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Quantum Information Processing

Quantum image edge detection based on Laplacian of Gaussian operator

Suzhen Yuan, Wenhao Zhao, Jeremiah D. Deng, Shuyin Xia, Xianli Li

Published May 10, 2024• 11 citations
Publisher

Abstract

Abstract With the increase in the quantity and quality of images that need to be processed, there are higher requirements for the speed of image processing. Thus, it is necessary to speed-up the image processing algorithms. In this paper, we design a quantum image edge detection algorithm based on Laplacian of Gaussian (LoG) operator, which has significant acceleration due to the quantum parallelism. Firstly, the quantum circuit of the novel enhanced quantum image representation (NEQR) model is improved to represent multiple quantum images simultaneously with lower time complexity. Secondly, the quantum subtractor and quantum comparator are optimized. Thirdly, quantum adder, quantum multiplier, quantum comparator, and quantum subtractor are adopted to design the quantum circuit of LoG operator and zero-crossing detector, which constitute the quantum edge detection algorithm. Finally, the algorithm is simulated on the IBM Quantum Experience (IBM Q) platform to verify its feasibility. Compared with the existing state-of-the-art algorithms, the proposed quantum image edge detection algorithm has significant improvement in time complexity.

DOI
10.1007/s11128-024-04392-z

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Abstract With the increase in the quantity and quality of images that need to be processed, there are higher requirements for the speed of image processing. Thus, it is necessary to speed-up the image processing algorithms. In this paper, we design a quantum image edge detection algorithm based on Laplacian of Gaussian (LoG) operator, which has significant acceleration due to the quantum parallelism. Firstly, the quantum circuit of the novel enhanced quantum image representation (NEQR) model is improved to represent multiple quantum images simultaneously with lower time complexity. Secondly, the quantum subtractor and quantum comparator are optimized. Thirdly, quantum adder, quantum multiplier, quantum comparator, and quantum subtractor are adopted to design the quantum circuit of LoG operator and zero-crossing detector, which constitute the quantum edge detection algorithm. Finally, the algorithm is simulated on the IBM Quantum Experience (IBM Q) platform to verify its feasibility. Compared with the existing state-of-the-art algorithms, the proposed quantum image edge detection algorithm has significant improvement in time complexity.
Quantum image processing, which is the application of quantum theory in image processing, has attracted increasing attention in recent years. In this paper, we propose a framework of Laplacian of Gaussian (LoG) edge detection algorithm for quantum images. The LoG is commonly employed as a second-order edge detector in image processing. Firstly, discrete LoG mask is obtained from the continuous Gaussian operator within certain detection error. Secondly, filter the quantum image with the LoG mask. Thirdly, to obtain the edge image, the searching for zero-crossing point of the filtered image is proposed. Finally, the time complexity is analyzed, which shows that this quantum LoG operator has polynomial-time complexity.
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 2n× 2nwhen the computational complexity is O(n2+ 2q+3). The improved algorithm can detect more edge details and has strong adaptability.
Line detection is a fundamental technique in image processing. It can extract the required information, while the information that does not need attention can be ignored, thus reducing the amount of data. At the same time, line detection is also the basis of image segmentation and plays an important role in this process. In this paper, we implement a quantum algorithm based on a line detection mask for novel enhanced quantum representation (NEQR). We build a quantum algorithm for line detection in different directions and design a quantum circuit for line detection. The detailed module designed is also provided. On a classical computer, we simulate the quantum method, and the simulation results prove the feasibility of the quantum method. By analyzing the complexity of quantum line detection, we find that the computation complexity of the proposed method is improved compared to some similar edge detection algorithms.
This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.
In this work, a quantum image processing algorithm is developed using the edge extraction method together with the Kirsch operator. In our approach, novel enhanced quantum representation (NEQR) is employed as the image representation model for processing quantum image, which generates results of edge extraction using the Kirsch operator. The proposed algorithm can perform real-time image processing with high accuracy. We carry out the design, analyses, and simulations of quantum circuits based on our approach, which shows that the image processing speed and acuracy are much better than the classical edge extraction algorithms.
In order to develop and validate the quantum image processing algorithm on quantum computer, combined with quantum computing operation on IBM quantum experiment platform (IBM Q) and quantum image processing theory, a quantum image segmentation method based on IBM Q platform was designed. An improved enhanced quantum representation (IEQR) was proposed based on the existing novel enhanced quantum representation (NEQR). The quantum image segmentation circuit, which consists of the quantum bit string comparator (QBSC) and the Controlswap (Cswap) gate, is initialized according to the IEQR. Finally, quantum image segmentation of 2×2 and 4×4 size images are realized on IBM Q and local classical computer simulator. The experimental results demonstrate the feasibility and effectiveness of the algorithm and the superiority of quantum computers is validated.