Towards a theory of a solution space for the biplane imaging geometry problem

Medical Physics

Volumn 33, Issue 10, 2006, Pages 3647-3665

  Singh, Vikas ^a,b   Xu, Jinhui ^a   Hoffmann, Kenneth R ^c   Xu, Guang ^a   Chen, Zhenming ^a   Gopal, Anant ^c  

^a State University of New York   (United States)

^b UNIVERSITY AT BUFFALO   (United States)

^c UNIVERSITY AT BUFFALO   (United States)

Author keywords

Arrangement; Biplane angiography; Biplane geometry; Coronary angiographic imaging; Geometric optimization; Topological peeling; Vascular imaging

Indexed keywords

ERRORS; GEOMETRY; IMAGE RECONSTRUCTION; UNCERTAINTY ANALYSIS;

ARRANGEMENT; BIPLANE ANGIOGRAPHIES; BIPLANE GEOMETRY; GEOMETRIC OPTIMIZATION; TOPOLOGICAL PEELING; VASCULAR IMAGING;

MEDICAL IMAGING;

ACCURACY; ARTICLE; BIPLANE IMAGING; CALCULATION; ERROR; GEOMETRY; IMAGING; MATHEMATICAL MODEL; PRIORITY JOURNAL; THEORY;

EID: 33749382318     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.2350658     Document Type: Article

References (31)

1. M. J. Potel, J. M. Rubin, S. A. MacKay, A. M. Aisen, J. Al-Sadir, and R. E. Sayre, "Methods for evaluating cardiac wall motion in three dimensions using bifurcation points of the coronary arterial tree," Invest. Radiol. 8, 47-57 (1983).
2. D. Parker, D. Pope, R. Van Bree, and H. Marshall, "Three-dimensional reconstruction of moving arterial beds from digital subtraction angiography," Comput. Biomed. Res. 20, 166-185 (1987).
3. H. Wollschlaeger, A. M. Zeiher, P. Lee, U. Solzbach, T. Bonzel, and H. Just, "Computed triple orthogonal projections for optimal radiological imaging with biplane isocentric multi-directional x-ray systems," Proc. IEEE Comput. Cardiology, 185-188 (1987).
4. 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. 16, 45-51 (1989).
5. 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. 22, 1219-1227 (1995).
6. 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 Trans. Med. Imaging 14, 230-241 (1995).
7. 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. 24, 633-654 (1997).
8. 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," Int. J. Card. Imaging 16, 315-330 (2000).
9. D. P. Nazareth, K. R. Hoffmann, A. Walczak, J. Dmochowski, L. Guterman, S. Rudin, and D. R. Bednarek, "Determination of biplane geometry and centerline curvature in vascular imaging," Proc. SPIE 4684, 883-892 (2002).
10. F. Cheriet and J. Meunier, "Self-calibration of a biplane x-ray imaging system," Comput. Med. Imaging Graph. 23, 133-141 (1999).
11. G. Xu and Z. Zhang, Epipolar Geometry in Stereo, Motion and Object Recognition: A Unified Approach (Kluwer, Dordrecht, The Netherlands, 1996).
12. Q. T. Luong and O. D. Faugeras, "The fundamental matrix: Theory, algorithms and stability analysis," Int. J. Comput. Vis. 1, 43-76 (1996).
13. Z. Zhang, Q. T. Luong, and O. Faugeras, "Motion of an uncalibrated stereo rig: Self-calibration and metric reconstruction," IEEE Trans. Rob. Autom. 12, 103-113 (1996).
14. Z. Zhang, "Determining the epipolar geometry and its uncertainty: A review," Int. J. Comput. Vis. 27, 161-195 (1998).
15. K. R. Hoffmann, A. Wahle, C. Pello-Barakat, J. Sklansky, and M. Sonka, "Biplane x-ray angiograms, intravascular ultrasound and 3D visualization of coronary vessels," Int. J. Card. Imaging 15, 495-512 (1999).
16. J. Xu, G. Xu, Z. Chen, V. Singh, and K. R. Hoffmann, "Efficient algorithms for determining 3-D biplane imaging geometry," J. Comb. Optim. 10, 113-132 (2005).
17. V. Singh, J. Xu, K. R. Hoffmann, G. Xu, Z. Chen, and A. Gopal, "A new algorithm for determining 3D biplane imaging geometry: Theory and implementation," Proc. SPIE 5747, 2118-2129 (2005).
18. H. Wollschlager, P. Lee, A. Zeiher, U. Solzbach, T. Bonzel, and H. Just, "Mathematical tools for spatial computations with biplane isocentric x-ray equipment," Biomedizinische Technik 31, 101-106 (1986).
19. J. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality (Princeton University Press, Princeton, NJ, 2002).
20. J. Dmochowski, K. R. Hoffmann, V. Singh, J. Xu, and D. P. Nazareth, "Effects of point configuration on the accuracy in 3D reconstruction from biplane images," Med. Phys. 32, 2862-2869 (2005).
21. M. de Berg, O. Schwarzkopf, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications (Springer-Verlag, Berlin, 2000).
22. D. Z. Chen, S. Luan, and J. Xu, "Topological peeling and implementation," Int. J. Comput. Geom. Appl. 13, 135-172 (2003).
23. T. Asano, L. J. Guibas, and T. Tokuyama, "Walking in an arrangement topologically," Int. J. Comput. Geom. Appl. 4, 123-151 (1994).
24. V. Singh, L. Mukherjee, J. Xu, K. R. Hoffmann, G. Xu, and Z. Chen, "Efficient geometric techniques for reconstructing 3D vessel trees from biplane image," In SCG '05: Proceedings of the 21st Annual Symposium on Computational Geometry (ACM Press, Pisa, 2005), pp. 368-369.
25. A. Fabri, G. J. Giezeman, L. Kettner, S. Schirra, and S. Schonherr, On the Design of CGAL, the Computational Geometry Algorithms Library (IN-RIA Sophia-Antipolis, 1999).
26. K. Mehlhorn, S. Naher, M. Seel, and C. Uhrig, The LEDA User Manual Version 3.8 (Max-Planck-Insitute for Informatik, 66123 Saarbrucken, Germany, 1999).
27. T. Granlund, The GNU Multiple Precision Arithmetic Library (GNU, 1996).
28. P. H. Schoeneman, "A generalized solution of the orthogonal procrustes problem," Psychometrika 31, 1-10 (1966).
29. P. H. Schoeneman and R. M. Carroll, "Fitting one matrix to another under choice of a central dilation and a rigid motion," Psychometrika 35, 245-254 (1970).
30. A. Jain, R. Kon, Y. Zhou, and G. Fichtinger, "C-arm calibration-Is it really necessary?" in Proceedings of of the 8th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2005), Palm Springs, CA, 639-646 (2005).
31. H. Edelsbrunner, Algorithms in Combinatorial Geometry, EATCS Monographs in Theoretical Computer Science (Springer, New York, 1987).