Skip to main content
Log in

Region based level sets for image segmentation: a brief comparative review with a fast model FREEST

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Region based level sets are one class of popular image segmentation models. Sorting out the inheritance relationship and comparing their performance on same image repositories are of guiding significance. In this paper, we first propose a generalization model to cover external forces of representative region based level sets and give a brief comparative review on them by describing their evolution process and performing a capacity and complexity analysis. We then briefly review regularizations on level sets, known as internal force in the literature. As the models become more and more complicated to perform well on challenging images, it is significant to ensure both segmentation performance and time performance. Thirdly, we propose a fast region based level set (FREEST) model to segment images with intensity inhomogeneities where smoothness of the estimated intensity bias field is ensured by a convolution operation. We then improve FREEST by introducing global intensity variances and rename it as FREESTσ to deal with images with different variances between objects of interest and the background. Experiments on representative 120 images (natural images from BSDS500 and well known synthetic images in the field) with simulated intensity biases show that time performances of the proposed models are close to the simplest but most famous level set model and its time incrementing is only about 1/20 of existing models. Qualitative and quantitative comparison with the representative models on the images in terms of Dice Similarity Coefficient and Jaccard Similarity Coefficient demonstrate advantages of the proposed models. Compared with the second-best model, the evaluation indicators increased by 0.09 and 0.13, respectively. Parameter settings and representative influence are discussed, which indicates robustness of the proposed models. Grand challenges and still open problems such as initialization sensitivity, complex background segmentation, and multi-class object segmentation are finally discussed. Codes will be released if this paper was accepted.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Algorithm 1
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Ali H, Rada L, Badshah N (2018) Image segmentation for intensity inhomogeneity in presence of high noise. IEEE Trans Image Process 27 (8):3729–3738

    MathSciNet  MATH  Google Scholar 

  2. Cai Q, Liu H, Zhou S, Sun J, Li J (2018) An adaptive-scale active contour model for inhomogeneous image segmentation and bias field estimation. Pattern Recogn 82:79–93

    Google Scholar 

  3. Chan T, Vese LA (2001) Active contours without edges. IEEE trans Image Process 10(2):266–277

    MATH  Google Scholar 

  4. Chan T, Zhu W (2005) Level set based shape prior segmentation. In: 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), vol 2. IEEE, pp 1164–1170

  5. Cremers D, Rousson M, Deriche R (2007) A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int J Comput Vis 72(2):195–215

    Google Scholar 

  6. Dai L, Ding J, Yang J (2015) Inhomogeneity-embedded active contour for natural image segmentation. Pattern Recogn 48(8):2513–2529

    Google Scholar 

  7. Fang J, Liu H, Zhang L, Liu J, Liu H (2021) Region-edge-based active contours driven by hybrid and local fuzzy region-based energy for image segmentation. Inf Sci 546:397–419

    MathSciNet  MATH  Google Scholar 

  8. Fang L, Wang X, Wang L (2020) Multi-modal medical image segmentation based on vector-valued active contour models. Inf Sci 513:504–518

    MathSciNet  Google Scholar 

  9. Feng C, Li C, Zhao D, Davatzikos C, Litt H (2013) Segmentation of the left ventricle using distance regularized two-layer level set approach. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 477–484

  10. Feng C, Yang J, Lou C, Li W, Yu K, Zhao D (2020) A global inhomogeneous intensity clustering-(GINC-) based active contour model for image segmentation and bias correction. Comput Math Methods Med 2020:7595174

    Google Scholar 

  11. Feng C, Zhang S, Zhao D, Li C (2016) Simultaneous extraction of endocardial and epicardial contours of the left ventricle by distance regularized level sets. Med Phys 43(6):2741–2755

    Google Scholar 

  12. Feng C, Zhao D, Huang M, segmentation Image, clustering bias correction using local inhomogeneous intensity (2017) (LINC): A region-based level set method. Neurocomputing 219:107–129

    Google Scholar 

  13. Fu X, Fang B, Zhou M, Kwong S (2021) Active contour driven by adaptively weighted signed pressure force combined with Legendre polynomial for image segmentation. Inf Sci 564:327–342

