Abstract
A frequently investigated problem in various applications of binary image processing is to ensure the topology preservation of image operators, where the concept of simple points plays a key role. The literature primarily focuses on 2D and 3D images that are sampled on the conventional square and cubic grids, respectively. This paper presents some new characterizations of simple points on the body-centered cubic grid.
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References
Chen, L., Rong, Y.: Digital topological method for computing genus and the Betti numbers. Topol. Appl. 157, 1931–1936 (2010)
Čomić, L., Nagy, B.: A combinatorial coordinate system for the body-centered cubic grid. Graph. Models 87, 11–22 (2016)
Čomić, L., Magillo, P.: Repairing 3D binary images using the BCC grid with a 4-valued combinatorial coordinate system. Inf. Sci. 499, 47–61 (2009)
Klette, G.: Simple points in 2D and 3D binary images. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 57–64. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45179-2_8
Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. Pattern Recogn. Artif. Intell. 9, 813–844 (1995)
Ahronovitz, E., Fiorio, C. (eds.): DGCI 1997. LNCS, vol. 1347. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0024825
Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48, 357–393 (1989)
Malandain, G., Bertrand, G.: Fast characterization of 3D simple points. In: Proceedings of 11th IEEE International Conference on Pattern Recognition, ICPR 1992, pp. 232–235 (1992)
Matej, S., Lewitt, R.M.: Efficient 3D grids for image reconstruction using spherically-symmetric volume elements. IEEE Trans. Nucl. Sci. 42(4), 1361–1370 (1995)
Morgenthaler, D.G., Rosenfeld, A.: Surfaces in three-dimensional digital images. Inf. Control 51(3), 227–247 (1981)
Stelldinger, P., Köthe, U.: Connectivity preserving digitization of blurred binary images in 2D and 3D. Comput. Graph. 30(1), 70–76 (2006)
Stelldinger, P., Strand, R.: Topology preserving digitization with FCC and BCC grids. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 226–240. Springer, Heidelberg (2006). https://doi.org/10.1007/11774938_18
Strand, R.: The face-centered cubic grid and the body-centered cubic grid - a literature survey. Internrapport, Centrum für Bildanalys, Uppsala University, Centre for Image Analysis (2005)
Strand, R.: Surface skeletons in grids with non-cubic voxels. In: Proceedings of the 17th International Conference on Pattern Recognition, 2004, ICPR 2004, vol. 1, pp. 548–551. Cambridge (2004)
Strand, R., Brunner, D.: Simple points on the body-centered cubic grid. Technical report 42, Centre for Image Analysis, Uppsala University, Uppsala, Sweden (2006)
Strand, R., Nagy, B.: Weighted neighbourhood sequences in non-standard three-dimensional grids – metricity and algorithms. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 201–212. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79126-3_19
Theussl, T., Moller, T., Groller, M.E.: Optimal regular volume sampling. In: Proceedings Visualization 2001, pp. 91–546 (2001)
Acknowledgments
This research was supported by the project “Integrated program for training new generation of scientists in the fields of computer science”, no. EFOP-3.6.3-VEKOP16-2017-00002. This research was supported by grant TUDFO/47138-1/2019-ITM of the Ministry for Innovation and Technology, Hungary.
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Kardos, P. (2020). Characterizations of Simple Points on the Body-Centered Cubic Grid. In: Lukić, T., Barneva, R., Brimkov, V., Čomić, L., Sladoje, N. (eds) Combinatorial Image Analysis. IWCIA 2020. Lecture Notes in Computer Science(), vol 12148. Springer, Cham. https://doi.org/10.1007/978-3-030-51002-2_5
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DOI: https://doi.org/10.1007/978-3-030-51002-2_5
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