DOI: 10.1007/s10851-006-9798-2. A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays

A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays

10.1007/s10851-006-9798-2

Crossref journal-article

Springer Science and Business Media LLC

Journal of Mathematical Imaging and Vision (297)

Bibliography

Batenburg, K. J. (2006). A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays. Journal of Mathematical Imaging and Vision, 27(2), 175â191.

Authors 1

Kees Joost Batenburg (first)

References 28 Referenced 31

R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory, Algorithms, and Applications, Prentice-Hall, 1993.
R.P. Anstee, “The network flows approach for matrices with given row and column sums”, Discrete Math., Vol. 44, pp. 125–138, 1983. (10.1016/0012-365X(83)90053-5) / Discrete Math. by R.P. Anstee (1983)
E. Barcucci, A. Del Lungo, M. Nivat, and R. Pinzani, “Reconstructing convex polyominoes from horizontal and vertical projections”, Theoret. Comput. Sci., Vol. 155, pp. 321–347, 1996. (10.1016/0304-3975(94)00293-2) / Theoret. Comput. Sci. by E. Barcucci (1996)
K.J. Batenburg, “A new algorithm for 3D binary tomography”,in Proceedings of the Workshop on Discrete Tomography and its Applications, New York, Electron. Notes Discrete Math., Vol. 20, 2005, pp. 247–261. (10.1016/j.endm.2005.05.067) / Electron. Notes Discrete Math. by K.J. Batenburg (2005)
S. Brunetti, A. Del Lungo, F. Del Ristoro, A. Kuba, and M. Nivat, “Reconstruction of 4- and 8-connected convex discrete sets from row and column projections”, Linear Algebra Appl., Vol. 339, pp. 37–57, 2001. (10.1016/S0024-3795(01)00435-9) / Linear Algebra Appl. by S. Brunetti (2001)
S. Brunetti and A. Daurat, “An algorithm for reconstructing lattice convex sets”, Theoret. Comput. Sci., Vol. 304, pp. 35–57, 2003. (10.1016/S0304-3975(03)00050-1) / Theoret. Comput. Sci. by S. Brunetti (2003)
P. Fishburn, P. Schwander, L. Shepp, and R. Vanderbei, “The discrete Radon transform and its approximate inversion via linear programming”, Discrete Appl. Math., Vol. 75, pp. 39–61, 1997. (10.1016/S0166-218X(96)00083-2) / Discrete Appl. Math. by P. Fishburn (1997)
H.N. Gabow and R.E. Tarjan, “Faster scaling algorithms for network problems”, SIAM J. Comput., Vol. 18, pp. 1013–1036, 1989. (10.1137/0218069) / SIAM J. Comput. by H.N. Gabow (1989)
D. Gale, “A theorem on flows in networks”, Pacific J. Math., Vol. 7, pp. 1073–1082, 1957. (10.2140/pjm.1957.7.1073) / Pacific J. Math. by D. Gale (1957)
R.J. Gardner, Geometric Tomography, Cambridge University Press, New York, 1995. / Geometric Tomography by R.J. Gardner (1995)
R.J. Gardner and P. Gritzmann, “Discrete tomography: determination of finite sets by X-rays”, Trans. Amer. Math. Soc., Vol. 349, pp. 2271–95, 1997. (10.1090/S0002-9947-97-01741-8) / Trans. Amer. Math. Soc. by R.J. Gardner (1997)
R.J. Gardner, P. Gritzmann, and D. Prangenberg, “On the computational complexity of reconstructing lattice sets from their X-rays”, Discrete Math., Vol. 202, pp. 45–71, 1999. (10.1016/S0012-365X(98)00347-1) / Discrete Math. by R.J. Gardner (1999)
A.V. Goldberg, “An efficient implementation of a scaling minimum-cost flow algorithm”, J. Algorithms, Vol. 22, pp. 1–29, 1997. (10.1006/jagm.1995.0805) / J. Algorithms by A.V. Goldberg (1997)
P. Gritzmann, S. de Vries, and M. Wiegelmann, “Approximating binary images from discrete X-rays”, SIAM J. Optim., Vol. 11, pp. 522–546, 2000. (10.1137/S105262349935726X) / SIAM J. Optim. by P. Gritzmann (2000)
P. Gritzmann, D. Prangenberg, S. de Vries, and M. Wiegelmann, “Success and failure of certain reconstruction and uniqueness algorithms in discrete tomography”, Int. J. Imag. Syst. Tech., Vol. 9, pp. 101–109, 1998. (10.1002/(SICI)1098-1098(1998)9:2/3<101::AID-IMA6>3.0.CO;2-F) / Int. J. Imag. Syst. Tech. by P. Gritzmann (1998)
