To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location ([Formula: see text], [Formula: see text]) is stored at the same location ([Formula: see text], [Formula: see text]) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.
To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location ([Formula: see text], [Formula: see text]) is stored at the same location ([Formula: see text], [Formula: see text]) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.
The dilation and erosion operations are the first fundamental step in classical image processing. They are important in many image processing algorithms to extract basic image features, such as geometric shapes; such shapes are then fed to higher level algorithms for object identification and recognition. In this paper, we present an improved quantum method to realize dilation and erosion in imaging processing. Unlike in the classical way, in the quantum version of imaging processing, all of the information is stored in quantum bits (qubits). We use qubits to code the location and other information of each pixel of the images and apply quantum operators (or quantum gates) to accomplish specific functions. Because of quantum entanglement and other nonintuitive features in quantum mechanics, qubits have many advantages over classical bits, but their nature presents challenges in designing quantum algorithms. We first built the quantum circuit theoretically, and then ran it on the IBM Quantum Experience platform to test and process real images. With this algorithm, we are looking forward to more potential applications in quantum computation.
The classical image segmentation algorithm based on grayscale morphology can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem will emerge. In order to solve this problem, a quantum image segmentation algorithm is proposed in this paper, which can use quantum mechanism to simultaneously perform morphological operations on all pixels in a grayscale image, and then quickly segment the image into a binary image. In addition, several quantum circuit units, including dilation, erosion, bottom hat transformation, top hat transformation, etc., are designed in detail, and then they are combined together to construct the complete quantum circuits for segmenting the NEQR images. For a2n×2nimage withqgrayscale levels, the complexity of our algorithm can be reduced to O(n2+q), which is an exponential speedup than the classic counterparts. Finally, the experiment is conducted on IBM Q to show the feasibility of our algorithm in the noisy intermediate-scale quantum (NISQ) era.
Abstract To further enhance the study of quantum image edge extraction algorithms, this paper proposes a color quantum image edge extraction algorithm based on an order of color vectors. The algorithm utilizes the NCQI (novel quantum representation of color digital images) model, which allows for fine processing of the color information in the image simultaneously. Our scheme extracts the edges of the color quantum image through operations such as cyclic shifts, color vectors ordering, dilation and erosion, and presents a complete quantum circuit. Finally, the complexity of the complete quantum circuit is calculated based on the quantum modules used, and simulation experimental results on classical computers are provided. Compared to all classical digital image edge extraction algorithms, our scheme can achieve exponential acceleration.
The quantum denoising technology efficiently removes noise from images; however, the existing algorithms are only effective for additive noise and cannot remove multiplicative noise, such as speckle noise in synthetic aperture radar (SAR) images. In this paper, based on the grayscale morphology method, a quantum SAR image denoising algorithm is proposed, which performs morphological operations on all pixels simultaneously to remove the noise in the SAR image. In addition, we design a feasible quantum adder to perform cyclic shift operations. Then, quantum circuits for dilation and erosion are designed, and the complete quantum circuit is then constructed. For a 2 n × 2 n quantum SAR image with q grayscale levels, the complexity of our algorithm is O ( n + q ) . Compared with classical algorithms, it achieves exponential improvement and also has polynomial-level improvements than existing quantum algorithms. Finally, the feasibility of our algorithm is validated on IBM Q.
Erosion and dilation are fundamental mathematical morphology operations used to modify the shape of objects in binary images. This study evaluated their implementation through a quantum circuit simulated in Qiskit, using classical processing in OpenCV as the reference. The Baboon image was analyzed at resolutions of 102×102, 128×128, and 256×256 pixels, with 16, 160, 1600, 16000, and 160000 circuit executions. The comparison included visual inspection, calculation of MSE, PSNR, and SSIM, and measurement of simulation times. The circuit reproduced the expected effect of both operations, although the reconstructed images did not fully match those obtained with OpenCV. Dilation showed more stable similarity than erosion. In addition, increasing the number of executions did not improve the metrics monotonically and substantially increased computation time.
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.