Abstract
In this chapter, reconstruction of plane figures from their two-projection data is discussed together with its stability, based on the discrete approximation. For this purpose, we introduce the notion of type 1 modification against nonuniquely reconstructed figures, and a kind of weight function to classify them. Many interesting open problems remain concerning theoretical justification of proposed algorithms for nonunique cases.
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References
G. G. Lorentz, “A problem of plane measure,” Amer. J. Math. 71, 417–426 (1949).
H. J. Ryser, Combinatorial Mathematics. (The Math. Association of America, Washington, DC), 1963.
A. Kuba and A. Volcic, “Characterization of measurable plane sets which are reconstructable from their two projections,” Inverse Problems, 4, 513–527 (1988).
A. Kuba, “Reconstruction of unique binary matrices with prescribed elements,” Acta Cybernetica, 12, 57–70 (1995).
L. Huang, The reconstruction of uniquely determined plane sets from two projections in discrete case. (Preprint Series UTMS 95–29,Univ. of Tokyo, Tokyo), 1995.
A. Kuba, “The reconstruction of two-directionally connected binary patterns from their two orthogonal projections,” Computer Vision, Graphics and Image Processing, 27, 249–265 (1984).
R. J. Gardner, Geometric Tomography. (Cambridge University Press, Cambridge, UK), 1995.
K. Nakayama, Ch. Kobayashi, and A. Kaneko, A deterministic algorithm for reconstruction from two projections. (Preprint Series OCHAIS 98–2, Ochanomizu Univ., Tokyo), 1998.
L. Huang and T. Takiguchi, “The reconstruction of uniquely determined plane sets from two projections,” J. Inverse and Ill-Posed Prob. 6, 217–242 (1988).
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© 1999 Springer Science+Business Media New York
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Kaneko, A., Huang, L. (1999). Reconstruction of Plane Figures from Two Projections. In: Herman, G.T., Kuba, A. (eds) Discrete Tomography. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1568-4_5
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DOI: https://doi.org/10.1007/978-1-4612-1568-4_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7196-3
Online ISBN: 978-1-4612-1568-4
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