L. Hajdu and R. Tijdeman, “Algebraic aspects of discrete tomography”, J. Reine Angew. Math., Vol. 534, pp. 119–128, 2001. / J. Reine Angew. Math. by L. Hajdu (2001)
L. Hajdu and R. Tijdeman, “An algorithm for discrete tomography”, Linear Algebra Appl., Vol. 339, pp. 147–169, 2001. (10.1016/S0024-3795(01)00483-9) / Linear Algebra Appl. by L. Hajdu (2001)
G.T. Herman and A. Kuba, (Eds.), Discrete Tomography: Foundations, Algorithms and Applications, Birkhäuser, Boston, 1999. / Discrete Tomography: Foundations, Algorithms and Applications (1999)
J.R. Jinschek, K.J. Batenburg, H. Calderon, D. Van Dyck, F.-R. Chen, and C. Kisielowski, “Prospects for bright field and dark field electron tomography on a discrete grid”, Microsc. Microanal., Vol. 10 Suppl. 3, Cambridge Journals Online, 2004. (10.1017/S1431927604555629)
J.R. Jinschek, H.A. Calderon, K.J. Batenburg, V. Radmilovic and C. Kisielowski, “Discrete Tomography of Ga and InGa Particles from HREM Image Simulation and Exit Wave Reconstruction”, MRS Proc., Vol. 839, pp. 4.5.1–4.5.6, 2004. (10.1557/PROC-839-P4.5) / MRS Proc. by J.R. Jinschek (2004)
C. Kisielowski, P. Schwander, F. Baumann, M. Seibt, Y. Kim, and A. Ourmazd, “An approach to quantitative high-resolution transmission electron microscopy of crystalline materials”, Ultramicroscopy, Vol. 58, pp. 131–155, 1995. (10.1016/0304-3991(94)00202-X) / Ultramicroscopy by C. Kisielowski (1995)
H.J. Ryser, “Combinatorial properties of matrices of zeros and ones”, Canad. J. Math., Vol. 9, pp. 371–377, 1957. (10.4153/CJM-1957-044-3) / Canad. J. Math. by H.J. Ryser (1957)
A. Schrijver, Combinatorial Optimization. Polyhedra and Efficiency, Springer-Verlag, Berlin, 2003. / Combinatorial Optimization. Polyhedra and Efficiency by A. Schrijver (2003)
P. Schwander, C. Kisielowski, F. Baumann, Y. Kim, and A. Ourmazd, “Mapping projected potential, interfacial roughness, and composition in general crystalline solids by quantitative transmission electron microscopy”, Phys. Rev. Lett., Vol. 71, pp. 4150–4153, 1993. (10.1103/PhysRevLett.71.4150) / Phys. Rev. Lett. by P. Schwander (1993)
C.H. Slump and J.J. Gerbrands, “A network flow approach to reconstruction of the left ventricle from two projections”, Comput. Gr. Im. Proc., Vol. 18, pp. 18–36, 1982. (10.1016/0146-664X(82)90097-1) / Comput. Gr. Im. Proc. by C.H. Slump (1982)
K. Tanabe, “Projection method for solving a singular system”, Numer. Math., Vol. 17, pp. 203–214, 1971. (10.1007/BF01436376) / Numer. Math. by K. Tanabe (1971)
B. Wang and F. Zhang, “On the precise number of (0,1)-matrices in A(R,S)”, Discrete Math., Vol. 187, pp. 211–220, 1998. (10.1016/S0012-365X(97)00197-0) / Discrete Math. by B. Wang (1998)
S. Weber, C. Schnörr, and J. Hornegger, “A linear programming relaxation for binary tomography with smoothness priors”, Electron. Notes Discrete Math., Vol. 12, 2003. (10.1016/S1571-0653(04)00490-1)

Dates

Type	When
Created	18 years, 11 months ago (Sept. 22, 2006, 7:53 a.m.)
Deposited	6 years, 3 months ago (May 30, 2019, 6:31 p.m.)
Indexed	1 week, 5 days ago (Aug. 21, 2025, 1:55 p.m.)
Issued	18 years, 11 months ago (Sept. 21, 2006)
Published	18 years, 11 months ago (Sept. 21, 2006)
Published Online	18 years, 11 months ago (Sept. 21, 2006)
Published Print	18 years, 7 months ago (Feb. 1, 2007)

Funders 0

None

BibTeX

@article{Batenburg_2006, title={A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays}, volume={27}, ISSN={1573-7683}, url={http://dx.doi.org/10.1007/s10851-006-9798-2}, DOI={10.1007/s10851-006-9798-2}, number={2}, journal={Journal of Mathematical Imaging and Vision}, publisher={Springer Science and Business Media LLC}, author={Batenburg, Kees Joost}, year={2006}, month=sep, pages={175–191} }

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