    MathSciNet  Google Scholar 

  14. Gibou F, Fedkiw R, Osher S (2018) A review of level-set methods and some recent applications. J Comput Phys 353:82–109

    MathSciNet  MATH  Google Scholar 

  15. Guopeng H, Hongbing J, Wenbo Z (2018) A fast level set method for inhomogeneous image segmentation with adaptive scale parameter. Magn Reson Imaging 52:33–45

    Google Scholar 

  16. He C, Wang Y, Chen Q (2012) Active contours driven by weighted region-scalable fitting energy based on local entropy. Signal Process 92(2):587–600

    Google Scholar 

  17. Li Y, Cao G, Wang T, Cui Q, Wang B (2020) A novel local region-based active contour model for image segmentation using Bayes theorem. Inf Sci 506:443–456

    MathSciNet  MATH  Google Scholar 

  18. Li C, Gore JC, Davatzikos C (2014) Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation. Magnet Resonance Imaging 32(7):913–923

    Google Scholar 

  19. Li C, Huang R, Ding Z, Gatenby JC, Metaxas DN, Gore JC (2011) A level set method for image segmentation in the presence of intensity inhomogeneities with application to mri. IEEE Trans Image Process 20(7):2007–2016

    MathSciNet  MATH  Google Scholar 

  20. Li C, Kao C-Y, Gore JC, Ding Z (2008) Minimization of region-scalable fitting energy for image segmentation. IEEE Trans Image Process 17 (10):1940–1949

    MathSciNet  MATH  Google Scholar 

  21. Li C, Xu C, Gui C, Fox MD (2005) Level set evolution without re-initialization: a new variational formulation. In: 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), vol 1. IEEE, pp 430–436

  22. Li C, Xu C, Gui C, Fox MD (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans Image Process 19 (12):3243–3254

    MathSciNet  MATH  Google Scholar 

  23. Liu S, Peng Y (2012) A local region-based Chan-Vese model for image segmentation. Pattern Recogn 45(7):2769–2779

    MATH  Google Scholar 

  24. Min H, Jia W, Zhao Y, Zuo W, Ling H, Luo Y (2018) Late: a level-set method based on local approximation of taylor expansion for segmenting intensity inhomogeneous images. IEEE Trans Image Process 27(10):5016–5031

    MathSciNet  MATH  Google Scholar 

  25. Min H, Lu J, Jia W, Zhao Y, Luo Y (2018) An effective local regional model based on salient fitting for image segmentation. Neurocomputing 311:245–259

    Google Scholar 

  26. Min H, Xia L, Han J, Wang X, Pan Q, Fu H, Wang H, Wong S, Li H (2019) A multi-scale level set method based on local features for segmentation of images with intensity inhomogeneity journal=Pattern Recognit, 91:69–85

    Google Scholar 

  27. Mumford D, Shah J (1989) Optimal approximations by piecewise smooth functions and associated variational problems. Commun Pure Appl Math 42(5):577–685

    MathSciNet  MATH  Google Scholar 

  28. Niu S, Chen Q, De Sisternes L, Ji Z, Zhou Z, Rubin DL (2017) Robust noise region-based active contour model via local similarity factor for image segmentation. Pattern Recogn 61:104–119

    Google Scholar 

  29. Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Google Scholar 

  30. Rousson M, Paragios N (2002) Shape priors for level set representations. In: European conference on computer vision. Springer, pp 78–92

  31. Rousson M, Paragios N (2008) Prior knowledge, level set representations & visual grouping. Int J Comput Vis 76(3):231–243

    Google Scholar 

  32. Shi Y, Karl WC (2005) Real-time tracking using level sets. In: 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), vol 2. Citeseer, pp 34–41

  33. Tsai A, Yezzi A Jr, Willsky AS (2001) Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans Image Process 10(8):1169–1186

    MATH  Google Scholar 

  34. Vese LA, Chan T (2002) A multiphase level set framework for image segmentation using the Mumford and Shah model. Int J Comput Vis 50(3):271–293

