Publications
Selected publications
- On the Reconstruction of Static and Dynamic Discrete Structures (Chapter - 2018)
- ON DOUBLE-RESOLUTION IMAGING AND DISCRETE TOMOGRAPHY (Journal article - 2017)
- Generalized balanced power diagrams for 3D representations of polycrystals (Journal article - 2014)
- Measurements of 3D slip velocities and plasma column lengths of a gliding arc discharge (Journal article - 2015)
- The two-dimensional Prouhet-Tarry-Escott problem (Journal article - 2007)
2023
Dynamic grain models via fast heuristics for diagram representations
Alpers, A., Fiedler, M., Gritzmann, P., & Klemm, F. (n.d.). Dynamic grain models via fast heuristics for diagram representations. Philosophical Magazine, 1-21. doi:10.1080/14786435.2023.2180679
Turning Grain Maps into Diagrams
Alpers, A., Fiedler, M., Gritzmann, P., & Klemm, F. (2023). Turning Grain Maps into Diagrams. SIAM JOURNAL ON IMAGING SCIENCES, 16(1), 223-249. doi:10.1137/22M1491988
2022
2021
Christmas Power Diagram
Alpers, A., & Zhai, Y. (2021). Christmas Power Diagram [Artefact]. Hurwitz Jahrbrief 2021.
2020
Power-SLIC: Fast Superpixel Segmentations by Diagrams
Power-SLIC: Diagram-based superpixel generation
Alpers, A., & Fiedler, M. (n.d.). Power-SLIC: Diagram-based superpixel generation. doi:10.48550/arXiv.2012.11772
2019
13. On the reconstruction of static and dynamic discrete structures
Alpers, A., & Gritzmann, P. (2019). 13. On the reconstruction of static and dynamic discrete structures. In The Radon Transform (pp. 297-342). De Gruyter. doi:10.1515/9783110560855-013
2018
On the Reconstruction of Static and Dynamic Discrete Structures
Alpers, A., & Gritzmann, P. (2018). On the Reconstruction of Static and Dynamic Discrete Structures. Retrieved from http://arxiv.org/abs/1809.06141v1
Habilitation Thesis: On the Tomography of Discrete Structures: Mathematics, Complexity, Algorithms, and its Applications in Materials Science and Plasma Physics
Alpers, A. (2018). Habilitation Thesis: On the Tomography of Discrete Structures: Mathematics, Complexity, Algorithms, and its Applications in Materials Science and Plasma Physics. (PhD Thesis, Technical University of Munich).
2017
Dynamic discrete tomography
Alpers, A., & Gritzmann, P. (2018). Dynamic discrete tomography. INVERSE PROBLEMS, 34(3). doi:10.1088/1361-6420/aaa202
Reconstructing Binary Matrices underWindow Constraints from their Row and Column Sums
Alpers, A., & Gritzmann, P. (2017). Reconstructing Binary Matrices underWindow Constraints from their Row and Column Sums. FUNDAMENTA INFORMATICAE, 155(4), 321-340. doi:10.3233/FI-2017-1588
ON DOUBLE-RESOLUTION IMAGING AND DISCRETE TOMOGRAPHY
Alpers, A., & Gritzmann, P. (2018). ON DOUBLE-RESOLUTION IMAGING AND DISCRETE TOMOGRAPHY. SIAM JOURNAL ON DISCRETE MATHEMATICS, 32(2), 1369-1399. doi:10.1137/17M1115629
2015
Measurements of 3D slip velocities and plasma column lengths of a gliding arc discharge
Zhu, J., Gao, J., Ehn, A., Alden, M., Li, Z., Moseev, D., . . . Schwenk, M. (2015). Measurements of 3D slip velocities and plasma column lengths of a gliding arc discharge. APPLIED PHYSICS LETTERS, 106(4). doi:10.1063/1.4906928
2014
The Smallest Sets of Points not Determined by Their X-rays
Alpers, A., & Larman, D. G. (2014). The Smallest Sets of Points not Determined by Their X-rays. Bulletin of the London Mathematical Society, 47(1), 171-176. doi:10.1112/blms/bdu111
Generalized balanced power diagrams for 3D representations of polycrystals
Alpers, A., Brieden, A., Gritzmann, P., Lyckegaard, A., & Poulsen, H. F. (2015). Generalized balanced power diagrams for 3D representations of polycrystals. PHILOSOPHICAL MAGAZINE, 95(9), 1016-1028. doi:10.1080/14786435.2015.1015469
Calendar Image, 1 of 12 winners of the image competition for the German Research Foundation (DFG) Calendar 2014
Alpers, A., Gritzmann, P., & support, S. F. (2014). Calendar Image, 1 of 12 winners of the image competition for the German Research Foundation (DFG) Calendar 2014. [Mathematical artwork, DFG].
