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Quantum Information Processing

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01-03-2024

A novel approach to threshold quantum images by using unsharp measurements

Authors: Ayan Barui, Mayukha Pal, Prasanta K. Panigrahi

Published in: Quantum Information Processing | Issue 3/2024

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Abstract

We propose a hybrid quantum approach to threshold and binarize a grayscale image through unsharp measurements (UM) relying on image histogram. Generally, the histograms are characterized by multiple overlapping normal distributions corresponding to objects, or image features with small but significant overlaps, making it challenging to establish suitable thresholds. The proposed methodology uses peaks of the overlapping Gaussians and the distance between neighboring local minima as the variance, based on which the UM parameters are chosen, that maps the normal distribution into a localized delta function. To demonstrate its efficacy, subsequent implementation is done on noisy quantum environments in Qiskit. This process is iteratively repeated for a multimodal histogram to obtain more thresholds, which are then applied to various life-like pictures to get high-contrast images, resulting in comparable peak signal-to-noise ratio and structural similarity index measure values. The obtained thresholds are used to binarize a grayscale image by using novel enhanced quantum image representation integrated with a threshold encoder and an efficient quantum comparator (QC) that depicts the whole binarized picture. This approach significantly reduces the complexity of the proposed QC and of the whole algorithm when compared to earlier models.

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Sahoo, P.K., Soltani, S., Wong, A.K.C.: A survey of thresholding techniques. Comput. Vis. Graph. Image Process. 41(2), 233–260 (1988). https://doi.org/10.1016/0734-189X(88)90022-9CrossRef

Wiley, V., Lucas, T.: Computer vision and image processing: a paper review. Int. J. Artif. Intell. Res. 2(1), 29–36 (2018)CrossRef

Ruan, Y., Xue, X., Shen, Y.: Quantum image processing: opportunities and challenges. Math. Probl. Eng. 2021, 1–8 (2021)CrossRef

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, 63–84 (2011). https://doi.org/10.1007/s11128-010-0177-yMathSciNetCrossRef

Sun, B., Le, P.Q., Iliyasu, A.M., Yan, F., Garcia, J.A., Dong, F., Hirota, K.: A multi-channel representation for images on quantum computers using the rgb\(\alpha \) color space. In: 2011 IEEE 7th International Symposium on Intelligent Signal Processing, pp. 1–6 (2011). https://doi.org/10.1109/WISP.2011.6051718 . IEEE

Zhang, Y., Lu, K., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12, 2833–2860 (2013). https://doi.org/10.1007/s11128-013-0567-zADSMathSciNetCrossRef

Vlasov, A.Y.: Quantum Computations and Images Recognition. arXiv e-prints, 9703010 (1997) https://doi.org/10.48550/arXiv.quant-ph/9703010arXiv:quant-ph/9703010 [quant-ph]

Venegas-Andraca, S., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proc. SPIE Int. Soc. Opt. Eng. (2003). https://doi.org/10.1117/12.485960CrossRef

Srivastava, M., Moulick, S.R., Panigrahi, P.K.: Quantum image representation through two-dimensional quantum states and normalized amplitude. arXiv preprint arXiv:1305.2251 (2013)

10.

Mandal, A., Banerjee, S., Panigrahi, P.K.: Hybrid phase-based representation of quantum images. Int. J. Theor. Phys. 62(6), 115 (2023). https://doi.org/10.1007/s10773-023-05354-4CrossRef

11.

Su, J., Guo, X., Liu, C., Lu, S., Li, L.: An improved novel quantum image representation and its experimental test on IBM quantum experience. Sci. Rep. 11(1), 13879 (2021). https://doi.org/10.1038/s41598-021-93471-7ADSCrossRef

12.

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)

13.

Al-Rabadi, A.N.: Closed-system quantum logic network implementation of the Viterbi algorithm. Facta Univ. Ser. Electron. Energetics 22(1), 1–33 (2009)MathSciNetCrossRef

14.

Thapliyal, H., Ranganathan, N., Ferreira, R.: Design of a comparator tree based on reversible logic. In: 10th IEEE International Conference on Nanotechnology, pp. 1113–1116 (2010). https://doi.org/10.1109/NANO.2010.5697872

15.

Xia, H., Li, H., Zhang, H., Liang, Y., Xin, J.: An efficient design of reversible multi-bit quantum comparator via only a single ancillary bit. Int. J. Theor. Phys. 57, 3727–3744 (2018). https://doi.org/10.1007/s10773-018-3886-0CrossRef

16.

Vudadha, C., Phaneendra, P.S., Ahmed, S.E., Sreehari, V., Muthukrishnan, N.M., Srinivas, M.B.: Design and analysis of reversible ripple, prefix and prefix-ripple hybrid adders. In: 2012 IEEE Computer Society Annual Symposium on VLSI, pp. 225–230 (2012). https://doi.org/10.1109/ISVLSI.2012.50

17.

Caraiman, S., Manta, V.I.: Histogram-based segmentation of quantum images. Theor. Comput. Sci. 529, 46–60 (2014). https://doi.org/10.1016/j.tcs.2013.08.005MathSciNetCrossRef

18.

Caraiman, S., Manta, V.I.: Image segmentation on a quantum computer. Quantum Inf. Process. 14, 1693–1715 (2015). https://doi.org/10.1007/s11128-015-0932-1ADSMathSciNetCrossRef

19.

Du, S., Luo, K., Zhi, Y., Situ, H., Zhang, J.: Binarization of grayscale quantum image denoted with novel enhanced quantum representations. Results Phys. 39, 105710 (2022). https://doi.org/10.1016/j.rinp.2022.105710CrossRef

20.

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

21.

