pith. sign in

arxiv: 2605.00744 · v1 · submitted 2026-05-01 · 💻 cs.CV · eess.IV

Quantum Gradient-Based Approach for Edge and Corner Detection Using Sobel Kernels

Mohammad Aamir Sohail , Gabriela Pinheiro , Yasemin Poyraz Kocak , Batuhan Hangun , Emre Camkerten , Simge Yigit , Hafize Asude Ertan This is my paper

Pith reviewed 2026-05-09 19:14 UTC · model grok-4.3

classification 💻 cs.CV eess.IV
keywords edge detectioncorner detectionquantum image encodingSobel operatorHarris detectorFRQIQPIEquantum computing
0
0 comments X

The pith

Quantum circuits using lag-2 gradients and QPIE encoding reproduce classical Sobel edge and Harris corner detection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents quantum implementations of Sobel-based edge detection and Harris-style corner detection. It uses FRQI and QPIE to encode images and computes gradients via a lag-2 difference scheme in quantum circuits. The outputs match classical results, with QPIE providing more stable detections especially with limited measurements. Classical post-processing refines the corner candidates. The work shows a functional quantum approach to these tasks in simulation, though costs are dominated by preparation and measurement rather than offering speedup.

Core claim

The proposed quantum circuits, employing a lag-2 difference scheme for gradient computation in superposition along with FRQI or QPIE encodings, generate edge and corner detections that align with those from classical Sobel and Harris operators. The QPIE configuration demonstrates greater stability and coherence compared to FRQI, particularly when measurement shots are limited. Although gradient evaluation occurs efficiently at the circuit level, the overall process is governed by state preparation, measurement, and post-processing steps.

What carries the argument

The lag-2 difference quantum gradient scheme, which computes gradient-like features directly in quantum superposition for use in edge and corner detection.

If this is right

  • The quantum approach yields outputs consistent with classical Sobel and Harris operators.
  • QPIE-based encoding produces more stable and coherent results than FRQI under limited measurement shots.
  • A classical post-processing step improves detection quality by reducing false positives in corner identification.
  • Gradient computation can be performed efficiently within the quantum circuit.
  • The method functions as a scalable quantum realization of classical detection techniques in noiseless simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Quantum image processing techniques like this may scale to other feature extraction tasks if similar superposition-based computations are designed.
  • Real hardware implementation would need to account for noise effects not present in the simulations.
  • Hybrid methods combining quantum gradient computation with classical refinement could be practical on near-term devices.
  • Optimizing state preparation could unlock potential advantages beyond current classical post-processing dominance.

Load-bearing premise

The lag-2 difference quantum gradient scheme, when used with FRQI or QPIE, accurately reproduces the essential behavior of classical Sobel kernels and Harris measures without losing key image information.

What would settle it

Comparing the quantum circuit outputs, after measurement and post-processing, to classical Sobel and Harris results on a set of test images with known edges and corners; any systematic deviation in detected features would falsify the consistency claim.

read the original abstract

Edge detection refers to identifying points in a digital image where intensity changes sharply, indicating object boundaries or structural features. Corners are locations where gray-level intensity changes abruptly in multiple directions and are widely used in feature extraction, object tracking, and 3D modeling. In this study, we present a quantum implementation of Sobel-based edge detection and Harris-style corner detection. Two quantum image encoding methods - Flexible Representation of Quantum Images (FRQI) and Quantum Probability Image Encoding (QPIE) - are used to encode the input data and are comparatively analyzed. The proposed approach introduces a quantum gradient computation scheme based on lag-2 differences, enabling the evaluation of gradient-like features in superposition. To improve detection quality and reduce false positives, a classical post-processing step is applied to candidate corner points identified by the quantum circuit. Results show that the proposed quantum circuits produce outputs consistent with classical Sobel and Harris operators. Furthermore, the QPIE-based configuration yields more stable and coherent results than FRQI, especially under limited measurement shots. While gradient computation can be performed efficiently at the circuit level, the overall cost remains dominated by state preparation, measurement, and classical post-processing. All experiments are conducted under noiseless simulation, and performance on NISQ hardware may be affected by noise and measurement limitations. Therefore, this work demonstrates a functional and scalable quantum realization of classical edge and corner detection methods rather than an end-to-end speedup.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a quantum implementation of Sobel-based edge detection and Harris-style corner detection. It encodes images via FRQI or QPIE, computes gradients using a lag-2 finite-difference scheme applied in superposition, and applies classical post-processing to candidate corners. Experiments are performed in noiseless simulation; the central claim is that the quantum outputs are consistent with classical Sobel and Harris operators, with QPIE yielding more stable results than FRQI under limited measurement shots. No end-to-end quantum speedup is claimed; state preparation and measurement dominate the cost.

