiograms. In Yang, G.-Z., Hawkes, D. J., Rueckert, D., Noble, J. A., & Taylor, C. J. (Eds.), Lecture notes in computer science : Vol. 5761. International conference on medical image computing and computer assisted intervention (1) (pp. 222–229). Berlin: Springer. Google Scholar
  38. Lesage, D., Angelini, E. D., Bloch, I., & Funka-Lea, G. (2009b). A review of 3D vessel lumen segmentation techniques: models, features and extraction schemes. Medical Image Analysis, 13(6), 819–845. CrossRefGoogle Scholar
  39. Li, H., & Yezzi, A. (2006). Vessels as 4D curves: global minimal 4D paths to extract 3D tubular surfaces. In IEEE conference on computer vision and pattern recognition (CVPR’06), Workshop MMBIA06 (p. 82). Google Scholar
  40. Li, H., & Yezzi, A. (2007). Vessels as 4-D curves: global minimal 4-D paths to extract 3-D tubular surfaces and centerlines. IEEE Transactions on Medical Imaging, 26(9), 1213–1223. CrossRefGoogle Scholar
  41. Lin, Q. (2003). Enhancement, extraction, and visualization of 3D volume data. Ph.D. Thesis, Linkopings Universitet. Google Scholar
  42. Lindeberg, T. (1998). Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision, 30, 465–470. Google Scholar
  43. Lions, P. L. (1982). Generalized solutions of Hamilton-Jacobi equations. Research notes in mathematics (Vol. 69). London: Pitman. zbMATHGoogle Scholar
  44. Lorenz, C., Carlsen, I.-C., Buzug, T. M., Fassnacht, C., & Weese, J. (1997). Multi-scale line segmentation with automatic estimation of width, contrast and tangential direction in 2D and 3D medical images. In CVRMed-MRCAS’97: Proceedings of the first joint conference on computer vision, virtual reality and robotics in medicine and medial robotics and computer-assisted surgery, London, UK (pp. 233–242). Berlin: Springer. Google Scholar
  45. Manniesing, R., Viergever, M. A., & Niessen, W. J. (2006). Vessel enhancing diffusion: a scale space representation of vessel structures. Medical Image Analysis, 10(6), 815–825. CrossRefGoogle Scholar
  46. Manniesing, R., Viergever, M. A., & Niessen, W. J. (2007). Vessel axis tracking using topology constrained surface evolution. IEEE Transactions on Medical Imaging, 26(3), 309–316. CrossRefGoogle Scholar
  47. Melonakos, J., Pichon, E., Angenent, S., & Tannenbaum, A. (2008). Finsler active contours. IEEE Transactions Pattern Analysis and Machine Intelligence, 30(3), 412–423. CrossRefGoogle Scholar
  48. Mille, J., Benmansour, F., & Cohen, L. D. (2009). Carotid lumen segmentation based on tubular anisotropy and contours without edges. Insight Journal. http://www.insight-journal.org/browse/publication/670.
  49. Mohan, V., Sundaramoorthi, G., Melonakos, J., Niethammer, M., Kubicki, M., & Tannenbaum, A. (2008). Tubular surface evolution for segmentation of the cingulum bundle from DW-MRI. In Mathematical methods in computational anatomy. Google Scholar
  50. Nain, D., Yezzi, A., & Turk, G. (2004). Vessel segmentation using a shape driven flow. In Medical imaging computing and computer-assisted intervention (MICCAI’04) (pp. 51–59). Google Scholar
  51. Nemitz, O., Rumpf, M., Tasdizen, T., & Whitaker, R. (2007). Anisotropic curvature motion for structure enhancing smoothing of 3D MR angiography data. Journal of Mathematical Imaging and Vision, 27(3), 217–229. MathSciNetCrossRefGoogle Scholar
  52. Orkisz, M., Flórez Valencia, L., & Hernández Hoyos, M. (2008). Models, algorithms and applications in vascular image segmentation. Machine Graphics and Vision, 17(1), 5–33. Google Scholar
  53. Rouy, E., & Tourin, A. (1992). A viscosity solution approach to shape from shading. SIAM Journal on Numerical Analysis, 29, 867–884. MathSciNetzbMATHCrossRefGoogle Scholar
  54. Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., Gerig, G., & Kikinis, R. (1998). Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Medical Image Analysis, 2(2), 143–168. CrossRefGoogle Scholar
  55. Sethian, J. A. (1996). A fast marching level set for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93, 1591–1595. MathSciNetzbMATHCrossRefGoogle Scholar
  56. Sethian, J. A., & Vladimirsky, A. (2000). Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes. Proceedings of the National Academy of Sciences, 97(11), 5699–5703. MathSciNetzbMATHCrossRefGoogle Scholar
  57. Siddiqi, K., & Vasilevskiy, A. (2001). 3d flux maximizing flows. In EMMCVPR’01: Proceedings of the third international workshop on energy minimization methods in computer vision and pattern recognition, London, UK (pp. 636–650). Berlin: Springer. CrossRefGoogle Scholar
  58. Sundaramoorthi, G., Yezzi, A., Mennucci, A. C., & Sapiro, G. (2009). New possibilities with Sobolev active contours. International Journal of Computer Vision, 84(2), 113–129. CrossRefGoogle Scholar
  59. Tsitsiklis, J. N. (1995). Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control, 40, 1528–1538. MathSciNetzbMATHCrossRefGoogle Scholar
  60. Weber, O., Devir, Y. S., Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2008). Parallel algorithms for approximation of distance maps on parametric surfaces. ACM Transactions on Graphics, 27(4). http://portal.acm.org/citation.cfm?id=1409625.1409626.
  61. Weickert, J. (1999). Coherence-enhancing diffusion filtering. International Journal of Computer Vision, 31(2–3), 111–127. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.CEREMADE, UMR CNRS 7534Université Paris DauphineParis Cedex 16France

Personalised recommendations