Abstract
This paper presents an automatic method for obtaining formulas to calculate the Euler number in 2D binary images. This problem is addressed as a combinatorial optimization problem, where specific bit-quad patterns are optimally combined. An algorithm based on simulated annealing is devised to find optimal expressions to compute the Euler number, considering 4- and 8-connectivity. The proposed approach found the complete family of expressions using three bit-quad patterns that correctly estimate the Euler number. Besides, another 58 new expressions are found that use more than three bit-quads. Hence, the proposed method can obtain automatically explainable formulas of the Euler number, and it can be potentially extended to other image representations.
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Acknowledgements
The authors would like to thank the Cinvestav-IPN, Centro de Investigaciones en Óptica A.C., and Instituto Politécnico Nacional for the economic support under projects: FidSC2018/145 (Fondo SEP-Cinvestav), 20200630 and 20210788 (SIP-IPN), 65 (Frontiers of Science, CONACYT), 6005 (FORDECYT-PRONACES, CONACYT) to undertake this research.
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Gómez-Flores, W., Sossa, H., Arce, F. (2021). Finding the Optimal Bit-Quad Patterns for Computing the Euler Number of 2D Binary Images Using Simulated Annealing. In: Roman-Rangel, E., Kuri-Morales, Á.F., Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A., Olvera-López, J.A. (eds) Pattern Recognition. MCPR 2021. Lecture Notes in Computer Science(), vol 12725. Springer, Cham. https://doi.org/10.1007/978-3-030-77004-4_23
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DOI: https://doi.org/10.1007/978-3-030-77004-4_23
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