Skip to main content
SpringerLink
Log in

A Novel Image Segmentation Algorithm based on Continuous-Time Quantum Walk using Superpixels

  • RESEARCH
  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The application of continuous-time quantum walk in the field of image segmentation has attracted much attention due to the advantages of quantum computation. However, the proposed image segmentation algorithm constructs the continuous-time quantum walk model based on pixels, which will cause a huge burden on quantum resources, and the various feature information of the image cannot be better considered. In addition, this pixel-based processing method requires a lot of manual annotation to achieve the desirable segmentation effect. To address these issues, we propose an image segmentation algorithm using continuous-time quantum walk based on superpixels. In our segmentation algorithm, the original image is firstly segmented into superpixels, and then a weighted graph is constructed with superpixels as nodes, where the weight of edges in graph is measured by the feature similarity of two adjacent superpixels, which consists of color features and texture features. Next, the continuous-time quantum walk model is constructed based on the weighted graph by redefining the new Hamiltonian operator. Finally, continuous-time quantum walk is executed and the image segmentation result can be obtained, which is realized by assigning each superpixel the class label corresponding to the greatest probability. Experiments on the BSD500 dataset show that the proposed algorithm can significantly improve segmentation efficiency and accuracy while the manually selected seeds is reduced by 91%. More importantly, the new algorithm reduce the demision of the quantum walk system by more than 99%, which will yield a huge saving on the quantum resources.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability

The data that support the findings of this study are openly available at https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/.

References

  1. Chen, X., Pan, L.: A survey of graph cuts/graph search based medical image segmentation. IEEE Rev. Biomed. Eng. 11, 112–124 (2018)

    Article  PubMed  Google Scholar 

  2. Tarkhaneh, O., Shen, H.: An adaptive differential evolution algorithm to optimal multi-level thresholding for MRI brain image segmentation. Expert Syst. Appl. 138, 112820 (2019)

    Article  Google Scholar 

  3. Tajbakhsh, N., et al.: Embracing imperfect datasets: A review of deep learning solutions for medical image segmentation. Med. Image Anal. 63, 101693 (2020)

    Article  PubMed  Google Scholar 

  4. Siriapisith, T., Kusakunniran, W., Haddawy, P.: Pyramid graph cut: Integrating intensity and gradient information for grayscale medical image segmentation. Comput. Biol. Med. 126, 103997 (2020)

    Article  PubMed  Google Scholar 

  5. Treml, M., et al.: Speeding up semantic segmentation for autonomous driving. 29th Conference on Neural Information Processing Systems (NIPS). (2016)

  6. Fechter, T., et al.: Esophagus segmentation in CT via 3D fully convolutional neural network and random walk. Med. Phys. 44(12), 6341–6352 (2017)

    Article  PubMed  Google Scholar 

  7. Kaymak, Ç., Uçar, A.: A brief survey and an application of semantic image segmentation for autonomous driving. Handbook of Deep Learning Applications 136, 161–200 (2019)

    Article  Google Scholar 

  8. Zhou, W., et al.: Automated evaluation of semantic segmentation robustness for autonomous driving. IEEE Trans. Intell. Transport. Syst. 21(5), 1951–1963 (2019)

    Article  Google Scholar 

  9. Feng, D., et al.: Deep multi-modal object detection and semantic segmentation for autonomous driving: Datasets, methods, and challenges. IEEE Trans. Intell. Transport. Syst. 22(3), 1341–1360 (2020)

    Article  Google Scholar 

  10. Milioto, A., et al.: Lidar panoptic segmentation for autonomous driving. 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, (2020)

  11. Cheng, D., et al.: FusionNet: Edge aware deep convolutional networks for semantic segmentation of remote sensing harbor images. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 10(12), 5769–5783 (2017)

    Article  ADS  Google Scholar 

  12. Hossain, M.D., Chen, D.: Segmentation for Object-Based Image Analysis (OBIA): A review of algorithms and challenges from remote sensing perspective. ISPRS J. Photogramm. Remote. Sens. 150, 115–134 (2019)

    Article  ADS  Google Scholar 

  13. Wang, S., et al.: Weakly supervised deep learning for segmentation of remote sensing imagery. Remote Sens. 12(2), 207 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  14. Jiang, J., et al.: RWSNet: a semantic segmentation network based on SegNet combined with random walk for remote sensing. Int. J. Remote Sens. 41(2), 487–505 (2020)

    Article  Google Scholar 

  15. Ghosh, S., et al.: Understanding deep learning techniques for image segmentation. ACM Comput. Surv. (CSUR). 52(4), 1–35 (2019)