Significance. If the consistency between the quantum lag-2 gradient scheme and classical Sobel/Harris operators is rigorously established, the work supplies a concrete, reproducible demonstration of a classical image-processing primitive on quantum circuits. The FRQI-vs-QPIE comparison under shot-limited conditions offers practical guidance for encoding choices. The absence of a claimed quantum advantage or asymptotic speedup, together with the dominance of classical post-processing, positions the contribution as foundational rather than immediately transformative for quantum computer vision.

major comments (2)
  1. [Abstract / §3] Abstract and §3 (gradient scheme): The claim that the lag-2 difference operator, when applied after FRQI or QPIE encoding, produces outputs consistent with the classical Sobel kernel rests on an unproven numerical equivalence. Sobel kernels combine central differences with perpendicular smoothing weights; a pure lag-2 difference omits this smoothing, so edge strength and localization can differ even before measurement noise or normalization artifacts from the encodings are considered. An explicit derivation or side-by-side pixel-wise comparison (e.g., via an equation relating the quantum operator to the 3×3 Sobel mask) is required to support the consistency result.
  2. [Abstract / Results] Abstract and results section: No quantitative metrics, error bars, correlation coefficients, or circuit diagrams are supplied to substantiate the consistency claim. Statements such as “outputs consistent with classical Sobel and Harris operators” and “QPIE yields more stable results” remain qualitative; tables reporting, for example, mean absolute deviation per edge pixel or corner localization error across shot counts would be needed to make the claim load-bearing.
minor comments (2)
  1. [Introduction] Ensure all acronyms (FRQI, QPIE, NISQ) are defined at first use and that the manuscript cites the original FRQI and QPIE references.
  2. [Method] Clarify whether the classical post-processing step is applied identically to both quantum and classical pipelines; any asymmetry could affect the fairness of the consistency comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our quantum implementation of edge and corner detection. We address each major comment below and will revise the manuscript to strengthen the claims with additional derivations, comparisons, and quantitative metrics.

read point-by-point responses

  1. Referee: [Abstract / §3] Abstract and §3 (gradient scheme): The claim that the lag-2 difference operator, when applied after FRQI or QPIE encoding, produces outputs consistent with the classical Sobel kernel rests on an unproven numerical equivalence. Sobel kernels combine central differences with perpendicular smoothing weights; a pure lag-2 difference omits this smoothing, so edge strength and localization can differ even before measurement noise or normalization artifacts from the encodings are considered. An explicit derivation or side-by-side pixel-wise comparison (e.g., via an equation relating the quantum operator to the 3×3 Sobel mask) is required to support the consistency result.

    Authors: We acknowledge the distinction: the lag-2 finite-difference scheme was selected for its efficient superposition implementation on quantum circuits, but it lacks the perpendicular smoothing present in the standard Sobel kernel. The manuscript's consistency claim is currently supported by empirical results in noiseless simulations rather than a formal equivalence proof. In the revision, we will add an explicit derivation relating the quantum lag-2 operator to the 3×3 Sobel mask (including the smoothing weights) and provide side-by-side pixel-wise numerical comparisons on standard test images to quantify any differences in edge strength and localization. revision: yes

  2. Referee: [Abstract / Results] Abstract and results section: No quantitative metrics, error bars, correlation coefficients, or circuit diagrams are supplied to substantiate the consistency claim. Statements such as “outputs consistent with classical Sobel and Harris operators” and “QPIE yields more stable results” remain qualitative; tables reporting, for example, mean absolute deviation per edge pixel or corner localization error across shot counts would be needed to make the claim load-bearing.

