In the rapidly advancing field of image analysis and processing, accurately segmenting images into meaningful regions remains a critical challenge. Drawing from recent advancements in quantum computing and information theory, our research introduces an innovative approach to image segmentation. This work presents a novel multilevel segmentation method that utilizes a two-dimensional quantum image representation, offering a more sophisticated and efficient technique for image thresholding. In this framework, the image's 2D histogram is treated as a quantum system, with quantum Rényi entropy used to quantify the information contained within the image. To enhance segmentation quality, we first improve the contrast of the images by applying a new contrast enhancement algorithm before performing the segmentation. The resulting entropy-based fitness function is then optimized using Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to determine the optimal thresholding values. A comprehensive comparative analysis is conducted between the proposed quantum method and traditional classical approaches, evaluated on a set of benchmark images using nine metrics, including the Wilcoxon test for statistical significance. Experimental results demonstrate the effectiveness of the PSO optimizer, the superiority of the two-dimensional quantum image representation.
In the rapidly advancing field of image analysis and processing, accurately segmenting images into meaningful regions remains a critical challenge. Drawing from recent advancements in quantum computing and information theory, our research introduces an innovative approach to image segmentation. This work presents a novel multilevel segmentation method that utilizes a two-dimensional quantum image representation, offering a more sophisticated and efficient technique for image thresholding. In this framework, the image's 2D histogram is treated as a quantum system, with quantum Rényi entropy used to quantify the information contained within the image. To enhance segmentation quality, we first improve the contrast of the images by applying a new contrast enhancement algorithm before performing the segmentation. The resulting entropy-based fitness function is then optimized using Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to determine the optimal thresholding values. A comprehensive comparative analysis is conducted between the proposed quantum method and traditional classical approaches, evaluated on a set of benchmark images using nine metrics, including the Wilcoxon test for statistical significance. Experimental results demonstrate the effectiveness of the PSO optimizer, the superiority of the two-dimensional quantum image representation.
Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, respectively. Then, the method based on global quantum entropy maximization (GQEM) is proposed, which has an equivalent object function to Otsu's, but gives a more explicit physical interpretation of image thresholding in the language of quantum mechanics. To reduce the time consumption for searching for optimal thresholds, the method of quantum lossy-encoding-based entropy maximization (QLEEM) is presented, in which the eigenvalues of density matrices can give direct clues for thresholding, and then, the process of optimal searching can be avoided. Meanwhile, the QLEEM algorithm achieves two additional effects: (1) the upper bound of the thresholding level can be implicitly determined according to the eigenvalues; and (2) the proposed approaches ensure that the local information in images is retained as much as possible, and simultaneously, the inter-class separability is maximized in the segmented images. Both of them contribute to the structural characteristics of images, which the human visual system is highly adapted to extract. Experimental results show that the proposed methods are able to achieve a competitive quality of thresholding and the fastest computation speed compared with the state-of-the-art methods.
Image segmentation is a fundamental operation in computer vision, used to partition an image into meaningful regions according to various attributes or spatial relationships among pixels. This paper presents a novel quantum circuit for two-threshold image segmentation implemented in the Novel Enhanced Quantum Representation (NEQR) format. Threshold-based segmentation is particularly attractive for quantum implementation due to its conceptual simplicity and inherent parallelism, but existing approaches suffer from a critical correctness issue: quantum RESET operations are applied to auxiliary qubits that may become entangled with the image data register during the segmentation process. We demonstrate, both theoretically and experimentally, that such RESET operations implicitly perform a measurement that collapses the superposition of the entangled quantum state, leading to non-reproducible segmentation results across repeated executions. To address this limitation, we propose a seven-step quantum segmentation pipeline that explicitly preserves entanglement integrity by allocating dedicated auxiliary qubits for each comparison stage, thereby eliminating unsafe qubit reuse. The proposed circuit encodes pixel intensities using the NEQR representation, applies upper and lower threshold comparators in sequence, and integrates both comparison outcomes to classify pixels into three intensity regions. Experiments conducted on a Qiskit StatevectorSimulator demonstrate that the proposed design produces stable and reproducible segmentation results across all test images, in contrast to the inconsistent behaviour observed in prior work. For images requiring 33 qubits, simulations consumed up to 128 GB of RAM with a total execution time of approximately 27 h on an Intel® Xeon® Gold 6240 CPU @ 2.60 GHz. The proposed approach establishes a robust foundation for quantum image segmentation on future fault-tolerant hardware.