    Article  Google Scholar 

  16. Minaee, S., et al.: Image segmentation using deep learning: a survey. IEEE Trans. Pattern Anal. Mach. Intell. 44(7), 3523–3542 (2021)

    Google Scholar 

  17. Boykov, Y.Y., Jolly, M.-P.: Interactive graph cuts for optimal boundary & region segmentation of objects in ND images. Proceedings eighth IEEE international conference on computer vision. ICCV 2001. IEEE, Vol. 1 (2001)

  18. Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient graph-based image segmentation. Int. J. Comput. Vis. 59(2), 167–181 (2004)

    Article  Google Scholar 

  19. Grady, L.: Random walks for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1768–1783 (2006)

    Article  PubMed  Google Scholar 

  20. Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26(9), 1124–1137 (2004)

    Article  PubMed  Google Scholar 

  21. Boykov, Y., Funka-Lea, G.: Graph cuts and efficient ND image segmentation. Int. J. Comput. Vis. 70(2), 109–131 (2006)

    Article  Google Scholar 

  22. Xia, F., Liu, J., Nie, H., et al.: Random walks: A review of algorithms and applications[J]. IEEE Trans. Emerg. Topics Comput. Intell. 4(2), 95–107 (2019)

    Article  Google Scholar 

  23. Kim, T.H., Lee, K.M., Lee, S.U.: Generative image segmentation using random walks with restart. European conference on computer vision. Springer, Berlin, Heidelberg (2008)

  24. Kim, J.-S., Sim, J.-Y., Kim, C.-S.: Multiscale saliency detection using random walk with restart. IEEE Trans. Circuits Syst. Video Technol. 24(2), 198–210 (2013)

    Google Scholar 

  25. Dong, X., et al.: Sub-Markov random walk for image segmentation. IEEE Trans. Image Process. 25(2), 516–527 (2015)

  26. Shen, J., Du, Y., Wang, W., et al.: Lazy random walks for superpixel segmentation[J]. IEEE Trans. Image Process. 23(4), 1451–1462 (2014)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  27. Bertasius, G., et al.: Convolutional random walk networks for semantic image segmentation. Proceedings of the IEEE conference on computer vision and pattern recognition. (2017)

  28. Long, J., Shelhamer, E., Darrell, T.: Fully convolutional networks for semantic segmentation. Proceedings of the IEEE conference on computer vision and pattern recognition. (2015)

  29. Zhou, N.-R., et al.: Hybrid quantum–classical generative adversarial networks for image generation via learning discrete distribution. Signal Process. Image Commun. 110, 116891 (2023)

    Article  Google Scholar 

  30. Youssry, A., El-Rafei, A., Elramly, S.: A quantum mechanics-based framework for image processing and its application to image segmentation[J]. Quantum Inf. Process. 14, 3613–3638 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. Wang, X., Yang, C., Xie, G.S., et al.: Image thresholding segmentation on quantum state space[J]. Entropy 20(10), 728 (2018)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  32. Huo, F., Sun, X., Ren, W.: Multilevel image threshold segmentation using an improved Bloch quantum artificial bee colony algorithm[J]. Multimed. Tools Appl. 79(3-4), 2447–2471 (2020)

    Article  Google Scholar 

  33. Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48(2), 1687 (1993)

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Flitney, A.P., Abbott, D.: Quantum models of Parrondo’s games. Phys. A. 324(1-2), 152–156 (2003)

    Article  MathSciNet  Google Scholar 

  35. Flitney, A.P., Abbott, D., Johnson, N.F.: Quantum walks with history dependence. J. Phys. A: Math. Gen. 37(30), 7581 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  36. Watrous, J.: Quantum simulations of classical random walks and undirected graph connectivity. J. Comput. Syst. Sci. 62(2), 376–391 (2001)

    Article  MathSciNet  Google Scholar 

  37. Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A. 58(2), 915 (1998)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  38. Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44(4), 307–327 (2003)

    Article  ADS  Google Scholar 

  39. Ambainis, A.: Quantum walks and their algorithmic applications. Int. J. Quantum Inform. 1(04), 507–518 (2003)

    Article  Google Scholar 

  40. Childs, A.M., et al.: Exponential algorithmic speedup by a quantum walk. Proceedings of the thirty-fifth annual ACM symposium on Theory of computing (2003)