    Authors: We agree that the current results section relies primarily on qualitative descriptions. To make the consistency and stability claims rigorous, the revised manuscript will include quantitative tables reporting mean absolute deviation per edge pixel, Pearson correlation coefficients between quantum and classical outputs, corner localization errors, and error bars across varying shot counts for both FRQI and QPIE. Circuit diagrams for the gradient computation and post-processing steps will also be added. revision: yes

Circularity Check

0 steps flagged

No circularity: direct comparison of quantum circuits to classical Sobel/Harris without fitted predictions or self-referential definitions

full rationale

The paper implements quantum edge/corner detection via FRQI/QPIE encodings and a lag-2 difference gradient, then verifies consistency by direct simulation against classical Sobel and Harris operators. No parameters are fitted on a data subset and renamed as predictions; no self-citations justify core claims; the lag-2 scheme is presented as an explicit quantum approximation rather than derived from the target result itself. The derivation chain is self-contained as an empirical demonstration of functional equivalence under noiseless simulation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum computing assumptions plus the paper-specific choice of lag-2 differences as a gradient proxy; no free parameters or new physical entities are introduced.

axioms (2)
  • domain assumption Quantum states prepared via FRQI or QPIE can faithfully represent classical image intensity values for subsequent gradient operations
    Invoked when encoding the input image before applying the quantum circuit.
  • ad hoc to paper Lag-2 finite differences computed in superposition yield gradient-like features equivalent to the classical Sobel operator
    This is the core proposed scheme for quantum gradient computation.

pith-pipeline@v0.9.0 · 5583 in / 1539 out tokens · 65875 ms · 2026-05-09T19:14:28.555892+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages

  1. [1]

    Pearson Prentice Hall, Upper Saddle River, NJ (2008)

    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Pearson Prentice Hall, Upper Saddle River, NJ (2008)

    work page 2008

  2. [2]

    Quantum Information Processing22(8) (2023) https://doi.org/10.1007/ s11128-023-04047-5

    Yuan, S., Lin, W., Hang, B., Meng, H.: Quantum fast corner detection algo- rithm. Quantum Information Processing22(8) (2023) https://doi.org/10.1007/ s11128-023-04047-5

    work page 2023

  3. [3]

    In: Proceedings of Informing Science & IT Education Conference (InSITE), vol

    Vincent, O.R., Folorunso, O.,et al.: A descriptive algorithm for sobel image edge detection. In: Proceedings of Informing Science & IT Education Conference (InSITE), vol. 40, pp. 97–107 (2009)

    work page 2009

  4. [4]

    In: 2011 4th International Congress on Image and Signal Processing, vol

    Yang, L., Wu, X., Zhao, D., Li, H., Zhai, J.: An improved prewitt algorithm for edge detection based on noised image. In: 2011 4th International Congress on Image and Signal Processing, vol. 3, pp. 1197–1200 (2011). IEEE

    work page 2011

  5. [5]

    Canny, ‘A Computational Approach to Edge Detection’, IEEE Trans

    Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine IntelligencePAMI-8(6), 679–698 (1986) https: //doi.org/10.1109/TPAMI.1986.4767851 30

    work page doi:10.1109/tpami.1986.4767851 1986

  6. [6]

    Computer-Aided Civil and Infrastructure Engineering37(3), 354–369 (2022)

    Xu, B., Liu, C.: A 3d reconstruction method for buildings based on monocu- lar vision. Computer-Aided Civil and Infrastructure Engineering37(3), 354–369 (2022)

    work page 2022

  7. [7]

    International Journal of Remote Sensing43(12), 4477–4516 (2022)

    Misra, I., Rohil, M.K., Manthira Moorthi, S., Dhar, D.: Feature based remote sensing image registration techniques: a comprehensive and comparative review. International Journal of Remote Sensing43(12), 4477–4516 (2022)

    work page 2022

  8. [8]

    Journal of emerging technologies and innovative research (2017)

    Bisen, V.: Image mosaicing using harris corner detection for medical applications. Journal of emerging technologies and innovative research (2017)

    work page 2017

  9. [9]

    In: Journal of Physics: Conference Series, vol

    Abbadi, N.K.E., Al Hassani, S.A., Abdulkhaleq, A.H.: A review over panoramic image stitching techniques. In: Journal of Physics: Conference Series, vol. 1999, p. 012115 (2021). IOP Publishing

    work page 1999

  10. [10]

    IET Image Processing18(6), 1385–1410 (2024)

    Huang, Q., Guo, X., Wang, Y., Sun, H., Yang, L.: A survey of feature matching methods. IET Image Processing18(6), 1385–1410 (2024)

    work page 2024

  11. [11]

