Skip to main content
SpringerLink
Log in

Quantum image edge extraction based on Laplacian operator and zero-cross method

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Edge detection, as a fundamental problem in image processing and computer vision, is an indispensable task in digital image processing. Because of the sharp increase in the image data in the actual applications, real-time problem has become a limitation in classical image processing. In this paper, based on the novel enhanced quantum image representation (NEQR) of digital images, an enhanced quantum edge detection algorithm is investigated, which combines the classical Laplacian operator and zero-cross method. Because NEQR utilizes the superposition state of qubit sequence to store all the pixels of an image, the corresponding quantum image edge detection algorithm can realize parallel computation to implement the Laplacian filter and further calculate the image intensity of all the pixels according zero-cross method. The circuit complexity analysis demonstrates that our presented quantum image edge algorithm can reach a significant and exponential speedup compared to classical counterparts. Hence, our proposed quantum image edge detection algorithm would resolve the real-time problem of image edge extraction in practice image processing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Yan, F., Iliyasu, A.M., Le, P.Q.: Quantum image processing: A review of advances in its security technologies. Int. J. Quant. Inf. 15(03), 1730001 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. Yan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A Survey of Quantum Image Representations, vol. 15, pp. 1–35. Kluwer Academic Publishers, Hingham (2016)

    MATH  Google Scholar 

  3. Iliyasu, A.M.: Towards the realisation of secure and efficient image and video processing applications on quantum computers. Entropy 15, 2874–2974 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Iliyasu, A.M.: Algorithmic frameworks to support the realisation of secure and efficient image-video processing applications on quantum computers. Ph.D. (Dr Eng.) Thesis, Tokyo Institute of Technology, Tokyo, Japan. 25 Sept. 2012

  5. Iliyasu, A.M., Le, P.Q., Yan, F., Bo, S., Garcia, J.A.S., Dong, F., Hirota, K.: A two-tier scheme for greyscale quantum image watermarking and recovery. Int. J. Innov. Comput. Appl. 5, 85–101 (2013)

    Article  Google Scholar 

  6. Feynman, R.: Simulating Physics with Computers, vol. 21, pp. 467–488. Perseus Books, Cambridge (1999)

    Google Scholar 

  7. Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. 400, 97–117 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)

  9. Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

  10. Vlasov, A.Y.: Quantum computations and images recognition (1997). arXiv:quant-ph/9703010

  11. Lugiato, L.A., Gatti, A., Brambilla, E.: Quantum imaging. J. Opt. B 4, 176–184 (2002)

    Article  ADS  Google Scholar 

  12. Eldar, Y.C., Oppenheim, A.V.: Quantum signal processing. IEEE Signal Process. Mag. 19, 12–32 (2001)

    Article  ADS  Google Scholar 

  13. Schützhold, R.: Pattern recognition on a quantum computer. Phys. Rev. A 67(6), 062311 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  14. Venegas-Andraca,S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation, vol. 5105, pp. 134–147 (2003)

  15. Venegas-Andraca, S., Ball, J.: Processing images in entangled quantum systems. Quant. Inf. Process. 9, 1–11 (2010)

    Article  MathSciNet  Google Scholar 

  16. Latorre, J.: Image compression and entanglement (2005). arXiv:quant-ph/0510031

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, Y., Lu, K., Gao, Y., Mao, W.: NEQR: a novel enhanced quantum representation of digital images. Quant. Inf. Process. 12, 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quant. Inf. Process. 12, 3103–3126 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Li, H., Zhu, Q., Lan, S., Shen, C., Zhou, R., et al.: Image storage, retrieval, compression and segmentation in a quantum system. Quant. Inf. Process. 12, 2269–2290 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Li, H., Zhu, Q., Zhou, R., Song, L., Yang, X.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quant. Inf. Process. 13, 991–1011 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., et al.: SQR: a simple quantum representation of infrared images. Quant. Inf. Process. 13, 1353–1379 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quant. Inf. Process. 16, 42 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Le, P.Q., Iliyasu, A.M., Dong, F., et al.: Fast geometric transformations on quantum images. Iaeng Int. J. Appl. Math. 40(3), 113–123 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Le, P.Q., Iliyasu, A.M., Dong, F., et al.: Strategies for designing geometric transformations on quantum images. Theoret. Comput. Sci. 412, 1406–1418 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Fan, P., Zhou, R., Jing, N., Li, H.: Geometric transformations of multidimensional color images based on NASS. Inf. Sci. 340, 191–208 (2016)

    Article  Google Scholar 

  27. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quant. Inf. Process. 14, 1589–1604 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Zhou, R.-G., Tan, C., Ian, H.: Global and local translation designs of quantum image based on FRQI. Int. J. Theor. Phys. 56, 1382–1398 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  29. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quant. Inf. Process. 14, 1559–1571 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Sang, J., Wang, S., Niu, X.: Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR. Quant. Inf. Process. 15, 37–64 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Zhou, R.-G., Hu, W., Fan, P., Ian, H.: Quantum realization of the bilinear interpolation method for NEQR. Sci. Rep. 7(1), 2511 (2017)