2013
3D particle tracking velocimetry using dynamic discrete tomography
Alpers, A., Gritzmann, P., Moseev, D., & Salewski, M. (2015). 3D particle tracking velocimetry using dynamic discrete tomography. COMPUTER PHYSICS COMMUNICATIONS, 187, 130-136. doi:10.1016/j.cpc.2014.10.022
2012
Geometric reconstruction methods for electron tomography
Alpers, A., Gardner, R. J., Koenig, S., Pennington, R. S., Boothroyd, C. B., Houben, L., . . . Batenburg, K. J. (2013). Geometric reconstruction methods for electron tomography. ULTRAMICROSCOPY, 128, 42-54. doi:10.1016/j.ultramic.2013.01.002
2011
Reconstruction of an InAs nanowire using geometric and algebraic tomography
Pennington, R. S., Koenig, S., Alpers, A., Boothroyd, C. B., & Dunin-Borkowski, R. E. (2011). Reconstruction of an InAs nanowire using geometric and algebraic tomography. In 17TH INTERNATIONAL CONFERENCE ON MICROSCOPY OF SEMICONDUCTING MATERIALS 2011 Vol. 326. doi:10.1088/1742-6596/326/1/012045
2010
Phase retrieval for superposed signals from multiple binary objects
Alpers, A., Herman, G. T., Poulsen, H. F., & Schmidt, S. (2010). Phase retrieval for superposed signals from multiple binary objects. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 27(9), 1927-1937. doi:10.1364/JOSAA.27.001927
3D Grain Reconstruction from Boxscan Data
Lyckegaard, A., Alpers, A., Ludwig, W., Fonda, R. W., Margulies, L., Goetz, A., . . . Lauridsen, E. M. (2010). 3D Grain Reconstruction from Boxscan Data. Defense Technical Information Center. doi:10.21236/ada530190
2009
A GREEDY METHOD FOR RECONSTRUCTING POLYCRYSTALS FROM THREE-DIMENSIONAL X-RAY DIFFRACTION DATA
Kulshreshth, A. K., Alpers, A., Herman, G. T., Knudsen, E., Rodek, L., & Poulsen, H. F. (2009). A GREEDY METHOD FOR RECONSTRUCTING POLYCRYSTALS FROM THREE-DIMENSIONAL X-RAY DIFFRACTION DATA. INVERSE PROBLEMS AND IMAGING, 3(1), 69-85. doi:10.3934/ipi.2009.3.69
3DXRD and TotalCryst Geometry
Poulsen, H. F., Schmidt, S., Wright, J., Sørensen, H. O., Oddershede, J., & Alpers, A. (2009). 3DXRD and TotalCryst Geometry. SourceForge.
A short introduction to tomographic grain map reconstruction
Alpers, A. (2009). A short introduction to tomographic grain map reconstruction. In Pure Mathematics and Applications, PU.M.A. Vol. 20 (pp. 157-163). Retrieved from http://puma.dimai.unifi.it/20_1_2/10_Alpers_7.pdf
Teaching Computational Discrete Optimization at the Undergraduate Level
Alpers, A., & Trotter, L. E. (2009). Teaching Computational Discrete Optimization at the Undergraduate Level. INFORMS Transactions on Education, 9(2), 63-69. doi:10.1287/ited.1090.0020
2007
Stability results for the reconstruction of binary pictures from two projections
Alpers, A., & Brunetti, S. (2007). Stability results for the reconstruction of binary pictures from two projections. IMAGE AND VISION COMPUTING, 25(10), 1599-1608. doi:10.1016/j.imavis.2006.06.014
The two-dimensional Prouhet-Tarry-Escott problem
Alpers, A., & Tijdeman, R. (2007). The two-dimensional Prouhet-Tarry-Escott problem. JOURNAL OF NUMBER THEORY, 123(2), 403-412. doi:10.1016/j.jnt.2006.07.001
Discrete Tomography for Generating Grain Maps of Polycrystals
Alpers, A., Rodek, L., Poulsen, H. F., Knudsen, E., & Herman, G. T. (2007). Discrete Tomography for Generating Grain Maps of Polycrystals. In ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS (pp. 271-301). doi:10.1007/978-0-8176-4543-4_13
2006
On stability, error correction, and noise compensation in discrete tomography
Alpers, A., & Gritzmann, P. (2006). On stability, error correction, and noise compensation in discrete tomography. SIAM JOURNAL ON DISCRETE MATHEMATICS, 20(1), 227-239. doi:10.1137/040617443
A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps
Alpers, A., Poulsen, H. F., Knudsen, E., & Herman, G. T. (2006). A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps. JOURNAL OF APPLIED CRYSTALLOGRAPHY, 39, 582-588. doi:10.1107/S002188980601939X
2005
Resolving Ambiguities in Reconstructed Grain Maps using Discrete Tomography
Alpers, A., Knudsen, E., Poulsen, H. F., & Herman, G. T. (2005). Resolving Ambiguities in Reconstructed Grain Maps using Discrete Tomography. Electronic Notes in Discrete Mathematics, 20, 419-437. doi:10.1016/j.endm.2005.05.076
On the stability of reconstructing lattice sets from X-rays along two directions
Alpers, A., & Brunetti, S. (2005). On the stability of reconstructing lattice sets from X-rays along two directions. DISCRETE GEOMETRY FOR COMPUTER IMAGERY, PROCEEDINGS, 3429, 92-103. Retrieved from https://www.webofscience.com/
2003
Instability and Stability in Discrete Tomography
Alpers, A. (2003). Instability and Stability in Discrete Tomography. (PhD Thesis, Technical University of Munich).
2002
Digital topology: Regular sets and root images of the cross-median filter
Alpers, A. (2002). Digital topology: Regular sets and root images of the cross-median filter. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 17(1), 7-14. doi:10.1023/A:1020766406935
2001
Stability and Instability in Discrete Tomography
Alpers, A., Gritzmann, P., & Thorens, L. (2001). Stability and Instability in Discrete Tomography. Unknown Journal, 175-186. doi:10.1007/3-540-45576-0_11