    International Journal of computer vision37(2), 151–172 (2000)

    Schmid, C., Mohr, R., Bauckhage, C.: Evaluation of interest point detectors. International Journal of computer vision37(2), 151–172 (2000)

    work page 2000

  12. [12]

    ACM Transactions on Quantum Computing6(1) (2025) https://doi

    Yan, F., Venegas-Andraca, S.E.: Lessons from twenty years of quantum image processing. ACM Transactions on Quantum Computing6(1) (2025) https://doi. org/10.1145/3663577

    work page doi:10.1145/3663577 2025

  13. [13]

    International Journal of Information Technology 14(1), 475–489 (2022) https://doi.org/10.1007/s41870-018-0227-8

    Chakraborty, S., Mandal, S.B., Shaikh, S.H.: Quantum image processing: chal- lenges and future research issues. International Journal of Information Technology 14(1), 475–489 (2022) https://doi.org/10.1007/s41870-018-0227-8

    work page doi:10.1007/s41870-018-0227-8 2022

  14. [14]

    Computer Science Review 57, 100763 (2025) https://doi.org/10.1016/j.cosrev.2025.100763

    Farooq, U., Singh, P., Kumar, A.: A systematic review of quantum image pro- cessing: Representation, applications and future perspectives. Computer Science Review57, 100763 (2025) https://doi.org/10.1016/j.cosrev.2025.100763

    work page doi:10.1016/j.cosrev.2025.100763 2025

  15. [15]

    Physical Review X7(3) (2017) https://doi.org/10.1103/physrevx.7.031041

    Yao, X.-W., Wang, H., Liao, Z., Chen, M.-C., Pan, J., Li, J., Zhang, K., Lin, X., Wang, Z., Luo, Z., Zheng, W., Li, J., Zhao, M., Peng, X., Suter, D.: Quantum image processing and its application to edge detection: Theory and experiment. Physical Review X7(3) (2017) https://doi.org/10.1103/physrevx.7.031041

    work page doi:10.1103/physrevx.7.031041 2017

  16. [16]

    https://arxiv.org/abs/2203.12072

    Geng, A., Moghiseh, A., Redenbach, C., Schladitz, K.: A hybrid quantum image edge detector for the NISQ era (2022). https://arxiv.org/abs/2203.12072

    work page arXiv 2022

  17. [17]

    Computers13(8) (2024) https://doi.org/10.3390/ computers13080185

    Deb, S.K., Pan, W.D.: Quantum image compression: Fundamentals, algo- rithms, and advances. Computers13(8) (2024) https://doi.org/10.3390/ computers13080185

    work page 2024

  18. [18]

    31 Journal of Artificial Intelligence, Applications and Innovations1(2), 9–25 (2024)

    Ebrahimpour-Komleh, H., Hadipour, A.: Quantum computing in image process- ing: A comprehensive survey of applications, challenges, and future directions. 31 Journal of Artificial Intelligence, Applications and Innovations1(2), 9–25 (2024)

    work page 2024

  19. [19]

    Quantum Information Processing 23(8), 302 (2024) https://doi.org/10.1007/s11128-024-04513-8

    Wang, G., Zhao, W., Zou, P., Wang, J., Yin, H., Yu, Y.: Quantum image edge detection based on haar wavelet transform. Quantum Information Processing 23(8), 302 (2024) https://doi.org/10.1007/s11128-024-04513-8

    work page doi:10.1007/s11128-024-04513-8 2024

  20. [20]

    In: 4th Alvey Vision Conference, vol

    Harris, C., Stephens, M.,et al.: A combined corner and edge detector. In: 4th Alvey Vision Conference, vol. 15 (1988). Citeseer. https://api.semanticscholar. org/CorpusID:1694378

    work page 1988

  21. [21]

    Multimedia Tools and Applications83(8), 23173–23199 (2024) https://doi.org/10.1007/ s11042-023-16428-0

    Lav´ ın-Delgado, J.E., G´ omez-Aguilar, J.F., Urueta-Hinojosa, D.E., Zamudio- Beltr´ an, Z., Alan´ ıs-Navarro, J.A.: An efficient technique for object recogni- tion using fractional harris–stephens corner detection algorithm. Multimedia Tools and Applications83(8), 23173–23199 (2024) https://doi.org/10.1007/ s11042-023-16428-0

    work page 2024

  22. [22]

