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Quantum image edge extraction based on classical Sobel operator for NEQR

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Abstract

As the basic problem in image processing and computer vision, the purpose of edge detection is to identify the point where the brightness of the digital image changes obviously. It is an indispensable task in digital image processing that image edge detection significantly reduces the amount of data and eliminates information that can be considered irrelevant, preserving the important structural properties of the image. However, 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, quantum image edge extraction for the novel enhanced quantum representation (NEQR) is designed based on classical Sobel operator. The quantum image model of NEQR utilizes the inherent entanglement and superposition properties of quantum mechanics to store all the pixels of an image in a superposition state, which can realize parallel computation for calculating the gradients of the image intensity of all the pixels simultaneously. Through constructing and analyzing the quantum circuit of realization image edge extraction, we demonstrate that our proposed scheme can extract edges in the computational complexity of \(\mathrm{O}({n^2} + {2^{q + 4}})\) for a NEQR quantum image with a size of \({2^n} \times {2^n}\). Compared with all the classical edge extraction algorithms and some existing quantum edge extraction algorithms, our proposed scheme can reach a significant and exponential speedup. Hence, our proposed scheme would resolve the real-time problem of image edge extraction in practice image processing.

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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 Nos. 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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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 & Wenwen Hu

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

    Naihuan Jing

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  1. Ping Fan
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Correspondence to Ping Fan.

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Fan, P., Zhou, RG., Hu, W. et al. Quantum image edge extraction based on classical Sobel operator for NEQR. Quantum Inf Process 18, 24 (2019). https://doi.org/10.1007/s11128-018-2131-3

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