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.
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.
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.
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.
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.
A. Fusiello, “Uncalibrated Euclidean reconstruction: A review,” Image and Vision Computing, vol. 18, pp. 555–563, 2000.
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.
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.
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.
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.
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.
T. Huang and A. Netravali, “Motion and structure from feature correspondences: A review,” Proc. IEEE, vol. 82, no. 2, pp. 252–268, 1994.
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.
N. Megiddo, “Applying parallel computation algorithms in the design of serial algorithms,” Journal of ACM, vol. 30, no. 4, pp. 852–865, 1983.
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.
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.
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.
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.
Z. Zhang, “Determining the Epioplar geometry and its uncertainty: A review,” International Journal of Computer Vision, vol. 27, no. 2, pp. 161–195.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported in part by NIH under USPHS grant numbers HL52567.
Rights 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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10878-005-2266-x