基于补码浮点表示的量子图像 Harris 角点检测方法

Harris Corner Detection Method Based on Complement Floating-Point Representation for Quantum Images

摘要

针对量子图像的特征点提取问题, 提出了 Harris 角点检测算法在量子计算机上的实现方案。首先, 为解决Harris 角点检测量子线路中涉及的有理数高效编码及运算问题, 提出了基于补码浮点表示的量子图像表示模型。其中像素值使用基于补码的浮点数形式表示, 像素的位置信息采用无符号数表示, 每种数据结构均基于量子比特序列的基态进行信息表示。然后, 根据经典 Harris 角点检测算法的相关理论设计了 Harris 角点检测的具体量子线路, 并对其进行了复杂度分析, 验证该方案相较于经典方案的指数级加速。最后, 通过在经典计算机上的仿真实验证明, 经典 Harris 角点检测算法与量子 Harris 角点检测方案所检测的角点重合率超过85%, 验证了所提方案的可行性与有效性。

Abstract

In order to solve the problem of feature point extraction in quantum images, the implementation scheme of Harris corner detection algorithm on quantum computers is studied. Firstly, to address the efficient encoding and computation of rational numbers in Harris corner detection quantum circuits, a quantum image representation model based on complement floating-point representation is proposed. In this model, pixel values are represented in the form of complement-based floating-point numbers, and the position information of pixels is represented by unsigned numbers. Each data structure is based on the basic state of quantum bit sequences for information representation. Secondly, based on the relevant theories of the classical Harris corner detection algorithm, a specific quantum circuit for Harris corner detection is designed, and its complexity analysis is conducted to verify its exponential acceleration compared to classical schemes. Finally, through simulation experiments on classical computers, it is demonstrated that the overlap rate between the classical Harris corner detection algorithm and the quantum Harris corner detection scheme exceeds 85%, which to some extent verifies the feasibility and effectiveness of the proposed scheme.

关键词

量子图像处理 / 量子图像表示 / 特征点检测 / Harris 角点

Key words

quantum image processing / quantum image representation / feature point detection / Harris corner

参考文献

[1] FEYNMAN R P. Simulating Physics with Computers[J]. International Journal of Theoretical Physics, 1982, 21(6-7): 467-488.

[2] DEUTSCH D. Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985, 400(1818): 97-117.

[3] SHOR P W. Algorithms for Quantum Computation: Discrete Logarithms and Factoring[C]// Proceedings 35th Annual Symposium on Foundations of Computer Science. Santa Fe, NM, USA: IEEE Comput Soc Press, 1994: 124-134.

[4] GROVER L K. A Fast Quantum Mechanical Algorithm for Database Search[C]// Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing-STOC’96. Philadelphia, Pennsylvania, United States: ACM Press, 1996: 212-219.

[5] VENEGAS-ANDRACA S E, BOSE S. Storing, Processing, and Retrieving an Image Using Quantum Mechanics [C/OL]// AeroSense 2003. Orlando, FL, 2003: 137 [2023-10-13]. http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.485960.

[6] LE P Q, DONG F, HIROTA K. A Flexible Representation of Quantum Images for Polynomial Preparation, Image Compression, and Processing Operations[J]. Quantum Information Processing, 2011, 10(1): 63-84.

[7] ZHANG Y, LU K, GAO Y, et al. NEQR: A Novel Enhanced Quantum Representation of Digital Images[J]. Quantum Information Processing, 2013, 12(8): 2833-2860.

[8] LIU K, ZHANG Y, LU K, et al. An Optimized Quantum Representation for Color Digital Images[J]. International Journal of Theoretical Physics, 2018, 57(10): 2938-2948.

[9] ŞAHİN E, YILMAZ ŞIH. QRMW: Quantum Representation of Multi Wavelength Images[J]. Turkish Journal of Electrical Engineering & Computer Sciences, 2018, 26(2): 768-779.

[10] WANG B, HAO M Q, LI P C, et al. Quantum Representation of Indexed Images and Its Applications[J]. International Journal of Theoretical Physics, 2020, 59(2): 374-402.

[11] KHAN M, RASHEED A. A Secure Controlled Quantum Image Steganography Scheme Based on the Multi-Channel Effective Quantum Image Representation Model [J/OL]. Quantum Information Processing, 2023, 22(7): 268 [2025-06-24]. https://link.springer.com/article/10.1007/s11128-023-04022-0.

