Procesamiento morfológico de imágenes binarias mediante circuitos cuánticos: una implementación en qiskit
DOI:
https://doi.org/10.71112/nankke17Palabras clave:
procesamiento cuántico de imágenes, morfología matemática, erosión, dilatación, Qiskit, OpenCVResumen
La erosión y la dilatación son operaciones fundamentales de la morfología matemática para modificar la forma de objetos en imágenes binarias. En este trabajo se evaluó su implementación mediante un circuito cuántico simulado en Qiskit, utilizando como referencia el procesamiento clásico realizado con OpenCV. Se empleó la imagen Baboon en resoluciones de 102×102, 128×128 y 256×256 píxeles, con 16, 160, 1600, 16000 y 160000 ejecuciones del circuito. La comparación incluyó una revisión visual, el cálculo de MSE, PSNR y SSIM, y el registro de los tiempos de simulación. El circuito reprodujo el efecto esperado de ambas operaciones, aunque las imágenes no coincidieron completamente con las obtenidas en OpenCV. La dilatación mostró una similitud más estable que la erosión. Además, aumentar las ejecuciones no mejoró monotónicamente las métricas y sí incrementó considerablemente el tiempo de cómputo.
Descargas
Referencias
Caraiman, S., & Manta, V. I. (2014). Histogram-based segmentation of quantum images. Theoretical Computer Science, 529, 46–60. https://doi.org/10.1016/j.tcs.2013.08.005 DOI: https://doi.org/10.1016/j.tcs.2013.08.005
Deutsch, D. (1985). Quantum theory, the Church–Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 400(1818), 97–117. https://doi.org/10.1098/rspa.1985.0070 DOI: https://doi.org/10.1098/rspa.1985.0070
Feynman, R. P. (1982). Simulating physics with computers. International Journal of Theoretical Physics, 21(6–7), 467–488. https://doi.org/10.1007/BF02650179 DOI: https://doi.org/10.1007/BF02650179
Geng, A., Moghiseh, A., Redenbach, C., & Schladitz, K. (2022). A hybrid quantum image edge detector for the NISQ era. Quantum Machine Intelligence, 4, Article 15. https://doi.org/10.1007/s42484-022-00071-3 DOI: https://doi.org/10.1007/s42484-022-00071-3
Gonzalez, R. C., & Woods, R. E. (2018). Digital image processing (4th ed.). Pearson.
Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on theory of computing (pp. 212–219). ACM. https://doi.org/10.1145/237814.237866 DOI: https://doi.org/10.1145/237814.237866
Haque, M. E., Paul, M., Ulhaq, A., & Debnath, T. (2023). Advanced quantum image representation and compression using a DCT-EFRQI approach. Scientific Reports, 13, Article 4129. https://doi.org/10.1038/s41598-023-30575-2 DOI: https://doi.org/10.1038/s41598-023-30575-2
Haralick, R. M., Sternberg, S. R., & Zhuang, X. (1987). Image analysis using mathematical morphology. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9(4), 532–550. https://doi.org/10.1109/TPAMI.1987.4767941 DOI: https://doi.org/10.1109/TPAMI.1987.4767941
Horé, A., & Ziou, D. (2010). Image quality metrics: PSNR vs. SSIM. In 2010 20th International Conference on Pattern Recognition (pp. 2366–2369). IEEE. https://doi.org/10.1109/ICPR.2010.579 DOI: https://doi.org/10.1109/ICPR.2010.579
Huynh-Thu, Q., & Ghanbari, M. (2008). Scope of validity of PSNR in image/video quality assessment. Electronics Letters, 44(13), 800–801. https://doi.org/10.1049/el:20080522 DOI: https://doi.org/10.1049/el:20080522
Jiang, N., & Wang, L. (2015). Quantum image scaling using nearest neighbor interpolation. Quantum Information Processing, 14(5), 1559–1571. https://doi.org/10.1007/s11128-014-0841-8 DOI: https://doi.org/10.1007/s11128-014-0841-8
Le, P. Q., Dong, F., & Hirota, K. (2011). A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Information Processing, 10(1), 63–84. https://doi.org/10.1007/s11128-010-0177-y DOI: https://doi.org/10.1007/s11128-010-0177-y
Leymann, F., & Barzen, J. (2020). The bitter truth about gate-based quantum algorithms in the NISQ era. Quantum Science and Technology, 5(4), Article 044007. https://doi.org/10.1088/2058-9565/abae7d DOI: https://doi.org/10.1088/2058-9565/abae7d
Li, P., Shi, T., Lu, A., & Wang, B. (2019). Quantum circuit design for several morphological image processing methods. Quantum Information Processing, 18(12), Article 364. https://doi.org/10.1007/s11128-019-2479-z DOI: https://doi.org/10.1007/s11128-019-2479-z
Liu, W., Wang, L., & Cui, M. (2022). Quantum image segmentation based on grayscale morphology. IEEE Transactions on Quantum Engineering, 3, Article 3103012, 1–12. https://doi.org/10.1109/TQE.2022.3223368 DOI: https://doi.org/10.1109/TQE.2022.3223368
