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Discrete tomography with two directions

Dalen, B.E. van

Citation

Dalen, B. E. van. (2011, September 20). Discrete tomography with two directions. Retrieved from https://hdl.handle.net/1887/17845

Version: Not Applicable (or Unknown)

License: Leiden University Non-exclusive license Downloaded from: https://hdl.handle.net/1887/17845

Note: To cite this publication please use the final published version (if

applicable).

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[1] A. Alpers, Instability and stability in discrete tomography, Ph.D. thesis, Techni- sche Universit¨at M¨unchen, ISBN 3-8322-2355-X, Shaker Verlag, Aachen (2003).

[2] A. Alpers, S. Brunetti, Stability results for the reconstruction of binary pictures from two projections, Image and Vision Computing 25 (2007) 1599-1608.

[3] A. Alpers, P. Gritzmann, L. Thorens, Stability and instability in discrete to- mography, Lectures Notes in Computer Science 2243: Digital and Image Geom- etry (2001) 175-186.

[4] R.P. Anstee, The network flows approach for matrices with given row and col- umn sums, Discrete Mathematics 44 (1983) 125-138.

[5] E. Balogh, A. Kuba, C. D´ev´enyi, A. Del Lungo, Comparison of algorithms for reconstructing hv-convex discrete sets, Linear Algebra and its Applications 339 (2001) 23-35.

[6] E. Barcucci, A. Del Lungo, M. Nivat, R. Pinzani, Reconstructing convex poly- ominoes from horizontal and vertical projections, Theoretical Computer Science 155 (1996) 321-347.

[7] K.J. Batenburg, S. Bals, J. Sijbers, C. K¨ubel, P.A. Midgley, J.C. Hernandez, U. Kaiser, E.R. Encina, E.A. Coronado, G. Van Tendeloo, 3D imaging of nano- materials by discrete tomography, Ultramicroscopy 109 (2009) 730-740.

[8] M. Chrobak, C. D¨urr, Reconstructing hv-convex polyominoes from orthogonal projections, Information Processing Letters 69 (1999) 283-289.

[9] G. Dahl, T. Flatberg, Optimization and reconstruction of hv-convex (0,1)- matrices, Discrete Applied Mathematics 151 (2005) 93-105.

[10] A. Daurat, M. Nivat, Salient and reentrant points of discrete sets, Discrete Applied Mathematics 151 (2005) 106-121.

(3)

116 Bibliography

[11] R.J. Gardner, P. Gritzmann, D. Prangenberg, On the computational complexity of reconstructing lattice sets from their X-rays, Discrete Mathematics 202 (1999) 45-71.

[12] S.B. Gray, Local properties of binary images in two dimensions, IEEE Trans- actions on Computers 20 (1971) 551-561.

[13] G.T. Herman, Fundamentals of Computerized Tomography: Image Reconstruc- tion from Projections, Springer (2009).

[14] G.T. Herman, A. Kuba, editors, Discrete Tomography: Foundations, Algorithms and Applications, Birkh¨auser, Boston (1999).

[15] G.T. Herman, A. Kuba, Discrete tomography in medical imaging, Proceedings of the IEEE 91 (2003) 1612-1626.

[16] G.T. Herman, A. Kuba, editors, Advances in Discrete Tomography and Its Ap- plications, Birkh¨auser, Boston (2007).

[17] J.R. Jinschek, K.J. Batenburg, H.A. Calderon, R. Kilaas, V. Radmilovic and C. Kisielowski, 3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography, Ultramicroscopy 108 (2008) 589-604.

[18] R. Kopperman, J.L. Pfaltz, Jordan surfaces in discrete topologies IWCIS, 10th International Workshop on Combinatorial Image Analysis (IWCIA) (2004).

[19] A. Kuba, L. Rodek, Z. Kiss, L. Rusk´o, A. Nagy, M. Balask´o, Discrete to- mography in neutron radiography, Nuclear Instruments and Methods in Physics Research, Section A 542 (2005) 376-382.

[20] J.C. Palacios, L.C. Longoria, J. Santos, R.T. Perry, A PC-based discrete to- mography imaging software system for assaying radioactive waste containers, Nuclear Instruments and Methods in Physics Research, Section A 508 (2003) 500-511.

[21] A. Rosenfeld, Connectivity in digital pictures, Journal of the Association for Computing Machinery 17 (1970) 146-160.

[22] A. Rosenfeld, Compact Figures in Digital Pictures, IEEE Transactions on Sys- tem, Man and Cybernetics 4 (1974) 221-223.

[23] A. Rosenfeld, J.L. Pfaltz, Distance functions on digital pictures, Pattern Recog- nition 1 (1968) 33-61.

[24] H.J. Ryser, Combinatorial properties of matrices of zeros and ones, Canadian Journal of Mathematics 9 (1957) 371-377.

[25] H. Slump, J.J. Gerbrands, A network flow approach to reconstruction of the left ventricle from two projections, Computer Graphics and Image Processing 18 (1982) 18-36.

(4)

[26] Y.R. Wang, Characterization of binary patterns and their projections, IEEE Trans. Comput. 24 (1975) 1032-1035.

[27] Linbing Wang, Jin-Young Park, Yanrong Fu, Representation of real particles for DEM simulation using X-ray tomography, Construction and Building Materials 21 (2007) 338-346.

[28] G.J. Woeginger, The reconstruction of polyominoes from their orthogonal pro- jections, Information Processing Letters 77 (2001) 225-229.

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118 Bibliography

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