TY - GEN
T1 - Finding the Optimal Bit-Quad Patterns for Computing the Euler Number of 2D Binary Images Using Simulated Annealing
AU - Gómez-Flores, Wilfrido
AU - Sossa, Humberto
AU - Arce, Fernando
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Bit-quad patterns
KW - Combinatorial optimization
KW - Euler number
KW - Explainability
KW - Simulated annealing
UR - http://www.scopus.com/inward/record.url?scp=85111370180&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-77004-4_23
DO - 10.1007/978-3-030-77004-4_23
M3 - Contribución a la conferencia
AN - SCOPUS:85111370180
SN - 9783030770037
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 240
EP - 250
BT - Pattern Recognition - 13th Mexican Conference, MCPR 2021, Proceedings
A2 - Roman-Rangel, Edgar
A2 - Kuri-Morales, Ángel Fernando
A2 - Martínez-Trinidad, José Francisco
A2 - Carrasco-Ochoa, Jesús Ariel
A2 - Olvera-López, José Arturo
PB - Springer Science and Business Media Deutschland GmbH
T2 - 13th Mexican Conference on Pattern Recognition, MCPR 2021
Y2 - 23 June 2021 through 26 June 2021
ER -