Multimedia Tools and Applications

, Volume 78, Issue 24, pp 35813–35833 | Cite as

Prior distribution-based statistical active contour model

  • Zhiheng ZhouEmail author
  • Ming Dai
  • Tianlei Wang
  • Ruzheng Zhao


Employing prior information can greatly improve the segmentation result of many image segmentation problems. For example, a commonly used prior information is the shape of the object. In this paper, we introduce a different kind of prior information called the prior distribution. On the basis of non-parametric statistical active contour model, we add prior distribution energy to build a novel prior active contour model. During the convergence of contour curve, distribution difference between the inside and outside of the active contour is maximized while the distribution difference between the inside/outside of contour and the prior object/background is minimized. Furthermore, in order to improve the computation speed, a method to accelerate the computation speed is also proposed, which significantly relieves the burden of estimating probability density functions. As the experimental results suggest, satisfactory effects can be achieved in the segmentation of synthetic images and natural images via the our algorithm. Compared with the traditional non-parametric statistical active contour model without prior information, our method achieves a distinct improvement in both accuracy and computation efficiency.


Active contour model Level-set method Image segmentation Prior distribution 



The work is supported by National Key R&D Program of China (2018YFC0309400), National Natural Science Foundation of China (61871188), Guangzhou city science and technology research projects(201902020008).


