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Binary 3D-matrices under the microscope: a tomographical problem. (English) Zbl 1179.15029

Herman, Gabor T. (ed.) et al., Proceedings of the workshop on discrete tomography and its applictions, New York, NY, USA, June 13–15, 2005. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 20, 573-586 (2005).
Summary: A binary 3D-matrix can be scanned by moving a fixed 3D-window across it. We define scan matrix based on this and define smooth matrix. We present algorithm to reconstruct the original matrix from its 3D-scan matrix in the case of smooth matrix.
For the entire collection see [Zbl 1109.65003].

MSC:

15B36 Matrices of integers
65R30 Numerical methods for ill-posed problems for integral equations
92C55 Biomedical imaging and signal processing
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References:

[1] Frosini, A., and M. Nivat, Binary matrices under the microscope: A tomographical problem3322; Frosini, A., and M. Nivat, Binary matrices under the microscope: A tomographical problem3322 · Zbl 1113.68577
[2] Herman, G. T.; Kuba, A., Discrete tomography: Foundations algorithms and applications (1999), Birkhäuser: Birkhäuser Boston · Zbl 0946.00014
[3] Nivat. M., On Tomographic Equivalance Between (0,1)-Matrices3113; Nivat. M., On Tomographic Equivalance Between (0,1)-Matrices3113 · Zbl 1055.68142
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