Abstract
In this paper, based on the principle of classical morphology operations, the flat grayscale dilation and erosion operations are proposed for NEQR quantum image model. Furthermore, through combining these two morphology operations, we further realize the morphological gradient operation. As the basis of designing of grayscale morphology operations, a series of quantum circuit designs arepresented, which includes special add one operation UA1(n) and special subtract one operation US1(n) both for an n-length qubits sequence, quantum unitary operation UC, parallel subtractor (PS) module, quantum comparator output the large QCOL and quantum comparator output the small QCOS modules. When designsthe concrete quantum circuit, a sequence of UA1(n) and US1(n) modules are used to obtain the quantum image sets based on the shape of specific structuring element. Then, the searching for maximaor minima in a certain space is involved, which can be solved by cascading a series of QCOL and QCOS modules in certain order. Finally, the PS module can be used to calculate the difference of the maxima and minima for producing the morphological gradient. The circuit’s complexity analysis illustrate that our scheme is very lower to the classical morphology operations.
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References
Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)
Yan, F., Iliyasu, A.M., Le, P, Q.: Quantum image processing: A review of advances in its security technologies. International Int. J. Quantum. Inf. 15(3), 1730001(2017)
Yan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A survey of quantum image representations. Quantum Inf Process. 15(1), 1–35 (2016)
Vlasov, A.Y.: Quantum computations and images recognition. arXiv preprint quant-ph/9703010 (1997)
Schützhold, R.: Pattern recognition on a quantum computer. Phys. Rev. A. 67(6), 062311 (2002)
Beach, G., Lomont, C., Cohen, C.: Quantum image processing (QuIP)[C]// applied imagery pattern recognition workshop. Proceedings. IEEE. 2004, 39–44 (2003)
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Pro. Roy. Soc. Lond. A: Math. Phys. Eng. Sci. pp. 97–117 (1985)
Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science. 124–134(1994)
Grover, L.:A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing. 212–219(1996)
Iliyasu, A.M.: Towards the realisation of secure and efficient image and video processing applications on quantum computers. Entropy. 15, 2874–2974 (2013)
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
Iliyasu, A.M., Le, P.Q., Yan, F., et al.: A two-tier scheme for Greyscale Quantum Image Watermarking and Recovery. Int. J. Innov Comput Appl. 5(2), 85–101 (2013)
Venegas-Andraca, S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. Proc. SPIE 5105 Quantum Inf. Compu. 5105(8), 134–147 (2003)
Venegas-Andraca, S., Ball, J.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)
Latorre, J.: Image Compression and Entanglement. arXiv:quant-ph/0510031 (2005)
Le, 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)
Zhang, Y., Lu, K., Gao, Y., Mao, W.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)
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)
Li, H.S., Zhu, Q., Zhou, R.G., et al.: Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases. Inf Sci. 273(3), 212–232 (2014)
Li, H.S., Fan, P, Xia, H.Y., et al. Quantum Implementation Circuits of Quantum Signal Representation and Type Conversion. IEEE Trans Circuits Syst I: Reg Papers, (99):1–14 (2018)
Le, P. Q., Iliyasu, A.M., Dong, F., et al.: Fast geometric transformations on quantum images. Iaeng Int J Appl Math. 40(3),(2010)
Fan, P., Zhou, R., Jing, N., Li, H.: Geometric transformations of multidimensional color images based on NASS. Inf. Sci. 340–341, 191–208 (2016)
Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2015)
Zhou, R.G., Tan, C., Hou, I.: Global and local translation designs of quantum image based on FRQI. Int J Theor Phys. 56(4), 1382–1398 (2017)
Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015)