    MATH  Google Scholar 

  35. Wang L, Chang Y, Wang H, Wu Z, Pu J, Yang X (2017) An active contour model based on local fitted images for image segmentation. Inf Sci 418:61–73

    Google Scholar 

  36. Wang L, Chen G, Shi D, Chang Y, Chan S, Pu J, Yang X (2018) Active contours driven by edge entropy fitting energy for image segmentation. Signal Process 149:27–35

    Google Scholar 

  37. Wang L, He L, Mishra A, Li C (2009) Active contours driven by local Gaussian distribution fitting energy. Signal Process 89(12):2435–2447

    MATH  Google Scholar 

  38. Wang X-F, Huang D-S, Xu H (2010) An efficient local Chan-Vese model for image segmentation. Pattern Recogn 43(3):603–618

    MATH  Google Scholar 

  39. Wang H, Huang T-Z, Xu Z, Wang Y (2014) An active contour model and its algorithms with local and global Gaussian distribution fitting energies. Inf Sci 263:43–59

    Google Scholar 

  40. Wang Z, Ma B, Zhu Y (2021) Review of level set in image segmentation. Archives of Computational Methods in Engineering 28(4):2429–2446

    MathSciNet  Google Scholar 

  41. Wang X-F, Min H, Zou L, Zhang Y-G (2015) A novel level set method for image segmentation by incorporating local statistical analysis and global similarity measurement. Pattern Recogn 48(1):189–204

    Google Scholar 

  42. Wang L, Zhang L, Yang X, Yi P, Chen H (2020) Level set based segmentation using local fitted images and inhomogeneity entropy. Sign Process 167:107297

    Google Scholar 

  43. Weng G, Dong B, Lei Y (2021) A level set method based on additive bias correction for image segmentation. Expert Syst Appl 185:115633

    Google Scholar 

  44. Yan S, Tai X-C, Liu J, Huang H-Y (2020) Convexity shape prior for level set-based image segmentation method. IEEE Trans Image Process 29:7141–7152

    MathSciNet  MATH  Google Scholar 

  45. Yang Y, Hou X, Ren H (2021) Accurate and efficient image segmentation and bias correction model based on entropy function and level sets. Inf Sci 577:638–662

    MathSciNet  Google Scholar 

  46. Yu H, He F, Pan Y (2020) A scalable region-based level set method using adaptive bilateral filter for noisy image segmentation. Multimed Tools Appl 79:5743–5765

    Google Scholar 

  47. Zhang F, Liu H, Cao C, Cai Q, Zhang D (2022) RVLSM: Robust Variational level set method for image segmentation with intensity inhomogeneity and high noise. Inf Sci 596:439–459

    Google Scholar 

  48. Zhang K, Song H, Zhang L (2010) Active contours driven by local image fitting energy. Pattern Recognit 43(4):1199–1206

    MATH  Google Scholar 

  49. Zhang H, Tang L, He C (2019) A variational level set model for multiscale image segmentation. Inf Sci 493:152–175

    MathSciNet  MATH  Google Scholar 

  50. Zhao H-K, Chan T, Merriman B, Osher S (1996) A variational level set approach to multiphase motion. J Comput Phys 127(1):179–195

    MathSciNet  MATH  Google Scholar 

  51. Zhi X-H, Shen H-B (2018) Saliency driven region-edge-based top down level set evolution reveals the asynchronous focus in image segmentation. Pattern Recogn 80:241–255

    Google Scholar 

  52. Zhu J, Zeng Y, Xu H, Li J, Tian S, Liu H (2021) Maximum a posterior based level set approach for image segmentation with intensity inhomogeneity. Sign Process 181:107896

    Google Scholar 

Download references

Acknowledgements

This work was supported by the Natural Science Foundation of Liaoning Province of China under grant 2021-MS-085.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chaolu Feng.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

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

J. Yang is the Co-corresponding author.

D. Zhao is the Co-first author.

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

Feng, C., Chen, S., Zhao, D. et al. Region based level sets for image segmentation: a brief comparative review with a fast model FREEST. Multimed Tools Appl 82, 37065–37095 (2023). https://doi.org/10.1007/s11042-023-15073-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-15073-x

Keywords

Navigation