Abstract
Thinning is a frequently used approach to produce all kinds of skeleton-like shape features in a topology-preserving way. It is an iterative object reduction: some border points of binary objects are deleted, and the entire process is repeated until stability is reached. In the conventional implementation of thinning algorithms, we have to investigate the deletability of all border points in each iteration step. In this paper, we introduce the concept of k-attempt thinning (\(k\ge 1\)). In the case of a k-attempt algorithm, if a border point ‘survives’ at least k successive iterations, it is ‘immortal’ (i.e., it belongs to the produced feature). We propose a computationally efficient implementation scheme for k-attempt thinning. It is shown that an existing parallel thinning algorithm is 5-attempt, and the advantage of the new implementation scheme over the conventional one is also illustrated.
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References
Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual form, pp. 362–380. MIT Press, Cambridge (1967)
Eckhardt, U., Maderlechner, G.: Invariant thinning. Int. J. Pattern Recogn. Artif. Intell. 7(5), 1115–1144 (1993)
Hall, R.W.: Parallel connectivity-preserving thinning algorithms. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, vol. 19, pp. 145–179. Elsevier Science, Amsterdam (1996)
Hall, R.W., Kong, T.Y., Rosenfeld, A.: Shrinking binary images. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, pp. 31–98. Elsevier Science, Amsterdam (1996)
Holmgren, M., Wahlin, A., Dunas, T., Malm, J., Eklund, A.: Assessment of cerebral blood flow pulsatility and cerebral arterial compliance with 4D flow MRI. J. Magn. Reson. Imaging (2020). https://doi.org/10.1002/jmri.26978
Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. Pattern Recogn. Artif. Intell. 9(05), 813–844 (1995). https://doi.org/10.1142/S0218001495000341
Kong, T.Y.: Critical kernels, minimal nonsimple sets, and hereditarily simple sets in binary images on n-dimensional polytopal complexes. In: Saha, P.K., Borgefors, G., Sanniti di Baja, G. (eds.) Skeletonization: Theory, Methods and Applications, pp. 211–256. Academic Press, San Diego (2017)
Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48, 357–393 (1989). https://doi.org/10.1016/0734-189X(89)90147-3
Kovalevsky, V.A.: Geometry of Locally Finite Spaces. Publishing House, Berlin (2008). https://doi.org/10.1142/S0218654308001178
Lam, L., Lee, S.-W., Suen, C.Y.: Thinning methodologies - a comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992). https://doi.org/10.1109/34.161346
Marchand-Maillet, S., Sharaiha, Y.M.: Binary Digital Image Processing: A Discrete Approach. Academic Press (2000). https://doi.org/10.1117/1.1326456
Matejek, B., Wei, D., Wang, X., Zhao, J., Palágyi, K., Pfister, H.: Synapse-aware skeleton generation for neural circuits. In: Shen, D. (ed.) MICCAI 2019. LNCS, vol. 11764, pp. 227–235. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32239-7_26
Németh, G., Kardos, P., Palágyi, K.: 2D parallel thinning and shrinking based on sufficient conditions for topology preservation. Acta Cybernetica 20, 125–144 (2011). https://doi.org/10.14232/actacyb.20.1.2011.10
Palágyi, K., Németh, G., Kardos, P.: Topology preserving parallel 3D thinning algorithms. In: Brimkov, V.E., Barneva, R.P. (eds.) Digital Geometry Algorithms: Theoretical Foundations and Applications to Computational Imaging, pp. 165–188. Springer, Heidelberg (2012). https://doi.org/10.1007/978-94-007-4174-4_6
Palágyi, K., Németh, G.: Fixpoints of iterated reductions with equivalent deletion rules. In: Barneva, R.P., Brimkov, V.E., Tavares, J.M.R.S. (eds.) IWCIA 2018. LNCS, vol. 11255, pp. 17–27. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-05288-1_2
Palágyi, K., Németh, G.: Endpoint-based thinning with designating safe skeletal points. In: Barneva, R.P., Brimkov, V.E., Kulczycki, P., Tavares, J.R.S. (eds.) CompIMAGE 2018. LNCS, vol. 10986, pp. 3–15. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20805-9_1
Palágyi, K., Tschirren, J., Hoffman, E.A., Sonka, M.: Quantitative analysis of pulmonary airway tree structures. Comput. Biol. Med. 36, 974–996 (2006). https://doi.org/10.1016/j.compbiomed.2005.05.004
Palágyi, K.: A 3D fully parallel surface-thinning algorithm. Theor. Comput. Sci. 406, 119–135 (2008). https://doi.org/10.1016/j.tcs.2008.06.041
Saha, P.K., Borgefors, G., Sanniti di Baja, G.: A survey on skeletonization algorithms and their applications. Pattern Recogn. Lett. 76, 3–12 (2016)
Suen, C.Y., Wang, P.S.P. (eds.): Thinning Methodologies for Pattern Recognition. Series in Machine Perception and Artificial Intelligence, vol. 8. World Scientific (1994). https://doi.org/10.1142/9789812797858_0009
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-VEKOP-16-2017-00002. This research was supported by grant TUDFO/47138-1/2019-ITM of the Ministry for Innovation and Technology, Hungary.
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Palágyi, K., Németh, G. (2020). k-Attempt Thinning. 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_19
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