Advertisement

Order-encoded quantum image model and parallel histogram specification

  • Guanlei XuEmail author
  • Xiaogang Xu
  • Xun Wang
  • Xiaotong Wang
Article
  • 60 Downloads

Abstract

In this paper, the new quantum image representation model OQIM is proposed to provide a representation for digital images on quantum computers in the form of a normalized state. The newly proposed quantum image representation OQIM uses the basis state of a qubit sequence to store the ascending order of each pixel according to their gray values’ magnitude for the first time. Then OQIM uses the amplitude probability of a qubit to store the color and uses the amplitude probability of another qubit to store the coordinate position. Based on the OQIM, the mOQIM is proposed as well, which encodes more digital images via one model. Compared with other quantum image models, the OQIM effectively encodes the information of the histogram of the images. Based on the OQIM and the mOQIM, the histogram specification of two images and even the parallel histogram specification at the same time for multiple images are discussed. Experiments and theoretical analysis show that the proposed OQIM quantum image model is more flexible and better suited for histogram specification, histogram equalization and other similar image enhancement method such as luminance correction and so on than the existing models.

Keywords

Quantum computation Image representation Histogram specification (HS) Histogram equalization (HE) Quantum image retrieval and storage 

Notes

Acknowledgements

This work is fully supported by NSFCs (6197050275, 61471412, 61771020) and LZ15F020001.

References

  1. 1.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science. IEEE Computer Soc. Press, Los Almitos, CA, pp. 124–134 (1994)Google Scholar
  3. 3.
    Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings, 28th Annual ACM Symposium on the Theory of Computing (STOC 1996). ACM, New York, pp. 212–219 (1996)Google Scholar
  4. 4.
    Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)zbMATHGoogle Scholar
  5. 5.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice Hall, Upper Saddle River (2007)Google Scholar
  6. 6.
    Le, P.Q., 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 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proc. SPIE Conf. Quantum Inf. Comput. 5105, 137–147 (2003)ADSGoogle Scholar
  8. 8.
    Sun, B., Le, P.Q., Iliyasu, A.M.: A multi-channel representation for images on qunatum computers using the RGBα color space. In: IEEE 7th International Symposium on Intelligent Signal Processing, Floriana, Malta, 2011, pp. 1–6 (2011)Google Scholar
  9. 9.
    Li, H.S., Zhu, Q.X., Zhou, R.G., Li, M.C., et al.: Multidimensional color image storage, retrieval, and compression based on qunatum amplitudes and phases. Inf. Sci. 273, 212–232 (2014)CrossRefGoogle Scholar
  10. 10.
    Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3103–3126 (2013)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 3340–3343 (2013)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(42), 1–14 (2017)ADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: SQR: a simple quantum representation of infrared images. Quantum Inf. Process. 13, 1353–1379 (2014)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    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, 2269–2290 (2013)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Venegas-Andraca, S.E., Ball, J.L., Burnett, K., Bose, S.: Processing images in entangled quantum systems. Quantum Inf. Process. 9, 1–11 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Latorre, J.I.: Image compression and entanglement (2005). arXiv:quant-ph/0510031
  17. 17.
    Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Jiang, N., Dang, Y.J., Wang, J.: Quantum image matching. Quantum Inf. Process. 15(9), 3543–3572 (2016)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Jiang, N., Dang, Y.J., Zhao, N.: Quantum image location. Int. J. Theor. Phys. 55(10), 4501–4512 (2016)CrossRefGoogle Scholar
  21. 21.
    Coltuc, D., Bolon, P., Chassery, J.-M.: Exact histogram specification. IEEE Trans. Image Process. 15(5), 1143–1152 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Sun, C.-C., Ruan, S.-J., Shie, M.-C., Pai, T.-W.: Dnamic contrast enhancement based on histogram specification. IEEE Trans. Consum Electron 51(4), 1300–1305 (2005)CrossRefGoogle Scholar
  23. 23.
    Weiss, Y., Elovici, Y., Rokach, L.: The CASH algorithm-cost-sensitive attribute selection using histograms. Inf. Sci. 222, 247–268 (2013)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Stark, J.A.: Adaptive image contrast enhancement using generalizations of histogram equalization. IEEE Trans. Image Process. 9(5), 889–896 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    Villegas, M., Paredes, R.: Comparison of illumination normalization methods for face recognition. In: Third COST 275 Workshop, pp. 27–30 (2005)Google Scholar
  26. 26.
    Shan, S., Gao, W., Cao, B., Zhao, D.: Illumination normalization for robust face recognition against varying lighting conditions. In: Proceedings of the AMFG (2003)Google Scholar
  27. 27.
    Scabini, L.F., Condori, R.H., Gonçalves, W.M., Brunoa, O.M.: Multilayer complex network descriptors for color–texture characterization. Inf. Sci. 491, 30–47 (2019)MathSciNetCrossRefGoogle Scholar
  28. 28.
    ThanhNguyen, T., TruongDang, M., WeeChungLiew, A., Bezdek, J.C.: A weighted multiple classifier framework based on random projection. Inf. Sci. 490, 36–58 (2019)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Hai-Sheng, L., Ping, F., Hai-Ying, X., et al.: Quantum implementation circuits of quantum signal representation and type conversion. IEEE Trans. Circuits Syst. I: Regul. Pap. 2018, 1–14 (2018)Google Scholar
  30. 30.
    Li, H.S., Chen, X., Xia, H.Y., et al.: A quantum image representation based on bitplanes. IEEE Access 2018, 1–1 (2018)Google Scholar
  31. 31.
    Jiang, N., Dong, X., Hu, H., et al.: Quantum image encryption based on Henon mapping. Int. J. Theor. Phys. 58(3), 979–991 (2019)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Zhang, T.C., Zhang, J., Zhang, J.P., et al.: Review of methods of image segmentation based on quantum mechanics. J. Electron. Sci. Technol. 16(3), 53–62 (2018)Google Scholar
  33. 33.
    Li, H.S., Zhu, Q., Zhou, R.G., et al.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Guanlei Xu
    • 1
    Email author
  • Xiaogang Xu
    • 1
  • Xun Wang
    • 1
  • Xiaotong Wang
    • 2
  1. 1.College of Computer and Information EngineeringZhejiang Gongshang UniversityHangzhouChina
  2. 2.Dalian Navy AcademyDalianChina

Personalised recommendations