Skip to main content
Log in

Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiovascular system in medicine. A key problem in such a technique is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3-D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, we present in this paper new algorithmic solutions for this problem. Comparing with existing optimization-based approaches, our techniques yield better accuracy and have bounded execution time, thus is more suitable for on-line applications. Our techniques can easily detect outliers to further improve the accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • J. Aggarwal and N. Nandhakumar, “On the computation of motion from sequences of images-A review,” Proc. IEEE, vol 76, no. 8, pp. 917–935, 1988.

    Article  Google Scholar 

  • N.M. Amato, M.T. Goodrich, E.A. Ramos, “Computing the arrangement of curve segments: Divide-and-conquer algorithms via sampling,” in Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, 2000, pp. 705–706.

  • T. Asano, L.J. Guibas, and T. Tokuyama, “Walking in an arrangement topologically,” International Journal of Computational Geometry and Applications, vol. 4, no. 2, 1994, pp. 123–151.

    Article  Google Scholar 

  • D.Z. Chen, S. Luan, and J. Xu, “Topological peeling and implementation,” in Proc. 12th Annual International Symposium on Algorithms And Computation (ISAAC), Lecture Notes in Computer Science, vol. 2223, Springer Verlag, 2001, pp. 454–466.

  • S.Y.J. Chen and C.E. Metz, “Improved determination of biplane imaging geometry from two projection images and its application to three-dimensional reconstruction of coronary arterial trees,” Med. Phys., vol. 24, pp. 633–654, 1997.

    Article  PubMed  Google Scholar 

  • J. Esthappan, H. harauchi, and K. Hoffmann, “Evaulation of imaging geometries calculated from biplane images,” Med. Phys., vol. 25, no. 6, pp. 965–975, 1998.

    Article  PubMed  Google Scholar 

  • A. Fusiello, “Uncalibrated Euclidean reconstruction: A review,” Image and Vision Computing, vol. 18, pp. 555–563, 2000.

    Article  Google Scholar 

  • C.M. Grondin, I. Dyrda, A. Pasternac, L. Campeau, M.G. Bourassa, and J. Lesperance, “Discrepancies between cineangiographic and postmortem findings in patients with coronary artery disease and recent myocardial revascularization,” Circulation, vol. 49, pp. 703–708, 1974.

    PubMed  Google Scholar 

  • K.R. Hoffmann, K. Doi, H.P. Chan, and K.G. Chua, “Computer reproduction of the vasculature using an automated tracking method,” in Proc. SPIE 767, 1987, pp. 449–453.

    Google Scholar 

  • K.R. Hoffmann, K. Doi, H.P. Chan, and M. Takamiya, “Three dimensional reproduction of coronary vascular trees using the double-squre-box method of trackings,” Proc. SPIE 914, pp. 375–378, 1988.

    Google Scholar 

  • K.R. Hoffmann, C.E. Metz, and Y. Chen, “Determination of 3D imaging geometry and object configurations from two biplane views: An enhancement of the Metz-Fencil technique,” Med. Phys., vol. 22, pp. 1219–1227, 1995.

    Article  PubMed  Google Scholar 

  • K.R. Hoffmann, A. Sen, L. Lan, Kok-Gee Chua, J. Esthappan, and M. Mazzucco, “A system for determination of 3D vessel tree centerlines from biplane images,” The International Journal of Cardiac Imaging, vol. 16, pp. 315–330, 2000.

    Article  Google Scholar 

  • T. Huang and A. Netravali, “Motion and structure from feature correspondences: A review,” Proc. IEEE, vol. 82, no. 2, pp. 252–268, 1994.

    Article  Google Scholar 

  • Q.T. Luong and O.D. Faugeras, “The fundamental matrix: Theory, algorithms and stability analysis,” The International Journal of Computer Vision, vol. 1, no. 17, pp. 43–76, 1996.

    Article  Google Scholar 

  • N. Megiddo, “Applying parallel computation algorithms in the design of serial algorithms,” Journal of ACM, vol. 30, no. 4, pp. 852–865, 1983.

    Article  Google Scholar 

  • C.E. Metz and L.E. Fencil, “Determination of three-dimensional structure in biplane radiography without prior knowledge of the relationship between the two views,” Med. Phys., vol. 16, pp. 45–51, 1989.

    Article  PubMed  Google Scholar 

  • D.P. Nazareth, K.R. Hoffmann, A. Walczak, J. Dmochowski, L. Guterman, S. Rudin, D.R. Bednarek, “Determination of biplane geometry and centerline curvature in vascular imaging,” Manuscript, 2002.

  • L. Quan, “Invariants of six points and projective reconstruction from three uncalibrated images,” IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 17, no. 1, 1995.

  • P. Torr, A. Zisserman, and S. Maybank, “Robust detection of degenerate configurations for the fundamental matrix,” in Proc. of the 5th Int. Conf. on Computer Vision, 1995, pp. 1037–1042.

  • Z. Vlodaver, R. Frech, R.A. Van Tassel, and J.E. Edwards, “Correlation of the antemortem coronary angiogram and the postmortem specimen,” Circulation, vol. 47, pp. 162–169, 1973.

    PubMed  Google Scholar 

  • A. Wahle, E. Wellnhofer, I. Mugaragu, H.U. Sauer, H. Oswald, and E. Fleck, “Assessment of diffuse coronary artery disease by quantitative analysis of coronary morphology based upon 3-D reconstruction from biplane angiograms,” IEEE Transactions on Medical Imaging, vol. 14, pp. 230–241, 1995.

    Article  Google Scholar 

  • Z. Zhang, Q.T. Luong, and O. Faugeras, “Motion of an uncalibrated stereo rig: Self-calibration and metric reconstruction,” IEEE Trans. Robotics and Automation, vol. 12, no. 1, pp. 103–113, 1996.

    Article  Google Scholar 

  • Z. Zhang, “Determining the Epioplar geometry and its uncertainty: A review,” International Journal of Computer Vision, vol. 27, no. 2, pp. 161–195.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jinhui Xu.

Additional information

This research was supported in part by NIH under USPHS grant numbers HL52567.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, J., Xu, G., Chen, Z. et al. Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry. J Comb Optim 10, 113–132 (2005). https://doi.org/10.1007/s10878-005-2266-x

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-005-2266-x

Keywords

Navigation