    IEEE Signal Processing Letters30, 50–54 (2023) https://doi.org/10.1109/LSP.2023.3240371

    Sun, X., Zhong, B., Yang, J., Ma, K.-K.: Corner detection via scale-space behavior-guided trajectory tracing. IEEE Signal Processing Letters30, 50–54 (2023) https://doi.org/10.1109/LSP.2023.3240371

    work page doi:10.1109/lsp.2023.3240371 2023

  23. [23]

    Quantum Information Processing10, 63–84 (2011)

    Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Information Processing10, 63–84 (2011)

    work page 2011

  24. [24]

    Burbi, A

    Soria, X., Li, Y., Rouhani, M., Sappa, A.D.: Tiny and efficient model for the edge detection generalization. In: 2023 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW), pp. 1356–1365 (2023). https://doi.org/ 10.1109/ICCVW60793.2023.00147

    work page doi:10.1109/iccvw60793.2023.00147 2023

  25. [25]

    Sensors25(7), 2031 (2025)

    Feng, Z., Shi, R., Jiang, Y., Han, Y., Ma, Z., Ren, Y.: A multiscale gradient fusion method for color image edge detection using cbm3d filtering. Sensors25(7), 2031 (2025)

    work page 2031

  26. [26]

    International Journal of Artificial Intelligence & Robotics (IJAIR)6(1), 29–39 (2024)

    Zangana, H.M., Mohammed, A.K., Mustafa, F.M.: Advancements in edge detec- tion techniques for image enhancement: A comprehensive review. International Journal of Artificial Intelligence & Robotics (IJAIR)6(1), 29–39 (2024)

    work page 2024

  27. [27]

    In: Journal of Physics: Conference Series, vol

    Hennig, M., Mertsching, B.: Box filtering for real-time curvature scale-space com- putation. In: Journal of Physics: Conference Series, vol. 1958, p. 012020 (2021). IOP Publishing

    work page 1958

  28. [28]

    The Visual Computer39(2022) https://doi.org/10.1007/s00371-022-02474-6

    Wan, C., Cao, J., Wei, X., Huang, J., Chen, Z., Xu, D., Qiu, F.: Ipcs: An improved corner detector with intensity, pattern, curvature, and scale. The Visual Computer39(2022) https://doi.org/10.1007/s00371-022-02474-6

    work page doi:10.1007/s00371-022-02474-6 2022

  29. [29]

    Expert Systems with 32 Applications211, 118673 (2023) https://doi.org/10.1016/j.eswa.2022.118673

    Jing, J., Liu, C., Zhang, W., Gao, Y., Sun, C.: Ecfrnet: Effective corner fea- ture representations network for image corner detection. Expert Systems with 32 Applications211, 118673 (2023) https://doi.org/10.1016/j.eswa.2022.118673

    work page doi:10.1016/j.eswa.2022.118673 2023

  30. [30]

    Quantum Information Processing22(2), 104 (2023)

    Geng, A., Moghiseh, A., Redenbach, C., Schladitz, K.: Improved frqi on super- conducting processors and its restrictions in the nisq era. Quantum Information Processing22(2), 104 (2023)

    work page 2023

  31. [31]

    Quantum information processing12, 2833–2860 (2013) https://doi.org/10.1007/s11128-013-0567-z

    Zhang, Y., Lu, K., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum represen- tation of digital images. Quantum information processing12, 2833–2860 (2013) https://doi.org/10.1007/s11128-013-0567-z

    work page doi:10.1007/s11128-013-0567-z 2013

  32. [32]

    Quantum Information Pro- cessing14(5), 1647–1673 (2015)

    Mastriani, M.: Quantum boolean image denoising. Quantum Information Pro- cessing14(5), 1647–1673 (2015)

    work page 2015

  33. [33]

    Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.: An rgb multi-channel represen- tation for images on quantum computers. J. Adv. Comput. Intell. Intell. Inform 17(3) (2013)

    work page 2013

  34. [34]

    In: 2012 16th International Conference on System Theory, Control and Computing (ICSTCC), pp

    Caraiman, S., Manta, V.: Image processing using quantum computing. In: 2012 16th International Conference on System Theory, Control and Computing (ICSTCC), pp. 1–6 (2012). IEEE

    work page 2012

  35. [35]