Sang, J., Wang, S., Niu, X.: Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR. Quantum Inf. Process. 15(1), 37–64 (2016)
Zhou, R.G., Hu, W., Fan, P., Hou, I.: Quantum realization of the bilinear interpolation method for NEQR. Scientific Reports. (7), 2511 (2017)
Zhou, R.G., Tan, C., Fan, P.: Quantum multidimensional color image scaling using nearest-neighbor interpolation based on the extension of FRQI. Mod. Phys. Lett. B. 31(17), 1750184 (2017)
Zhou, R.G., Hu, W.W., Luo, G.F., et al.: Quantum realization of the nearest neighbor value interpolation method for INEQR. Quantum Inf. Process. 17(7), 166 (2018)
Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)
Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int J Theor Phys. 53(7), 2463–2484 (2014)
Zhou, R.G., Shun, Y.J., Fan, P.: Quantum image Gray-code and bit-plane scrambling. Quantum Inf. Process. 14(5), 1717–1734 (2015)
Mogos, G.: Hiding data in a QImage file. Lecture Notes Eng. Compu. Sci. 2174(1), 448–452 (2009)
Iliyasu, A.M., Le, P.Q., Dong, F., et al.: Watermarking and authentication of quantum images based on restricted geometric transformations. Information Sciences. 186(1), 126–149 (2012)
Zhang, W., Gao, F., Liu, B., et al.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(2), 793–803 (2013)
Song, X., Wang, S., El-Latif, A., et al.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimedia Systems. 20(4), 379–388 (2014)
Miyake, S., Nakamael, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf. Process. 15(5), 1849–1864 (2016)
Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. International J Theor Phys. 55(1), 107–123 (2016)
Heidari, S., Naseri, M.: A novel LSB based quantum watermarking. Int J Theor Phys. 55(10), 1–14 (2016)
Zhou, R.G., Shun, Y.J.: Novel morphological operations for quantum image. J Comput Inf Syst. 11(9), 3105–3112 (2015)
Zhou, R.G., Chang, Z., Fan, P., et al.: Quantum image morphology processing based on quantum set operation. Int J Theor Phys. 54(6), 1974–1986 (2015)
Yuan, S., Mao, X., Li, T., et al.: Quantum morphology operations based on quantum representation model. Quantum Inf. Process. 14(5), 1625–1645 (2015)
Fu, X., Ding, M., Sun, Y., et al.: A new quantum edge detection algorithm for medical images. Proc SPIE Int Soc Opt Eng. 7497(9), 749724–749724-7 (2009)
Zhang, Y., Lu, K., Gao, Y.H.: QSobel: A novel quantum image edge extraction algorithm. Science China Information Sciences. 58(1), 1–13 (2015)
Zhang, Y., Lu, K., Xu, K., et al.: Local feature point extraction for quantum images. Quantum Inf. Processing. 14(5), 1573–1588 (2015)
Jiang, N., Dang, Y., Wang, J.: Quantum image matching. Quantum Inf Process. 15(9), 3543–3572 (2016)
Barenco, A., Bennett, C.H., et al.: Elementary gates for quantum computation. Phys Rev A At Mol Opt Phys. 52(5), 3457–3488 (1995)
Feynman, R.: Quantum mechanical computers. Found. Phys. 16(6):507–531 (1986)
Toffoli, T.: Reversible computing. Int. Col. Aut. Lan. Prog. Springer, Berlin, Heidelberg (1980)
Peres, A.: Reversible logic and quantum computers. Phys. Rev. A, Gen. Phys. 32(32), 3266–3276 (1985)
Thapliyal, H., Ranganathan, N.: Design of efficient reversible binary subtractors based on a new reversible gate. IEEE Compu. Soc. Symp. VLSI. 229–234 (2009)
Gonzalez, R.C., Wood, R.E.: Digital Image Processing, 2nd edn. Prentice Hall, Englewood Cliffs (2002)
Thapliyal H., Ranganathan N. A new design of the reversible subtractor circuit.IEEE Conf. NANO. 1430-1435 (2011)
Xu, X., Xiao, F., et al.: Application of dichotomy in decomposition of multi-line quantum logic gate. J. Southeast Uni. 40(5), 928–931 (2010)
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.
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Fan, P., Zhou, RG., Hu, W. et al. Quantum Circuit Realization of Morphological Gradient for Quantum Grayscale Image. Int J Theor Phys 58, 415–435 (2019). https://doi.org/10.1007/s10773-018-3943-8
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DOI: https://doi.org/10.1007/s10773-018-3943-8