Li, P., Shi, T., Zhao, Y., Lu, A.: Design of threshold segmentation method for quantum image. Int. J. Theor. Phys. 59(2), 514–538 (2020)MathSciNetCrossRef

22.

Orts, F., Ortega, G., Cucura, A., Filatovas, E., Garzón, E.M.: Optimal fault-tolerant quantum comparators for image binarization. J. Supercomput. 77, 8433–8444 (2021). https://doi.org/10.1007/s11227-020-03576-5CrossRef

23.

Yuan, S., Zhao, W., Gao, S., Xia, S., Hang, B., Qu, H.: An adaptive threshold-based quantum image segmentation algorithm and its simulation. Quantum Inf. Process. 21(10), 359 (2022). https://doi.org/10.1007/s11128-022-03709-0ADSMathSciNetCrossRef

24.

Xia, H.-Y., Zhang, H., Song, S.-X., Li, H., Zhou, Y.-J., Chen, X.: Design and simulation of quantum image binarization using quantum comparator. Mod. Phys. Lett. A 35(09), 2050049 (2020). https://doi.org/10.1142/S0217732320500492ADSMathSciNetCrossRef

25.

Arora, S., Acharya, J., Verma, A., Panigrahi, P.K.: Multilevel thresholding for image segmentation through a fast statistical recursive algorithm. Pattern Recogn. Lett. 29(2), 119–125 (2008). https://doi.org/10.1016/j.patrec.2007.09.005ADSCrossRef

26.

Reddi, S.S., Rudin, S.F., Keshavan, H.R.: An optimal multiple threshold scheme for image segmentation. IEEE Trans. Syst. Man Cybern. SMC14(4), 661–665 (1984). https://doi.org/10.1109/TSMC.1984.6313341CrossRef

27.

Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861ADSCrossRef

28.

Sauvola, J., Pietikäinen, M.: Adaptive document image binarization. Pattern Recogn. 33(2), 225–236 (2000). https://doi.org/10.1016/S0031-3203(99)00055-2ADSCrossRef

29.

Niblack, W.: An Introduction to Image Processing, pp. 115–116. Prentice-Hall, Englewood Cliffs (1986)

30.

Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979). https://doi.org/10.1109/TSMC.1979.4310076CrossRef

31.

Hemachander, S., Verma, A., Arora, S., Panigrahi, P.K.: Locally adaptive block thresholding method with continuity constraint. Pattern Recogn. Lett. 28(1), 119–124 (2007). https://doi.org/10.1016/j.patrec.2006.06.005ADSCrossRef

32.

Wang, B., Fan, S.: An improved canny edge detection algorithm. In: 2009 Second International Workshop on Computer Science and Engineering 1, pp. 497–500 (2009)

33.

Chakraborty, S., Mali, K.: A balanced hybrid cuckoo search algorithm for microscopic image segmentation. Soft Comput. (2023). https://doi.org/10.1007/s00500-023-09186-6CrossRef

34.

Pal, M., Panigrahi, P.: Effective Clustering and Accurate Classification of the Chest X-ray Images of COVID-19 Patients from Healthy Ones Through the Mean Structural Similarity Index Measure. https://doi.org/10.13140/RG.2.2.33801.57441

35.

Saha, D., Mal, S., Panigrahi, P.K., Home, D.: Wigner’s form of the Leggett-Garg inequality, the no-signaling-in-time condition, and unsharp measurements. Phys. Rev. A 91, 032117 (2015). https://doi.org/10.1103/PhysRevA.91.032117ADSMathSciNetCrossRef

36.

Ludwig, G., Ludwig, G.: Ensembles and Effects. In: Foundations of Quantum Mechanics I, pp. 41–82. Springer, Cham (1983)CrossRef

37.

Giuntini, R., Greuling, H.: Toward a formal language for unsharp properties. Found. Phys. 19, 931–945 (1989). https://doi.org/10.1007/BF01889307ADSMathSciNetCrossRef

38.

Patil, S., Banerjee, S., Panigrahi, P.K.: Measurement-based quantum clustering algorithms. arXiv preprint arXiv:2302.00566 (2023)

39.

Sezan, M.I.: A peak detection algorithm and its application to histogram-based image data reduction. Comput. Vis. Graph. Image Process. 49(1), 36–51 (1990). https://doi.org/10.1016/0734-189X(90)90161-NCrossRef

40.

Papamarkos, N., Gatos, B.: A new approach for multilevel threshold selection. CVGIP Graph. Models Image Process. 56(5), 357–370 (1994). https://doi.org/10.1006/cgip.1994.1033CrossRef

41.

Pinto, D.F., Zanetti, M.S., Basso, M.L.W., Maziero, J.: Simulation of positive operator-valued measures and quantum instruments via quantum state-preparation algorithms. Phys. Rev. A 107, 022411 (2023). https://doi.org/10.1103/PhysRevA.107.022411ADSMathSciNetCrossRef

42.

Araujo, I.F., Park, D.K., Petruccione, F., Silva, A.J.: A divide-and-conquer algorithm for quantum state preparation. Sci. Rep. 11(1), 6329 (2021). https://doi.org/10.1038/s41598-021-85474-1CrossRef

43.

Thomsen, M.K., Glück, R., Axelsen, H.B.: Reversible arithmetic logic unit for quantum arithmetic. J. Phys. A Math. Theor. 43(38), 382002 (2010). https://doi.org/10.1088/1751-8113/43/38/382002MathSciNetCrossRef

Title: A novel approach to threshold quantum images by using unsharp measurements
Authors: Ayan Barui
Mayukha Pal
Prasanta K. Panigrahi
Publication date: 01-03-2024
Publisher: Springer US
Published in: Quantum Information Processing / Issue 3/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-024-04282-4

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