Ma, S.-Y., Khalil, A., Hajjdiab, H., & Eleuch, H. (2020). Quantum dilation and erosion. Applied Sciences, 10(11), Article 4040. https://doi.org/10.3390/app10114040 DOI: https://doi.org/10.3390/app10114040
Nasr, N., Younes, A., & Elsayed, A. (2021). Efficient representations of digital images on quantum computers. Multimedia Tools and Applications, 80(25), 34019–34034. https://doi.org/10.1007/s11042-021-11355-4 DOI: https://doi.org/10.1007/s11042-021-11355-4
Otsu, N. (1979). A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, and Cybernetics, 9(1), 62–66. https://doi.org/10.1109/TSMC.1979.4310076 DOI: https://doi.org/10.1109/TSMC.1979.4310076
Preskill, J. (2018). Quantum computing in the NISQ era and beyond. Quantum, 2, Article 79. https://doi.org/10.22331/q-2018-08-06-79 DOI: https://doi.org/10.22331/q-2018-08-06-79
Pulli, K., Baksheev, A., Kornyakov, K., & Eruhimov, V. (2012). Real-time computer vision with OpenCV. Communications of the ACM, 55(6), 61–69. https://doi.org/10.1145/2184319.2184337 DOI: https://doi.org/10.1145/2184319.2184337
Qiskit Community (2019). Qiskit: An open-source framework for quantum computing [Software de computadora]. Zenodo. https://doi.org/10.5281/zenodo.2562111
Shor, P. W. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science (pp. 124–134). IEEE. https://doi.org/10.1109/SFCS.1994.365700 DOI: https://doi.org/10.1109/SFCS.1994.365700
Vincent, L. (1993). Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Transactions on Image Processing, 2(2), 176–201. https://doi.org/10.1109/83.217222 DOI: https://doi.org/10.1109/83.217222
Wang, Z., & Bovik, A. C. (2002). A universal image quality index. IEEE Signal Processing Letters, 9(3), 81–84. https://doi.org/10.1109/97.995823 DOI: https://doi.org/10.1109/97.995823
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612. https://doi.org/10.1109/TIP.2003.819861 DOI: https://doi.org/10.1109/TIP.2003.819861
Wang, Z., Xu, M., & Zhang, Y. (2022). Review of quantum image processing. Archives of Computational Methods in Engineering, 29(2), 737–761. https://doi.org/10.1007/s11831-021-09599-2 DOI: https://doi.org/10.1007/s11831-021-09599-2
Yan, F., Iliyasu, A. M., & Jiang, Z. (2014). Quantum computation-based image representation, processing operations and their applications. Entropy, 16(10), 5290–5338. https://doi.org/10.3390/e16105290 DOI: https://doi.org/10.3390/e16105290
Yan, F., Iliyasu, A. M., & Venegas-Andraca, S. E. (2016). A survey of quantum image representations. Quantum Information Processing, 15(1), 1–35. https://doi.org/10.1007/s11128-015-1195-6 DOI: https://doi.org/10.1007/s11128-015-1195-6
Yan, F., & Venegas-Andraca, S. E. (2025). Lessons from twenty years of quantum image processing. ACM Transactions on Quantum Computing, 6(1), Article 5, 1–29. https://doi.org/10.1145/3663577 DOI: https://doi.org/10.1145/3663577
Yao, X.-W., Wang, H., Liao, Z., Chen, M.-C., Pan, J., Li, J., Zhang, K., Lin, X., Wang, Z., Luo, Z., Zheng, W., Li, J., Zhao, M., Peng, X., & Suter, D. (2017). Quantum image processing and its application to edge detection: Theory and experiment. Physical Review X, 7(3), Article 031041. https://doi.org/10.1103/PhysRevX.7.031041 DOI: https://doi.org/10.1103/PhysRevX.7.031041
Yuan, S., Mao, X., Li, T., Xue, Y., Chen, L., & Xiong, Q. (2015). Quantum morphology operations based on quantum representation model. Quantum Information Processing, 14(5), 1625–1645. https://doi.org/10.1007/s11128-014-0862-3 DOI: https://doi.org/10.1007/s11128-014-0862-3
Yuan, S., Mao, X., Chen, L., & Wang, X. (2016). Improved quantum dilation and erosion operations. International Journal of Quantum Information, 14(7), Article 1650036. https://doi.org/10.1142/S0219749916500362 DOI: https://doi.org/10.1142/S0219749916500362
Zhang, Y., Lu, K., Gao, Y., & Wang, M. (2013). NEQR: A novel enhanced quantum representation of digital images. Quantum Information Processing, 12(8), 2833–2860. https://doi.org/10.1007/s11128-013-0567-z DOI: https://doi.org/10.1007/s11128-013-0567-z
Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995). Elementary gates for quantum computation. Physical Review A, 52(5), 3457–3467. https://doi.org/10.1103/PhysRevA.52.3457 DOI: https://doi.org/10.1103/PhysRevA.52.3457
Nielsen, M. A., & Chuang, I. L. (2010). Quantum computation and quantum information (10th anniversary ed.). Cambridge University Press.
Publicado
Número
Sección
Licencia
Derechos de autor 2026 Leonardi Hernández Sánchez, Emily Andrea Franco Escudero, Roberto Arceo Reyes (Autor/a)

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.