  1. 1.
    Alpert S, Galun M, Brandt A, Basri R (2011) Image segmentation by probabilistic bottom-up aggregation and cue integration. IEEE Trans Pattern Anal Mach Intell 34(2):315–327CrossRefGoogle Scholar
  2. 2.
    Bresson X, Vandergheynst P, Thiran J-P (2006) A variational model for object segmentation using boundary information and shape prior driven by the Mumford-Shah functional. Int J Comput Vis 68(2):145–162CrossRefGoogle Scholar
  3. 3.
    Bresson X, Esedoḡlu S, Vandergheynst P, Thiran J-P, Osher S (2007) Fast global minimization of the active contour/snake model. J Math Imag Vis 28(2):151–167MathSciNetCrossRefGoogle Scholar
  4. 4.
    Brown ES, Chan TF, Bresson X (2012) Completely convex formulation of the chan-vese image segmentation model. Int J Comput Vis 98(1):103–121MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Caselles V, Kimmel R, Sapiro G (1997) Geodesic active contours. Int J Comput Vis 22(1):61–79zbMATHCrossRefGoogle Scholar
  6. 6.
    Chan T, Zhu W (2005) Level set based shape prior segmentation. In: Computer vision and pattern recognition, vol 2. IEEE, pp 1164–1170Google Scholar
  7. 7.
    Chan TF, Vese LA (2001) Active contours without edges. IEEE Trans Image Process 10(2):266–277zbMATHCrossRefGoogle Scholar
  8. 8.
    Chen Z, Fu Y, Xiang Y, Rong R (2017) A novel iterative shrinkage algorithm for CS-MRI via adaptive regularization. IEEE Signal Process Lett 24(10):1443–1447CrossRefGoogle Scholar
  9. 9.
    Chen Z, Fu Y, Xiang Y, Rong R (2018) A novel low-rank model for MRI using the redundant wavelet tight frame. Neurocomputing 289:180–187CrossRefGoogle Scholar
  10. 10.
    Cheng Z, Shen J, Miao H (2016) The effects of multiple query evidences on social image retrieval. Multimed Syst 22(4):509–523CrossRefGoogle Scholar
  11. 11.
    Cohen LD (1991) On active contour models and balloons. CVGIP: Image Underst 53(2):211–218MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Cremers D, Kohlberger T, Schnörr C (2003) Shape statistics in kernel space for variational image segmentation. Pattern Recogn 36(9):1929–1943zbMATHCrossRefGoogle Scholar
  13. 13.
    Foulonneau A, Charbonnier P, Heitz F (2006) Affine-invariant geometric shape priors for region-based active contours. IEEE Trans Pattern Anal Mach Intell 28 (8):1352–1357CrossRefGoogle Scholar
  14. 14.
    Gong M, Li H, Zhang X, Zhao Qn, Wang B (2016) Nonparametric statistical active contour based on inclusion degree of fuzzy sets. IEEE Trans Fuzzy Syst 24(5):1176–1192CrossRefGoogle Scholar
  15. 15.
    Hsieh C-W, Chen C-Y (2018) An adaptive level set method for improving image segmentation. Multimed Tools Appl 77(15):20087–20102CrossRefGoogle Scholar
  16. 16.
    Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models. Int J Comput Vis 1(4):321–331zbMATHCrossRefGoogle Scholar
  17. 17.
    Kim J, Fisher JW, Yezzi A, Çetin M, Willsky AS (2005) A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans Image Process 14(10):1486–1502MathSciNetCrossRefGoogle Scholar
  18. 18.
    Lankton S, Tannenbaum A (2008) Localizing region-based active contours. IEEE Trans Image Process 17(11):2029–2039MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Leventon ME, Faugeras O, Grimson ELW, Wells WM (2000) Level set based segmentation with intensity and curvature priors. In: Mathematical methods in biomedical image analysis. IEEE, pp 4–11Google Scholar
  20. 20.
    Leventon ME, Grimson ELW, Faugeras O (2000) Statistical shape influence in geodesic active contours. In: Computer vision and pattern recognition, vol 1. IEEE, pp 316–323Google Scholar
  21. 21.
    Li B, Acton ST (2007) Active contour external force using vector field convolution for image segmentation. IEEE Trans Image Process 16(8):2096–2106MathSciNetCrossRefGoogle Scholar
  22. 22.
    Li C, Xu C, Gui C, Fox MD (2005) Level set evolution without re-initialization: a new variational formulation. In: Computer vision and pattern recognition, vol 1. IEEE, pp 430–436Google Scholar
  23. 23.
    Li C, Kao C-Y, Gore JC, Ding Z (2007) Implicit active contours driven by local binary fitting energy. In: Computer vision and pattern recognition. IEEE, pp 1–7Google Scholar
  24. 24.
    Michailovich O, Rathi Y, Tannenbaum A (2007) Image segmentation using active contours driven by the Bhattacharyya gradient flow. IEEE Trans Image Process 16(11):2787–2801MathSciNetCrossRefGoogle Scholar
  25. 25.
    Mitiche A, Ayed IB (2010) Variational and level set methods in image segmentation, vol 5. Springer Science & Business MediaGoogle Scholar
  26. 26.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Paragios N, Deriche R (2002) Geodesic active regions: a new framework to deal with frame partition problems in computer vision. J Vis Commun Image Represent 13 (1–2):249–268CrossRefGoogle Scholar
  28. 28.
    Peng Y, Lu B-L (2017) Discriminative extreme learning machine with supervised sparsity preserving for image classification. Neurocomputing 261:242–252CrossRefGoogle Scholar
  29. 29.
    Ronfard R (1994) Region-based strategies for active contour models. Int J Comput Vis 13(2):229–251CrossRefGoogle Scholar
  30. 30.
    Schoenemann T, Kahl F, Masnou S, Cremers D (2012) A linear framework for region-based image segmentation and inpainting involving curvature penalization. Int J Comput Vis 99(1):53–68MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Shao D, Zhang Y, Wei W (2009) An aircraft recognition method based on principal component analysis and image model matching. Chinese J Stereol Image Anal 3:7Google Scholar
  32. 32.
    Unal G, Yezzi A, Krim H (2005) Information-theoretic active polygons for unsupervised texture segmentation. Int J Comput Vis 62(3):199–220CrossRefGoogle Scholar
  33. 33.
    Vese LA, Chan TF (2002) A multiphase level set framework for image segmentation using the mumford and shah model. Int J Comput Vis 50(3):271–293zbMATHCrossRefGoogle Scholar
  34. 34.
    Wu H, Appia V, Yezzi A (2013) Numerical conditioning problems and solutions for nonparametric iid statistical active contours. IEEE Trans Pattern Anal Mach Intell 35(6):1298–1311CrossRefGoogle Scholar
  35. 35.
    Xu C, Prince JL (1998) Snakes, shapes, and gradient vector flow. IEEE Trans Image Process 7(3):359–369MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Yu H, He F, Pan Y (2019) A novel segmentation model for medical images with intensity inhomogeneity based on adaptive perturbation. Multimed Tools Appl 78 (9):11779–11798CrossRefGoogle Scholar
  37. 37.
    Zhu SC, Yuille A (1996) Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans Pattern Anal Mach Intell 18(9):884–900CrossRefGoogle Scholar
  38. 38.
    Zhuo T, Cheng Z, Zhang P, Wong Y, Kankanhalli M (2018) Unsupervised online video object segmentation with motion property understanding. arXiv:1810.03783

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electronic and Information EngineeringSouth China University of TechnologyGuangZhouChina
  2. 2.Department of Intelligent ManufacturingWuyi UniversityJiangmenChina

Personalised recommendations