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The dual-threshold quantum image segmentation algorithm and its simulation

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Abstract

Various quantum computing simulation platforms have developed rapidly in the last 3 years. However, few quantum image processing algorithms are simulated in these platforms. In this paper, we design a dual-threshold quantum image segmentation algorithm and simulate it in IBM Q Experience platform through Qiskit extension. The NEQR quantum image representation model is firstly optimized and simulated, which is found that the number of the auxiliary qubits will not increase as the image’s size increases. Then, an efficient quantum comparator to realize the comparison of two numbers is designed. And finally, the high parallelism image segmentation algorithm is proposed and simulated. Suppose the size of an image is \({{2}^{n}}\times {{2}^{n}}\) and the gray-scale scope is [0, \({{2}^{q}}-1\)], the time complexity analysis for the quantum image segmentation algorithm shows that the number of basic quantum gate required is proportional to q and will not increase as image’s size increases. Thus, the proposed quantum segmentation algorithm is highly parallelism and has polynomial time complexity. In addition, the simulation part of this paper will provide reference for other quantum image processing algorithms.

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References

  1. Yan, F., Iliyasu, M.A., Venegas-Andraca, E.S.: A survey of quantum image representations. Quantum Inf. Process. 15(1), 1–35 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Salvador, E., Venegas, A., Sougato, B.: Storing, processing, and retrieving an image using quantum mechanics. In: Quantum Information and Computation. International Society for Optics and Photonics, vol. 5105, pp. 137–148 (2003)

  3. Le, Q.P., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10(1), 63–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Y., Kai, L., Gao, Y., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Yan, F., Chen, K., Venegas-Andraca, E.S., Zhao, J.: Quantum image rotation by an arbitrary angle. Quantum Inf. Process. 16(11), 282 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Yuan, S., Mao, X., Zhou, J., Wang, X.: Quantum image filtering in the spatial domain. Int. J. Theor. Phys. 56(8), 2495–2511 (2017)

    Article  MATH  Google Scholar 

  7. Li, P., Liu, X., Xiao, H.: Quantum image weighted average filtering in spatial domain. Int. J. Theor. Phys. 56(11), 3690–3716 (2017)

    Article  MATH  Google Scholar 

  8. Zhou, R., Liu, D.: Quantum image edge extraction base on improved sobel operator. Int. J. Theor. Phys. 58(9), 2965–2985 (2019)

    Article  Google Scholar 

  9. Zhou, R.-G., Han, Y., Cheng, Y., Li, F.-X.: Quantum image edge extraction based on improved prewitt operator. Quantum Inf. Process. 18, 09 (2019)

    Article  ADS  Google Scholar 

  10. Yuan, S., Mao, X., Li, T., Xue, Y., Chen, L., Xiong, Q.: Quantum morphology operations based on quantum representation model. Quantum Inf. Process. 14(5), 1625–1645 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Jiang, N., Dang, Y., Wang, J.: Quantum image matching. Quantum Inf. Process. 15(9), 3543–3572 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Zhiguo, Q., Cheng, Z., Luo, M., Liu, W.: A robust quantum watermark algorithm based on quantum log-polar images. Int. J. Theor. Phys. 56(11), 3460–3476 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, P., Xiao, H., Li, B.: Quantum representation and watermark strategy for color images based on the controlled rotation of qubits. Quantum Inf. Process. 15(11), 4415–4440 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Tan, R.C., Lei, T., Zhao, Q.M., Gong, L.H., Zhou, Z.H.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum Fourier transform. Int. J. Theor. Phys. 55(12), 5368–5384 (2016)

    Article  MATH  Google Scholar 

  15. Gong, L.H., He, X.T., Cheng, S., Hua, T.X., Zhou, N.R.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7), 3234–3250 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, N., Yiqun, H., Gong, L., Li, G.: Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations. Quantum Inf. Process. 16(6), 164 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Li, P., Liu, X., Xiao, H.: Quantum image median filtering in the spatial domain. Quantum Inf. Process. 17(3), 49 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Caraiman, S., Manta, I.V.: Histogram-based segmentation of quantum images. Theor. Comput. Sci. 529, 46–60 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Caraiman, S., Manta, I.V.: Image segmentation on a quantum computer. Quantum Inf. Process. 14(5), 1693–1715 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Li, H.S., Qingxin, Z., Lan, S., Shen, C.Y., Zhou, R., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12(6), 2269–2290 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Dwave leap. https://www.dwavesys.com/home. Accessed on 30 May 2019

  22. Google AI quantum. https://ai.google/research/teams/applied-science/quantum-ai. Accessed on 30 May 2019

  23. Ibm q. https://www.research.ibm.com/ibm-q/. Accessed on 30 May 2019

  24. cbjuan and jesusprubio. Qiskit/openqasm. https://github.com/Qiskit/openqasm. Accessed on 30 May 2019

