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Reconstruction of 3-D Binary Tree-Like Structures From Three Mutually Orthogonal Projections
March 1994 (vol. 16 no. 3)
pp. 241-248

A method is developed to generate the 3D binary representation for a tree-like object from three mutually orthogonal projections. This is done by first backprojecting the binarized images from three directions and then iteratively removing artifacts in the backprojection. Three different algorithms have been developed: the Lagrange multiplier algorithm, the conjugate gradient algorithm, and the minimum-voxel representation algorithm (MRA). The performance of these algorithms under noise-free conditions is evaluated using mathematically projected images of a 3D tree structure. While all three algorithms are capable of producing a relatively accurate reconstruction, the MRA is superior not only because it requires the least amount of computation but also because it uses binary instead of gray-scale information in the input images. Reconstruction of 3D coronary arterial structures using MRA is further verified with X-ray images of a human chest phantom and shows a satisfactory performance. The result of this study should be valuable for 3D imaging of blood vessels.

[1] Dr. Crypton, "The failure of the mind's eye,"Sci. Dig., vol. 93, pp. 74-77, 1985.
[2] I. Liu and Y. Sun, "Fully automated reconstruction of 3-D vascular tree structures from two orthogonal views using computational algorithms and production rules,"Opt. Eng., vol. 31, pp. 2197-2207, 1992.
[3] M. Soumekh, "Binary image reconstruction from four projections," inProc. IEEE Int. Conf. Acoustics, Speech,&Signal Processing, 1988, pp. 1281-1283.
[4] G. T. Herman and A. Lent, "Iterative reconstruction algorithms,"Computers in Biology and Medicine, vol. 6, pp. 273-294, 1976.
[5] A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation,"IEEE Trans. Circuits Syst., vol. 22, pp. 735-742, 1975.
[6] B. S. Gottfried and J. Weisman,Introduction to Optimization Theory. Englewood Cliffs, NJ: Prentice-Hall, 1973.
[7] T. Sarkar, "The conjugate gradient method as applied to electromagnetic field problems,"IEEE Antennas Propogat., pp. 5-14, 1986.
[8] L.O. Chua and P.M. Lin,Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice-Hall, Englewood Cliffs, N.J., 1975.
[9] S. Katawa and O. Nalcioglu, "Constrained iterative reconstruction by the conjugate gradient method,"IEEE Trans. Med. Imaging, vol. MI-4, pp. 65-70, 1985.
[10] B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, "Iterative convolution back-projection algorithms for image reconstruction from limited data,"J. Opt. Soc. Amer., vol. 73, pp. 1493-1500, 1983.
[11] H. Peng and H. Stark, "One-step image reconstruction from incomplete data in computer tomography,"IEEE Trans. Med. Imaging, vol. 8, pp. 16-31, 1989.
[12] R.C. Gonzalez and P. Wintz,Digital Image Processing, Addison-Wesley, Reading, Mass., 1987.

Index Terms:
image reconstruction; mathematical morphology; conjugate gradient methods; least squares approximations; medical image processing; cardiology; diagnostic radiography; filtering and prediction theory; 3D binary tree-like structures; mutually orthogonal projections; 3D binary representation; binarized images; backprojection; Lagrange multiplier algorithm; conjugate gradient algorithm; minimum-voxel representation algorithm; noise-free conditions; 3D coronary arterial structures; X-ray images; human chest phantom; 3D imaging; blood vessels; medical diagnostic imaging
Citation:
Y. Sun, I. Liu, J.K. Grady, "Reconstruction of 3-D Binary Tree-Like Structures From Three Mutually Orthogonal Projections," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 3, pp. 241-248, March 1994, doi:10.1109/34.276123
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