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.
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.
The classical image segmentation algorithm based on local adaptive threshold can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem gradually emerges. In this paper, a quantum segmentation algorithm based on local adaptive threshold for NEQR image is proposed, which can use quantum mechanism to simultaneously compute local thresholds for all pixels in a gray-scale image and quickly segment the image into a binary image. In addition, several quantum circuit units, including median calculation, quantum binarization, etc. are designed in detail, and then a complete quantum circuit is designed to segment NEQR images by using fewer qubits and quantum gates. For a [Formula: see text] image with [Formula: see text] gray-scale levels, the complexity of our algorithm can be reduced to O[Formula: see text], which is an exponential speedup compared to 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.
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.
The main goal of this paper is to present a new way of processing a video file using a combination of multiple quantum methods. The design is built upon the novel enhanced quantum representation technique, NEQR, which is then expanded using ideas such as image segmentation, implemented with the help of one or multiple comparators, binarization and cycle shift. This approach allows us to process all frames in parallel according to the desired parameters-one or more thresholds. A demonstration circuit for the proposed design, using a couple of frames, that sums together all the concepts is implemented using the Python programming language and Qiskit open-source framework, made available by IBM. The circuits are analyzed in the experimental section, using the Simulator component and configured using the noise properties of real devices, where we present different relevant metrics obtained by processing the simulation results.
Abstract The intrinsic high parallelism and entanglement characteristics of quantum computing have made quantum image processing techniques a focus of great interest. One of the most widely used techniques in image processing is segmentation, which in one of their most basic forms can be carried out using thresholding algorithms. In this paper, a fault-tolerant quantum dual-threshold algorithm has been proposed. This algorithm is based on Clifford+T gates. Because T gates add fault tolerance but have the trade-off of having a much higher cost than other quantum gates,our focus has been on reducing the number of T gates. This has allowed adding noise tolerance, computational cost reduction and fault toleranceto the state-of-the-art dual-threshold segmentation circuits. Sincethe dual-threshold image segmentation involves the comparison operation,as part of this work we have implemented two comparator circuits.These circuits optimise the metrics T-count and T-depth with respect to the best circuit comparators currently available in the literature.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
Quantum image processing represents a transformative approach to visual data analysis, leveraging the principles of quantum computing to overcome classical limitations. This work explores two prominent quantum image encoding methods: FRQI (Flexible Representation of Quantum Images) and NEQR (Novel Enhanced Quantum Representation). FRQI excels in qubit efficiency, making it suitable for hardware implementation, while NEQR offers superior precision in pixel intensity representation, ideal for complex image processing tasks. We detail the implementation of these algorithms, including preprocessing, quantum circuit design, and simulation, using platforms like Qiskit. The study highlights the potential of quantum image processing in fields such as medicine, industry, and environmental monitoring, while addressing challenges like qubit limitations and noise sensitivity. This research contributes to advancing quantum computing applications, paving the way for innovative and sustainable technological solutions.