  25. Aleksandrowicz, G., Alexander, T., Barkoutsos, P., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hernádez, F.J., Carballo-Franquis, J., Chen, A., Chen, C.-F., Chow, M.J.., Córcoles-Gonzales, D.A., Cross, J.A., Cross, A., Cruz-Benito, J., Culver, C., Puente González, De La S., Torre, De La E., Ding, D., Dumitrescu, E., Duran, I., Eendebak, P., Everitt, M., Faro Sertage, I., Frisch, A., Fuhrer, A., Gambetta, J., Godoy Gago, B., Gomez-Mosquera, J., Greenberg, D., Hamamura, I., Havlicek, V., Hellmers, J., Herok, Ł., Horii, H., Hu, S., Imamichi, T., Itoko, T., Javadi-Abhari, A., Kanazawa, N., Karazeev, A., Krsulich, K., Liu, P., Luh, Y., Maeng, Y., Marques, M., Martín-Fernández, F.J., McClure, T.D., McKay, D., Meesala, S., Mezzacapo, A., Moll, N., Rodríguez, D.M., Nannicini, G., Nation, P., Ollitrault, P., O’Riordan, L.J., Paik, H., Pérez, J., Phan, A., Pistoia, M., Prutyanov, V., Reuter, M., Rice, J., Davila, A.R., Harry Putra R., Raymond, R., Mingi, S., Ninad, S., Chris, S., Eddie, S., Kanav, S., Yunong, S., Adenilton, S., Yukio, S., Seyon, S., John, A.S., Mathias, T., Hitomi, T., Ivano, T., Charles, T., Pete, T., Kenso, T., Matthew, T., Wes, V.-L., Desiree, V., Christophe, W., Jonathan, A.W., Jessica, W., Erick, W., Christopher, W., Stephen, W., Stefan, A., Ismail, Y., Zoufal, C.: Qiskit: an open-source framework for quantum computing, (2019)

  26. Shende, V.V., Bullock, S.S., Markov, L.I.: Synthesis of quantum-logic circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 25(6), 1000–1010 (2006)

    Article  Google Scholar 

  27. Zhong, M., Hedges, P.M., Ahlefeldt, L.R., Bartholomew, G.J., Beavan, E.S., Wittig, M.S., Longdell, J.J., Sellars, J.M.: Optically addressable nuclear spins in a solid with a six-hour coherence time. Nature 517(7533), 177 (2015)

    Article  ADS  Google Scholar 

  28. David Sena Oliveira and Rubens Viana Ramos: Quantum bit string comparator: circuits and applications. Quantum Comput. Comput. 7(1), 17–26 (2007)

    Google Scholar 

  29. Cuccaro, A.S., Draper, G.T., Kutin, A.S., Moulton, D.P.: A new quantum ripple-carry addition circuit. arXiv:quant-ph/0410184 (2004)

  30. Xia, H., Li, H., Zhang, H., Liang, Y., Xin, J.: Novel multi-bit quantum comparators and their application in image binarization. Quantum Inf. Process. 18(7), 229 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  31. Li, H.S., Fan, P., Xia, H., Peng, H., Long, G.L.: Efficient quantum arithmetic operation circuits for quantum image processing. Sci. China Phys. Mech. Astron. 63(8), 280311 (2020)

  32. Barenco, A., Bennett, H.C., Cleve, R., DiVincenzo, P.D., Margolus, N., Shor, P., Sleator, T., Smolin, A.J., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)

    Article  ADS  Google Scholar 

  33. Nielsen, A.M., Chuang, L.I.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge (2011)

    MATH  Google Scholar 

  34. Sleator, T., Weinfurter, H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74(20), 4087 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (61801061), The Natural Science Foundation of Chongqing (CSTC2016jcyjA0028), The Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN201800607, KJ1704090), Discipline Open Fund of Hubei University of Arts and Science (No. XK2019040) and the valuable inputs of the reviewers.

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Authors and Affiliations

  1. The College of Opto Electronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Suzhen Yuan & Chao Wen

  2. Computer School, Hubei University of Arts and Science, Xiangyang, 441054, China

    Bo Hang

  3. College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China

    Yu Gong

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  1. Suzhen Yuan
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  2. Chao Wen
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Correspondence to Bo Hang or Yu Gong.

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Yuan, S., Wen, C., Hang, B. et al. The dual-threshold quantum image segmentation algorithm and its simulation. Quantum Inf Process 19, 425 (2020). https://doi.org/10.1007/s11128-020-02932-x

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