  41. Krovi, H., et al.: Quantum walks can find a marked element on any graph. Algorithmica 74(2), 851–907 (2016)

    Article  MathSciNet  Google Scholar 

  42. Paparo, G.D., Martin-Delgado, M.A.: Google in a quantum network. Sci. Rep. 2(1), 1–12 (2012)

    Article  Google Scholar 

  43. Li, H.-J., et al.: A new kind of flexible quantum teleportation of an arbitrary multi-qubit state by multi-walker quantum walks. Quantum Inf. Process. 18(9), 1–16 (2019)

    Article  ADS  Google Scholar 

  44. Yang, Y.-G., et al.: Novel image encryption based on quantum walks. Sci. Rep. 5(1), 1–9 (2015)

    MathSciNet  Google Scholar 

  45. Yan, F., Liang, W., Hirota, K.: An information propagation model for social networks based on continuous-time quantum walk. Neural Comput. Appl. 34(16), 13455–13468 (2022)

    Article  Google Scholar 

  46. Wang, Y., et al.: Continuous-time quantum walk based centrality testing on weighted graphs. Sci. Rep. 12(1), 1–8 (2022)

    Google Scholar 

  47. Krok, M., Rycerz, K., Bubak, M.: Application of Continuous Time Quantum Walks to Image Segmentation. International Conference on Computational Science. Springer, Cham (2019)

  48. Koch, J., et al.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76(4), 042319 (2007)

    Article  ADS  Google Scholar 

  49. Fowler, A.G., et al.: Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A. 86(3), 032324 (2012)

    Article  ADS  Google Scholar 

  50. Barends, R., et al.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508(7497), 500–503 (2014)

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Huang, H.-Y., Kueng, R., Preskill, J.: Predicting many properties of a quantum system from very few measurements. Nat. Phys. 16(10), 1050–1057 (2020)

    Article  CAS  Google Scholar 

  52. Ren, X., Malik, J.: Learning a classification model for segmentation. Computer Vision, IEEE International Conference on. Vol. 2. IEEE Computer Society (2003)

  53. Borovec, J., et al.: Supervised and unsupervised segmentation using superpixels, model estimation, and graph cut. J. Electron. Imaging 26(6), 061610 (2017)

    Article  ADS  Google Scholar 

  54. Zhao, W., et al.: An improved image semantic segmentation method based on superpixels and conditional random fields. Appl. Sci. 8(5), 837 (2018)

    Article  ADS  Google Scholar 

  55. Wu, L., et al.: Interactive segmentation algorithm based on superpixel and random walk. Appl. Res. Comput. 39(06), 1891–1896 (2022)

    Google Scholar 

  56. Achanta, R., et al.: SLIC superpixels compared to state-of-the-art superpixel methods. IEEE Trans. Pattern Anal. Mach. Intell. 34(11), 2274–2282 (2012)

    Article  PubMed  Google Scholar 

  57. Aharonov, D., Ambainis, A., Kempe, J., et al.: Quantum walks on graphs[C]//Proceedings of the thirty-third annual ACM symposium on Theory of computing. 50–59 (2001)

  58. Yang, D., Rao, G., Martinez, J., et al.: Evaluation of tumor-derived MRI-texture features for discrimination of molecular subtypes and prediction of 12-month survival status in glioblastoma[J]. Med. Phys. 42(11), 6725–6735 (2015)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Arbelaez, P., Maire, M., Fowlkes, C., et al.: Contour detection and hierarchical image segmentation[J]. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2010)

    Article  Google Scholar 

  60. Johansson, J.R., Nation, P.D., Nori, F.: QuTiP2: A Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234 (2013). https://doi.org/10.1016/j.cpc.2012.11.019

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work is supported by The National Natural Science Foundation of China (No. 61602019).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Beijing University of Technology, Beijing, 100124, China

    Wei-Min Shi, Feng-Xue Xu, Yi-Hua Zhou & Yu-Guang Yang

  2. Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China

    Wei-Min Shi, Feng-Xue Xu, Yi-Hua Zhou & Yu-Guang Yang

Authors
  1. Wei-Min Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng-Xue Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi-Hua Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu-Guang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Wei-Min Shi made substantial contributions to the conception and design of the work; Wei-Min Shi and Feng-Xue Xu conducted experiments and wrote the main manuscript text ; Yi-Hua Zhou and Yu-Guang Yang made substantial contributions to the acquisition, analysis, and interpretation of data; All authors reviewed the manuscript.

Corresponding author

Correspondence to Feng-Xue Xu.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, WM., Xu, FX., Zhou, YH. et al. A Novel Image Segmentation Algorithm based on Continuous-Time Quantum Walk using Superpixels. Int J Theor Phys 63, 4 (2024). https://doi.org/10.1007/s10773-023-05527-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05527-1

Keywords

Search

Navigation