Abstract
Quantum image processing is a system where both quantum computing and image processings are key. Now it is required to investigate how to apply image processing concepts such as image edge detection and improved Sobel operator, to quantum image processing. Just as traditional image processing helps to image manipulation, our efforts in quantum image processing contribute to the further development of quantum algorithm and quantum information theory. Edge detection is an important problem in traditional image processing, and image edge detection algorithm can filter image edge features and retain important attributes. We proposed a quantum edge detection algorithm, which employs improved Sobel operator to improve the performance, so as to solve the problem of unsatisfactory traditional image edge detection methods. In practical application, the amount of image data to be processed increases sharply, and the computing power of classical computer becomes a limitation. Quantum information processing can effectively accelerate many classical problems by virtue of quantum mechanical characteristics, such as quantum superposition, entanglement, parallelism. Our proposed method uses the novel enhanced quantum representation to store quantum images, which stores all the pixels in the image in a superimposed state, realizing parallel computation. The improved eight-direction Sobel operator is used to calculate the gray gradient, and the quantum circuit is designed to realize quantum edge detection. Simulation results have shown that our algorithm can extract edge with dimension $2^{n}\times 2^{n}$ when the computational complexity is $O(n^{2} + 2^{q+3})$ . The improved algorithm can detect more edge details and has strong adaptability.
Highlights
Q UANTUM computing [1] is a novel technical processing mode for effective computation based on the principle of quantum mechanics.Since the 1990s in which Shor algorithm and Grover algorithm were proposed, the quantum algorithm has been proved to effectively solve the NP problem [2] of computer and overcome the bottleneck caused by traditional computing methods
QUANTUM EDGE EXTRACTION ALGORITHM FOR IMPROVED SOBEL OPERATOR In this part, we introduce in detail the quantum image edge detection algorithm based on the improved Sobel operator
MAIN RESULTS This algorithm is improved based on Sobel quantum edge detection algorithm, and the traditional 2-directions Sobel algorithm is improved to 8 directions
Summary
Q UANTUM computing [1] is a novel technical processing mode for effective computation based on the principle of quantum mechanics.Since the 1990s in which Shor algorithm and Grover algorithm were proposed, the quantum algorithm has been proved to effectively solve the NP problem [2] of computer and overcome the bottleneck caused by traditional computing methods. Fan et al [26] proposed an image edge detection method based on Laplacian operator in 2019. In 2020, Xu et al [27] proposed a quantum image processing algorithm using edge extraction based on Kirsch operator. Classic image edge extraction algorithms such as Prewitt [31], Kirsch [32], Sobel [33], and Canny [34] have been continuously proposed. In 2019, Fan et al [35] completed the quantum edge detection algorithm based on Sobel. A quantum edge detection algorithm based on improved eight-direction Sobel operator [36] was proposed. Compared with all the classical edge extraction algorithms and some existing quantum edge extraction algorithms, our proposed scheme can achieve a significant exponential acceleration, thereby providing a computational speed. The simulation results have shown that our algorithm has higher accuracy in edge extraction
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