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Quantum morphology operations based on quantum representation model

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Abstract

Quantum morphology operations are proposed based on the novel enhanced quantum representation model. Two kinds of quantum morphology operations are included: quantum binary and grayscale morphology operations. Dilation and erosion operations are fundamental to morphological operations. Consequently, we focus on quantum binary and flat grayscale dilation and erosion operations and their corresponding circuits. As the basis of designing of binary morphology operations, three basic quantum logic operations AND, OR, and NOT involving two binary images are presented. Thus, quantum binary dilation and erosion operations can be realized based on these logic operations supplemented by quantum measurement operations. As to the design of flat grayscale dilation and erosion operations, the searching for maxima or minima in a certain space is involved; here, we use Grover’s search algorithm to get these maxima and minima. With respect that the grayscale is represented by quantum bit string, the quantum bit string comparator is used as an oracle in Grover’s search algorithm. In these quantum morphology operations, quantum parallelism is well utilized. The time complexity analysis shows that quantum morphology operations’ time complexity is much lower or equal to the classical morphology operations.

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Acknowledgments

This work is supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (20121102130001), the Innovation Foundation of BUAA for Ph.D. Graduates, the National Natural Science Foundation of China (61103097).

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Beihang University, Beijing, 100191, China

    Suzhen Yuan, Xia Mao, Tian Li, Yuli Xue, Lijiang Chen & Qingxu Xiong

  2. School of Physics and Electrical Engineering, Anyang Normal University, Anyang, 455002, China

    Suzhen Yuan

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  1. Suzhen Yuan
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  2. Xia Mao
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  3. Tian Li
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  4. Yuli Xue
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  5. Lijiang Chen
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  6. Qingxu Xiong
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Correspondence to Lijiang Chen.

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Yuan, S., Mao, X., Li, T. et al. Quantum morphology operations based on quantum representation model. Quantum Inf Process 14, 1625–1645 (2015). https://doi.org/10.1007/s11128-014-0862-3

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  • DOI: https://doi.org/10.1007/s11128-014-0862-3

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