Discrete tomography: from battleship to nanotechnology

Discrete tomography in four directions

Electronic Notes in Discrete Mathematics ◽

10.1016/s1571-0653(05)00767-5 ◽

2000 ◽

Vol 3 ◽

pp. 1-4

Author(s):

B TIJDEMAN

Keyword(s):

Discrete Tomography

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Discrete tomography and the Hodge conjecture for certain abelian varieties of CM-type

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.82.25 ◽

2006 ◽

Vol 82 (3) ◽

pp. 25-29

Author(s):

Fumio Hazama

Keyword(s):

Abelian Varieties ◽

Hodge Conjecture ◽

Discrete Tomography

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Reconstructing binary and colored matrices in discrete tomography

4OR ◽

10.1007/s10288-014-0258-3 ◽

2014 ◽

Vol 12 (3) ◽

pp. 297-298

Author(s):

Ghassen Tlig

Keyword(s):

Discrete Tomography

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Boundary Ghosts for Discrete Tomography

Journal of Mathematical Imaging and Vision ◽

10.1007/s10851-020-01010-2 ◽

2021 ◽

Author(s):

Matthew Ceko ◽

Timothy Petersen ◽

Imants Svalbe ◽

Rob Tijdeman

Keyword(s):

Discrete Tomography

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Generic iterative subset algorithms for discrete tomography

Discrete Applied Mathematics ◽

10.1016/j.dam.2008.05.033 ◽

2009 ◽

Vol 157 (3) ◽

pp. 438-451 ◽

Cited By ~ 20

Author(s):

K.J. Batenburg ◽

J. Sijbers

Keyword(s):

Discrete Tomography

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Multivalued Discrete Tomography Using Dynamical System That Describes Competition

Mathematical Problems in Engineering ◽

10.1155/2017/8160354 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Takeshi Kojima ◽

Tetsushi Ueta ◽

Tetsuya Yoshinaga

Keyword(s):

Dynamical System ◽

Theoretical Analysis ◽

Continuous Time ◽

Numerical Experiments ◽

Nonlinear Dynamical System ◽

Reconstructed Image ◽

Optimization Approach ◽

Discrete Tomography ◽

Nonlinear Dynamical ◽

Time Optimization

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.

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