    Quantum information processing12, 3103–3126 (2013)

    Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum information processing12, 3103–3126 (2013)

    work page 2013

  36. [36]

    Quantum Information Processing13, 1353–1379 (2014)

    Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: Sqr: a simple quantum representation of infrared images. Quantum Information Processing13, 1353–1379 (2014)

    work page 2014

  37. [37]

    Quantum information processing12(6), 2269–2290 (2013)

    Li, H.-S., Qingxin, Z., Lan, S., Shen, C.-Y., Zhou, R., Mo, J.: Image stor- age, retrieval, compression and segmentation in a quantum system. Quantum information processing12(6), 2269–2290 (2013)

    work page 2013

  38. [38]

    Quantum Information Processing13, 991–1011 (2014)

    Li, H.-S., Zhu, Q., Zhou, R.-G., Song, L., Yang, X.-j.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Information Processing13, 991–1011 (2014)

    work page 2014

  39. [39]

    Journal of Cyber Security and Mobility, 757–784 (2023)

    Zhou, X., He, J.: Quantum image encryption algorithm incorporating bit-plane color representation and real ket model. Journal of Cyber Security and Mobility, 757–784 (2023)

    work page 2023

  40. [40]

    EPJ Quantum Technology11(1), 28 (2024) https://doi.org/10.1140/epjqt/s40507-024-00241-1

    Hu, Y., Lu, D., Zhang, Q., Xu, M.: Quantum image representations based on density matrices in open quantum systems. EPJ Quantum Technology11(1), 28 (2024) https://doi.org/10.1140/epjqt/s40507-024-00241-1

    work page doi:10.1140/epjqt/s40507-024-00241-1 2024

  41. [41]

    Quantum Information Processing23(8), 288 (2024) https://doi.org/10.1007/s11128-024-04484-w 33

    Taheri Monfared, A., Ciriani, V., Haghparast, M.: Qutrit representation of quantum images: new quantum ternary circuit design. Quantum Information Processing23(8), 288 (2024) https://doi.org/10.1007/s11128-024-04484-w 33

    work page doi:10.1007/s11128-024-04484-w 2024

  42. [42]

    Scientific Reports 11(1), 13879 (2021) https://doi.org/10.1038/s41598-021-93471-7

    Su, J., Guo, X., Liu, C., Lu, S., Li, L.: An improved novel quantum image repre- sentation and its experimental test on ibm quantum experience. Scientific Reports 11(1), 13879 (2021) https://doi.org/10.1038/s41598-021-93471-7

    work page doi:10.1038/s41598-021-93471-7 2021

  43. [43]

    Scientific Reports 15(1), 40286 (2025) https://doi.org/10.1038/s41598-025-24168-4

    Alwan, N.A., Obaiys, S.J., Al-Saidi, N.M.G., Noor, N.F.B.M., Karaca, Y.: Multilayered quantum computing and simulation system for enhanced image rep- resentation of hsi based fourier transform and adjacency matrix. Scientific Reports 15(1), 40286 (2025) https://doi.org/10.1038/s41598-025-24168-4

    work page doi:10.1038/s41598-025-24168-4 2025

  44. [44]

    Minzhe Xu: Review of quantum image processing

    Zhaobin Wang, Y.Z. Minzhe Xu: Review of quantum image processing. Archives of Computational Methods in Engineering29(2020) https://doi.org/10.1007/ s11831-021-09599-2

    work page 2020

  45. [45]

    Quantum Information Processing23(5), 178 (2024) https://doi.org/10.1007/s11128-024-04392-z

    Yuan, S., Zhao, W., Deng, J.D., Xia, S., Li, X.: Quantum image edge detection based on laplacian of gaussian operator. Quantum Information Processing23(5), 178 (2024) https://doi.org/10.1007/s11128-024-04392-z

    work page doi:10.1007/s11128-024-04392-z 2024

  46. [46]

    IETE Journal of Research70(5), 5348–5363 (2024) https://doi.org/10

    Chetia, R., Sahu, P.P.: Quantum image edge extraction algorithm for noisy image. IETE Journal of Research70(5), 5348–5363 (2024) https://doi.org/10. 1080/03772063.2023.2248950 https://doi.org/10.1080/03772063.2023.2248950

    work page doi:10.1080/03772063.2023.2248950 2024

  47. [47]

