Abstract
Image segmentation is an important analysis tool in the field of computer vision. In this paper, on the basis of the traditional level set method, a novel segmentation model using generalized divergences is proposed. The main advantage of generalized divergences is their smooth connection performance among various kinds of well-known and frequently used fundamental divergences with one formula. Therefore, the discrepancy between two probability distributions of segmented image parts can be measured by generalized divergences. We also found a solution to determine the optimal divergence automatically for different images. Experimental results on a variety of synthetic and natural images are presented, which demonstrate the potential of the proposed method. Compared with the previous active contour models formulated to solve the same nonparametric statistical segmentation problem, our method performs better both qualitatively and quantitatively.
Similar content being viewed by others
References
S. Alpert, M. Galun, A. Brandt, R. Basri, Image segmentation by probabilistic bottom-up aggregation and cue integration. IEEE Trans. Pattern Anal. Mach. Intell. 34(2), 315–326 (2012)
S.I. Amari, Alpha-divergence is unique, belonging to both f-divergence and bregman divergence classes. IEEE Trans. Inf. Theory 55(11), 4925–4931 (2009)
X. Bresson, P. Vandergheynst, J.P. Thiran, A variational model for object segmentation using boundary information and shape prior driven by the Mumford–Shah functional. Int. J. Comput. Vis. 68(2), 145–162 (2006)
E.S. Brown, T.F. Chan, X. Bresson, Completely convex formulation of the Chan-Vese image segmentation model. Int. J. Comput. Vis. 98(1), 103–121 (2012)
V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours. Int. J. Comput Vis. 22(1), 61–79 (1997)
T.F. Chan, W. Zhu, Level set based shape prior segmentation, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2005), pp. 1164–1170
T.F. Chan, L.A. Vese, Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)
Z. Chen, Y. Fu, Y. Xiang, R. Rong, A novel iterative shrinkage algorithm for CS-MRI via adaptive regularization. IEEE Signal Process. Lett. 24(10), 1443–1447 (2017)
Z. Chen, Y. Fu, Y. Xiang, J. Xu, R. Rong, A novel low-rank model for MRI using the redundant wavelet tight frame. Neurocomputing 289, 180–187 (2018)
Z. Chen, C. Huang, S. Lin, A new sparse representation framework for compressed sensing MRI. Knowl. Based Syst. 188, 1–10 (2020)
A. Cichocki, S. Amari, Families of alpha- beta- and gamma- divergences: flexible and robust measures of similarities. Entropy 12, 1532–1568 (2010)
J. Dai, K. He, J. Sun, Instance-aware semantic segmentation via multi-task network cascades, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 3150–3158
A. Foulonneau, P. Charbonnier, F. Heitz, Affine-invariant geometric shape priors for region-based active contours. IEEE Trans. Pattern Anal. Mach. Intell. 28(8), 1352–1357 (2006)
R. Girshick, Fast R-CNN, in Proceedings of the IEEE International Conference on Computer Vision (2015), pp. 1440–1448
R. Girshick, J. Donahue, T. Darrell, J. Malik, Region-based convolutional networks for accurate object detection and segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 38(1), 142–158 (2016)
M. Gong, H. Li, X. Zhang, Q. Zhao, B. Wang, Nonparametric statistical active contour based on inclusion degree of fuzzy sets. IEEE Trans. Fuzzy Syst. 24(5), 1176–1192 (2016)
K. He, G. Gkioxari, P. Dollár, R. Girshick, Mask R-CNN, in Proceedings of the IEEE International Conference on Computer Vision (2017), pp. 2961–2969
P. Hu, B. Shuai, J. Liu, G. Wang, Deep level sets for salient object detection, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2017), pp. 540–549
J. Kim, J.W. Fisher, A. Yezzi, M. Çetin, A.S. Willsky, A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans. Image Process. 14(10), 1486–1502 (2005)
S. Lankton, A. Tannenbaum, Localizing region-based active contours. IEEE Trans. Image Process. 17(11), 2029–2039 (2008)
T.H.N. Le, K.G. Quach, K. Luu, C.N. Duong, M. Savvides, Reformulating level sets as deep recurrent neural network approach to semantic segmentation. IEEE Trans. Image Process. 27(5), 2393–2407 (2018)
C. Li, R. Huang, Z. Ding, J.C. Gatenby, D.N. Metaxas, J.C. Gore, 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 (2011)
C. Li, C.Y. Kao, J.C. Gore, Z. Ding, Minimization of region-scalable fitting energy for image segmentation. IEEE Trans. Image Process. 17(10), 1940–1949 (2008)
C. Li, C. Xu, C. Gui, M.D. Fox, Level set evolution without re-initialization: a new variational formulation, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2005), pp. 430–436
F. Liese, I. Vajda, On divergences and informations in statistics and information theory. IEEE Trans. Inf. Theory 52(10), 4394–4412 (2006)
J. Liu, C. Smith, H. Chebrolu, A local probabilistic prior-based active contour model for brain MR image segmentation, in Asian Conference on Computer Vision (Springer, New York, 2007), pp. 956–964
J. Long, E. Shelhamer, T. Darrell, Fully convolutional networks for semantic segmentation, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2015), pp. 3431–3440
O. Michailovich, Y. Rathi, A. Tannenbaum, Image segmentation using active contours driven by the Bhattacharyya gradient flow. IEEE Trans. Image Process. 16(11), 2787–2801 (2007)
H. Min, W. Jia, Y. Zhao, W. Zuo, H. Ling, Y. Luo, 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 (2018)
A. Mitiche, I.B. Ayed, Variational and Level Set Methods in Image Segmentation (Springer, Berlin, 2010)
M.N.H. Mollah, N. Sultana, M. Minami, S. Eguchi, Robust extraction of local structures by the minimum beta-divergence method. Neural Netw. 23(2), 226–238 (2010)
E. Parzen, On estimation of a probability density function and mode. Ann. Math. Stat. 33(3), 1065–1076 (1962)
S. Ren, K. He, R. Girshick, J. Sun, Faster R-CNN: Towards real-time object detection with region proposal networks. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017)
L. Wang, J. Zhu, M. Sheng, A. Cribb, S. Zhu, J. Pu, Simultaneous segmentation and bias field estimation using local fitted images. Pattern Recognit. 74, 145–155 (2018)
H. Wu, V. Appia, A. Yezzi, Numerical conditioning problems and solutions for nonparametric i.i.d. statistical active contours. IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1298–1311 (2013)
T. Yamano, A generalization of the Kullback–Leibler divergence and its properties. J. Math. Phys. 50(4), 79–561 (2009)
Z. Zhou, M. Dai, T. Wang, R. Zhao, Prior distribution-based statistical active contour model. Multimed. Tools Appl. 78(24), 35813–35833 (2019)
Z. Zhou, M. Dai, H. Zhong, Parametric shape prior model used in image segmentation. J. Syst. Eng. Electron. 27(5), 1115–1121 (2016)
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Dai, M., Zhou, Z., Wang, T. et al. Image Segmentation Using Level Set Driven by Generalized Divergence. Circuits Syst Signal Process 40, 719–737 (2021). https://doi.org/10.1007/s00034-020-01491-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-020-01491-x