    Article  ADS  Google Scholar 

  32. Zhou, R., Hu, W., Luo, G., Liu, X., Fan, P.: Quantum realization of the nearest neighbor value interpolation method for INEQR. Quant. Inf. Process. 7(1), 2511 (2017)

    MATH  Google Scholar 

  33. Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quant. Inf. Process. 13, 1223–1236 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53, 2463–2484 (2014)

    Article  MATH  Google Scholar 

  35. Ri-Gui Zhou; Ya-Juan Sun; Ping Fan: Quantum image Gray-code and bit-plane scrambling. Quant. Inf. Process. 14, 1717–1734 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Mogos, G.: Hiding data in a QImage file. Lect. Notes Eng. Comput. Sci. 2174, 448–452 (2009)

    Google Scholar 

  37. Iliyasu, A.M., Le, P.Q., Dong, F., et al.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186, 126–149 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhang, W.W., Gao, F., Liu, B., Wen, Q.Y., Chen, H.: A watermark strategy for quantum images based on quantum Fourier transform. Quant. Inf. Process. 12, 793–803 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Song, X., Wang, S., El-Latif, A.A.A., Niu, X.M.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimed. Syst. 20, 379–388 (2014)

    Article  Google Scholar 

  40. Miyake, S., Nakamael, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quant. Inf. Process. 15, 1849–1864 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55(1), 107–123 (2016)

    Article  MATH  Google Scholar 

  42. Shahrokh, H., Mosayeb, N.: A novel LSB based quantum watermarking. Int. J. Theor. Phys. 55, 1–14 (2016)

    Article  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Dang, Y., Jiang, N., Hu, H., Zhang, W.: Analysis and improvement of the quantum imagematching. Quant. Inf. Process 16(11), 269 (2017)

    Article  ADS  Google Scholar 

  45. Tseng, C., Hwang, T.: Quantum digital image processing algorithms. In: Proceedings of the 16th IPPR Conference on Computer Vision, Graphics and Image Processing, pp. 827–834 (2003)

  46. Fu, X, Ding, M, Sun, Y, et al.: A new quantum edge detection algorithm for medical images. In: Proceedings of SPIE—The International Society for Optical Engineering, vol. 7497, pp. 749724–749724-7 (2009)

  47. Zhang, Y., Lu, K., Gao, Y.H.: QSobel: a novel quantum image edge extraction algorithm. Sci. China Inf. Sci 58, 1–13 (2015)

    MATH  Google Scholar 

  48. Zhang, Y., Lu, K., Xu, K., et al.: Local feature point extraction for quantum images. Quant. Inf. Process. 14, 1573–1588 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Image, A.F.: Algorithms for Image Processing and Computer Vision, 2nd edn. Wiley, New York (1997)

    Google Scholar 

  50. Marr, D., Hildreth, E.: Theory of edge detection. Proc. R. Soc. Lond. B Biol. Sci. B, 187–217 (1980)

    ADS  Google Scholar 

  51. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice-Hall, Inc. (2007)

  52. Wang, D., Liu, Z.H., Zhu, W.N., Li, S.Z.: Design of quantum comparator based on extended general Toffoli gates with multiple targets. Comput. Sci. 39(9), 302–306 (2012)

    Google Scholar 

  53. Cuccaro, S.A., Draper, T.G., Kutin, S.A., et al.: A new quantum ripple-carry addition circuit (2004). arXiv:quant-ph/0410184

  54. Sobel, L.: Camera Models and Machine Perception. Stanford University Press, Stanford (1970)

    Google Scholar 

  55. Canny, J.: A computational approach to edge detection. IEEE TPAMI 8, 679–697 (1986)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 61763014, 61463016, 61462026, and 61762012, the National Key R&D Plan under Grant No. 2018YFC1200200 and 2018YFC1200205, the Fund for Distinguished Young Scholars of Jiangxi Province under Grant No. 2018ACB21013, Science and technology research project of Jiangxi Provincial Education Department under Grant No. GJJ170382, Project of International Cooperation and Exchanges of Jiangxi Province under Grant No. 20161BBH80034, Project of Humanities and Social Sciences in colleges and universities of Jiangxi Province under Grant No. JC161023.

Author information

Authors and Affiliations

  1. School of Information Engineering, East China Jiaotong University, Nanchang, 330013, Jiangxi, China

    Ping Fan

  2. College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Ri-Gui Zhou & Wen Wen Hu

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    NaiHuan Jing

Authors
  1. Ping Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ri-Gui Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen Wen Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. NaiHuan Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ri-Gui Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, P., Zhou, RG., Hu, W.W. et al. Quantum image edge extraction based on Laplacian operator and zero-cross method. Quantum Inf Process 18, 27 (2019). https://doi.org/10.1007/s11128-018-2129-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-2129-x

Keywords

Search

Navigation