    Quantum Information Processing22(1), 46 (2023) https://doi.org/10

    Fan, P., Xiao, K.: Quantum image edge extraction based on difference of gaussian operator. Quantum Information Processing22(1), 46 (2023) https://doi.org/10. 1007/s11128-022-03762-9

    work page 2023

  48. [48]

    International Journal Of Computational Intelligence Systems18(1) (2025) https://doi.org/10

    Nandal, P., Pahal, S., Upadhyay, G.M.: Image denoising using quantum deep convolutional generative adversarial network for medical images. International Journal Of Computational Intelligence Systems18(1) (2025) https://doi.org/10. 1007/s44196-025-00920-6

    work page 2025

  49. [49]

    iScience27(5), 109627 (2024) https://doi.org/10.1016/j.isci.2024.109627

    Wang, L., Liu, Y., Meng, F., Luan, T., Liu, W., Zhang, Z., Yu, X.: A quantum syn- thetic aperture radar image denoising algorithm based on grayscale morphology. iScience27(5), 109627 (2024) https://doi.org/10.1016/j.isci.2024.109627

    work page doi:10.1016/j.isci.2024.109627 2024

  50. [50]

    Advanced Quantum Technologies6(12), 2300248 (2023) https: //doi.org/10.1002/qute.202300248

    Liu, W., Wang, L., Wu, Q.: A quantum moving target segmentation algorithm for grayscale video. Advanced Quantum Technologies6(12), 2300248 (2023) https: //doi.org/10.1002/qute.202300248

    work page doi:10.1002/qute.202300248 2023

  51. [51]

    Kaltenbaek, M

    Wang, L., Liu, Y., Meng, F., Liu, W., Zhang, Z., Yu, X.: A quantum moving target segmentation algorithm for grayscale video based on background difference method. EPJ Quantum Technology11(1) (2024) https://doi.org/10.1140/epjqt/ s40507-024-00234-0

    work page doi:10.1140/epjqt/ 2024

  52. [52]

    Edge detection quantumized: A novel quantum algorithm for image processing,

    Shubha, S.E.U., Islam, M.M., Sadi, T.A., Miraz, M.H.H., Mahdy, M.R.C.: Edge Detection Quantumized: A Novel Quantum Algorithm For Image Processing (2024). https://arxiv.org/abs/2404.06889 34

    work page arXiv 2024

  53. [53]

    Quantum Information Processing18, 1–19 (2019)

    Khan, R.A.: An improved flexible representation of quantum images. Quantum Information Processing18, 1–19 (2019)

    work page 2019

  54. [54]

    In: Quantum Computing and Quantum Communications: First NASA International Conference, QCQC’98 Palm Springs, California, USA February 17–20, 1998 Selected Papers, pp

    Fijany, A., Williams, C.P.: Quantum wavelet transforms: Fast algorithms and complete circuits. In: Quantum Computing and Quantum Communications: First NASA International Conference, QCQC’98 Palm Springs, California, USA February 17–20, 1998 Selected Papers, pp. 10–33 (1999). Springer

    work page 1998

  55. [55]

    Stanford University, Stanford, CA, USA (1980)

    Moravec, H.P.: Obstacle Avoidance and Navigation in the Real World by a Seeing Robot Rover. Stanford University, Stanford, CA, USA (1980)

    work page 1980

  56. [56]

    Image and vision computing 16(2), 75–87 (1998)

    Trajkovi´ c, M., Hedley, M.: Fast corner detection. Image and vision computing 16(2), 75–87 (1998)

    work page 1998

  57. [57]

    https://www.ibm.com/quantum/qiskit

    IBM: Qiskit Library. https://www.ibm.com/quantum/qiskit. Accessed: 01 Oct 2024

    work page 2024

  58. [58]

    https://github.com/yangzhangcv/ Urban Corner-datasets

    Zhang, Y.: Urban Corner Detection Dataset. https://github.com/yangzhangcv/ Urban Corner-datasets. Accessed: June 4, 2025 (2021)

    work page 2025

  59. [59]

    In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

    Huang, J.-B., Singh, A., Ahuja, N.: Single image super-resolution from trans- formed self-exemplars. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5197–5206 (2015) 35 Table 1: Edge detection performance comparison between Sobel and QHED for QPIE and FRQI image encoding methods. The edge-quality metrics are Edge Den...

    work page 2015