Three Dimensional Curvilinear Structure Detection Using Optimally Oriented Flux

  • Max W. K. Law
  • Albert C. S. Chung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5305)


This paper proposes a novel curvilinear structure detector, called Optimally Oriented Flux (OOF). OOF finds an optimal axis on which image gradients are projected in order to compute the image gradient flux. The computation of OOF is localized at the boundaries of local spherical regions. It avoids considering closely located adjacent structures. The main advantage of OOF is its robustness against the disturbance induced by closely located adjacent objects. Moreover, the analytical formulation of OOF introduces no additional computation load as compared to the calculation of the Hessian matrix which is widely used for curvilinear structure detection. It is experimentally demonstrated that OOF delivers accurate and stable curvilinear structure detection responses under the interference of closely located adjacent structures as well as image noise.


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  1. 1.
    Aylward, S., Bullitt, E.: Initialization, noise, singularities, and scale in height ridge traversal for tubular object centerline extraction. TMI 21(2), 61–75 (2002)Google Scholar
  2. 2.
    Bouix, S., Siddiqi, K., Tannenbaum, A.: Flux driven fly throughs. CVPR 1, 449–454 (2003)Google Scholar
  3. 3.
    Bouix, S., Siddiqi, K., Tannenbaum, A.: Flux driven automatic centerline extraction. MedIA 9(3), 209–221 (2005)Google Scholar
  4. 4.
    Bracewell, R.: The Fourier Transform and Its Application. McGraw-Hill, New York (1986)Google Scholar
  5. 5.
    Dimitrov, P., Damon, J.N., Siddiqi, K.: Flux invariants for shape. CVPR 1, I–835–I–841(2003)Google Scholar
  6. 6.
    Frangi, A., Niessen, W., Viergever, M.: Multiscale vessel enhancement filtering. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 130–137. Springer, Heidelberg (1998)Google Scholar
  7. 7.
    Koller, T., Gerig, G., Szekely, G., Dettwiler, D.: Multiscale detection of curvilinear structures in 2-d and 3-d image data. In: IEEE International Conference on Computer Vision, pp. 864–869 (1995)Google Scholar
  8. 8.
    Krissian, K.: Flux-based anisotropic diffusion applied to enhancement of 3-d angiogram. TMI 21(11), 1440–1442 (2002)Google Scholar
  9. 9.
    Krissian, K., Malandain, G., Ayache, N., Vaillant, R., Trousset, Y.: Model-based multiscale detection of 3d vessels. CVPR 3, 722–727 (1998)Google Scholar
  10. 10.
    Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. IJCV 30(2), 117–156 (1998)CrossRefGoogle Scholar
  11. 11.
    Manniesing, W.N.R., Viergever, M.A.: Vessel enhancing diffusion a scale space representation of vessel structures. MedIA 10(6), 815–825 (2006)Google Scholar
  12. 12.
    Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., Gerig, G., Kikinis, R.: Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. MedIA 2(2), 143–168 (1998)Google Scholar
  13. 13.
    Schey, H.M.: div, grad, curl, and all that, 3rd edn. W.W.Norton & Company (1997)Google Scholar
  14. 14.
    Steger, C.: An unbiased detector of curvilinear structures. PAMI 20(2), 113–125 (1998)Google Scholar
  15. 15.
    Vasilevskiy, A., Siddiqi, K.: Flux maximizing geometric flows. PAMI 24(12), 1565–1578 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Max W. K. Law
    • 1
  • Albert C. S. Chung
    • 1
  1. 1.Lo Kwee-Seong Medical Image Analysis Laboratory, Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyHong Kong 

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