Abstract Image segmentation remains one of the most extensively studied problems in computer vision, with applications ranging from medical image analysis and autonomous driving to remote sensing and industrial inspection. While deep learning approaches currently dominate the field, interest in quantum computing has motivated the development of quantum and quantum-inspired segmentation techniques that explore alternative strategies for image representation, optimization, and learning. This survey provides a comprehensive review of quantum and quantum-inspired image segmentation methods within the broader context of modern segmentation research. To establish this context, we first examine the evolution of image segmentation methodologies, covering classical image processing techniques, machine learning approaches, and contemporary deep learning architectures.We then organize the existing quantum image segmentation literature into four categories: quantum-inspired, tensor network-based, hybrid quantum-classical, and fully quantum methods. Across these categories, we analyze computational principles, image encoding and representation strategies, application domains, and datasets. We further compare quantum and quantum-inspired approaches with established segmentation paradigms in terms of supervision, scalability, and hardware requirements. Our analysis indicates that quantum-inspired methods currently represent the most developed direction, while hybrid approaches are emerging and fully quantum methods remain constrained by quantum hardware, data encoding costs, and scalability challenges. By connecting quantum image segmentation with the broader evolution of segmentation research, this survey provides a unified perspective on the field. It identifies current trends, open challenges, and promising future directions for researchers exploring the emerging role of quantum computing in image segmentation.
Breast cancer remains the leading cause of cancer-related mortality among women worldwide, necessitating the meticulous examination of mammograms by radiologists to characterize abnormal lesions. This manual process demands high accuracy and is often time-consuming, costly, and error-prone. Automated image segmentation using artificial intelligence offers a promising alternative to streamline this workflow. However, most existing methods are supervised, requiring large, expertly annotated datasets that are not always available, and they experience significant generalization issues. Thus, unsupervised learning models can be leveraged for image segmentation, but they come at a cost of reduced accuracy, or require extensive computational resourcess. In this paper, we propose the first end-to-end quantum-enhanced framework for unsupervised mammography medical images segmentation that balances between performance accuracy and computational requirements. We first introduce a quantum-inspired image representation that serves as an initial approximation of the segmentation mask. The segmentation task is then formulated as a QUBO problem, aiming to maximize the contrast between the background and the tumor region while ensuring a cohesive segmentation mask with minimal connected components. We conduct an extensive evaluation of quantum and quantum-inspired methods for image segmentation, demonstrating that quantum annealing and variational quantum circuits achieve performance comparable to classical optimization techniques. Notably, quantum annealing is shown to be an order of magnitude faster than the classical optimization method in our experiments. Our findings demonstrate that this framework achieves performance comparable to state-of-the-art supervised methods, including UNet-based architectures, offering a viable unsupervised alternative for breast cancer image segmentation.
Quantum algorithms have emerged as a transformative approach to address the computational challenges of high-dimensional image processing tasks. This research investigates the integration of quantum computing principles, such as Quantum Fourier Transform (QFT) and Quantum Principal Component Analysis (QPCA), to optimize processes like edge detection, noise reduction, and image segmentation. These quantum-enhanced techniques promise significant improvements in computational efficiency and accuracy compared to classical methods, especially when handling complex visual data in real-time applications like medical imaging, satellite imagery, and autonomous systems. Additionally, the study explores hybrid quantum-classical architectures to bridge current limitations in noisy intermediate-scale quantum (NISQ) devices, ensuring resource optimization and scalability. The potential of quantum algorithms to provide faster, more precise solutions is evaluated alongside challenges like error mitigation and algorithmic stability. This research highlights the future role of quantum computing in revolutionizing image processing, paving the way for breakthroughs in computer vision and artificial intelligence.
We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image. The core idea of this scheme is to embed information into object and background of cover image in different ways. First, a threshold method adopting the quantum informational entropy is employed to determine a threshold value. The threshold value can then be further used for segmenting the cover image to a binary image, which is an authentication key for embedding and extraction information. By a careful analysis of the quantum circuits of the scheme, that is, translating into the basic gate sequences which show the low complexity of the scheme. One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image. Furthermore, the analyses of peak signal-to-noise ratio, histogram and capacity of the scheme are also provided.