[12] HOU C, LIU X, FENG S. Quantum Image Scrambling Algorithm Based on Discrete Baker Map [J/OL]. Modern Physics Letters A, 2020, 35(17): 2050145 [2025-06-24]. https://www.worldscientific.com/doi/abs/10.1142/S021773232050145X.

[13] 刘志飞, 朱尚超, 魏战红, 等. 基于 IBM Qiskit 的量子图像伪彩色增强方法[J]. 计算机与现代化, 2023(4): 47-55.

[14] LIU Z F, ZHU S C, WEI Z H, et al. Pseudo-Color Enhancement Method for Quantum Images Based on IBM Qiskit[J]. Computer and Modernization, 2023(4): 47-55.

[15] MA Y, ZHOU N R. Quantum Color Image Compression and Encryption Algorithm Based on Fibonacci Transform [J/OL]. Quantum Information Processing, 2023, 22(1): 39 [2025-06-24]. https://link.springer.com/article/10.1007/s11128-022-03749-6.

[16] YUAN S Z, LIN W, HANG B, et al. Quantum Fast Corner Detection Algorithm [J/OL]. Quantum Information Processing, 2023, 22(8): 313 [2025-06-24]. https://link.springer.com/article/10.1007/s11128-023-04047-5.

[17] RAHMAN A U, ALAHMADI T J, ALSENANI Y S, et al. Enhancing Handwritten Text Feature Extraction through Key Point Detection and Graph Representation[J]. Soft Computing, 2024, 28(21): 12977-12990.

[18] KAUR A, KUMAR M, JINDAL M K. Cattle Identification System: a Comparative Analysis of Sift, Surf and Orb Feature Descriptors[J]. Multimedia Tools and Applications, 2023, 82: 27391-27413.

[19] ZHANG Y, LU K, XU K, et al. Local Feature Point Extraction for Quantum Images[J]. Quantum Information Processing, 2015, 14(5): 1573-1588.

[20] JIANG N, JI Z X, LI H, et al. Quantum Images Interest Point Extraction [J/OL]. Modern Physics Letters A, 2021, 36(9): 2150063 [2025-06-24]. https://www.worldscientific.com/doi/abs/10.1142/S0217732321500632.

[21] 唐朔飞. 计算机组成原理[M]. 3版. 北京: 高等教育出版社, 2020: 228-230.

[22] TANG S F. Principles of Computer Organization[M]. 3rd Ed. Beijing: Higher Education Press, 2020: 228-230.

[23] 王兵, 周冰琪, 李盼池, 等. 数字信号的量子补码浮点表示及运算研究[J]. 信号处理, 2024, 40(12): 2167-2177.

[24] WANG B, ZHOU B Q, LI P C, et al. Study on Quantum Complement Floating Point Representation and Operations of Digital Signals[J]. Journal of Signal Processing, 2024, 40(12): 2165-2177.

[25] 王冬, 刘志昊, 朱皖宁, 等. 基于多目标扩展通用 Toffoli 门的量子比较器设计[J]. 计算机科学, 2012, 39(9): 302-306.

[26] WANG D, LIU Z H, ZHU W N, et al. Design of Quantum Comparator Based on Extended General Toffoli Gates with Multiple Targets[J]. Computer Science, 2012, 39(9): 302-306.

[27] 鲍华良, 赵娅. 经典 Canny 边缘检测的量子实现[J]. 吉林大学学报(信息科学版), 2022, 40(1): 36-50.

[28] BAO H L, ZHAO Y. Quantum Implementation of Classical Canny Edge Detection[J]. Journal of Jilin University (Information Science Edition), 2022, 40(1): 36-50.

[29] 鲍华良, 赵娅. 经典 Marr-Hildreth 边缘检测的量子实现[J]. 吉林大学学报(理学版), 2022, 60(3): 617-628.

[30] BAO H L, ZHAO Y. Quantum Implementation of Classical Marr-Hildreth Edge Detection[J]. Journal of Jilin University (Science Edition), 2022, 60(3): 617-628.

基金资助

黑龙江省自然科学基金联合引导基金资助项目(LH2024E012)