We propose a novel edge detection algorithm based on quantum entropy using a flexible representation of the quantum image. We use information entropy to measure the amount of information contained in digital images in view of quantum information processing. Quantum entropy can take correlations among quantum bases into the calculation of entropy, while Shannon entropy is powerless on this, namely, quantum entropy is more accurate than Shannon entropy in quantum information measurements. Therefore, the quasithreshold that leads to maximum quantum entropy should be adopted as the optimal threshold, because the maximum amount of information is obtained under this circumstance. The quantum version of the image segmentation works with computational basis states, exclusively. We prove the efficiency of the approach proposed on examples from the real world, microscopy, microarray, medical, and satellite images. We present the performance evaluation of the proposed technique based on the peak-signal-to-noise ratio.
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I. Williams, N. Bowring, and D. Svoboda, Comput. Vis. Image Understand., 122, 115 (2014).
S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum algorithms for supervised and unsupervised machine learning, arXiv:1307.0411 (2013).
N. Wiebe, A. Kapoor, and K. Svore, Quantum nearest-neighbor algorithms for machine learning, arXiv:1401.2142 (2014).
M. Gut and W. Kotlowski, New J. Phys., 12, 123032 (2010).
C. A. Trugenberger, Phys. Rev. Lett., 87, 1 (2001).
Y. C. Eldar and A. V. Oppenheim, IEEE Signal Process. Mag., 19, 12 (2002).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, UK (2000).
R. J. Schalko, Digital Image Processing and Computer Vision, Wiley, New York (1989).
S. Venegas-Andraca and S. Bose, “Storing, processing and retrieving an image using quantum mechanics,” in: Quantum Information and Computation, SPIE Proc., 147 (2003).
P. Le, F. Dong, and K. Hirota, Quantum Inform. Process., 10, 63 (2011).
P. Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, Theor. Comput. Sci., 412, 1406 (2011).
P. Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, J. Adv. Comput. Intell. Inform., 15, 698 (2011).
F. Yan, P. Q. Le, A. M. Iliyasu, et al., “Assessing the similarity of quantum images based on probability measurements,” in: IEEE Congress on Evolutionary Computation (2012), p. 1.
J. Liu, K. Doi, A. Fenster, and S. C. Chan, “A new quantum edge detection algorithm for medical images,” in: MIPPR 2009: Medical Imaging, Parallel Processing of Images, and Optimization Techniques, Proc. SPIE, 7497 (2009); doi:10.1117/12.832499.
M. Lanzagorta and J. Uhlmann, “Hybrid quantum-classical computing with applications to computer graphics,” in: SIGGRAPH’05: A CMSIG GRAPH 2005 Courses, ACM, New York, USA (2005).
S. Caraiman, “Towards quantum computer graphics,” in: Proceedings of the 14 International Conference on System Theory and Control, 17–19 October 2010, Sinaia, Romania (2010), p. 127 [http://ace.ucv.ro/sintes14/ICSTC 2010 Conference Proceedings.pdf].
S. Yuana, X. Maoa, L. Chena, and Y. Xue, Optik, 124, 6386 (2013).
M. Lanzagorta and J. Uhlmann, “Quantum computational geometry,” in: E. Donkor, A. Pirich, and H. Brandt (Eds.), Quantum Information and Computation II, Proc. SPIE, 5436, 332 (2004).
L. Tang, Comput. Model. New Technol., 18, 517 (2014).
S. Caraiman and V. Manta, Theor. Comput. Sci., 529, 46 (2014).
D. U. Songlin, W. U. Guoping, M. A. Li, and M. A. Yide, J. Comput. Inform. Syst., 10, 3359 (2014).
Y. C. Kittler and A. V. Oppenheim, IEEE Signal Process. Mag., 19, 12 (2002).
C. Trugenberger, Phys. Rev. Lett., 87, 1 (2001).
Phuc Q. Le, F. Dong, and K. Hirota, Quantum Inform. Process., 10, 63 (2011).
Phuc Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, Theor. Comput. Sci., 412, 1406 (2011).
F. Xiaozuo, D. Mingyue, Z. Chengping, et al., Acta Electron. Sin., 7, 1590 (2010).
A. D. Brink, N. E. Pendock, Pattern Recogn., 29, 179 (1996).
P. Sahoo, C. Wilkins, and J. Yeager, Pattern Recogn., 30, 71 (1997).
A. D. Brink, Pattern Recogn., 25, 803 (1992).
Y. Zhang, Principles of Quantum Information Physics, Science Press, Beijing (2005).
S. Alpert, M. Galun, A. Brandt, and R. Basri, “Image segmentation by probabilistic bottom-up aggregation and cue integration,” in: IEEE Conference on Computer Vision and Pattern Recognition (Minneapolis, 2007), IEEE Trans. Pattern, 34, 315 (2012).
M. A. El-Sayed, IJCSI Int. J. Comput. Sci., 8, 1694 (2011).
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Abdel-Khalek, S., Abdel-Azim, G., Abo-Eleneen, Z.A. et al. New Approach to Image Edge Detection Based on Quantum Entropy. J Russ Laser Res 37, 141–154 (2016). https://doi.org/10.1007/s10946-016-9554-z
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DOI: https://doi.org/10.1007/s10946-016-9554-z