Abstract
In this paper, we introduce a new variational image segmentation model based on a non-convex regularization and an efficient parameter selection to better conserve the image structures and control the segmentation of the boundary with less intensity inhomogeneities. The proposed regularization associated to the automatic selection of the parameter \(\lambda \) allows us to segment an image with low intensities loss. In addition, we introduce fast and efficient optimization algorithms that can handle the non-smoothness of the objective function. In fact, the output segmented regions in the image, as well as edges construction are better conserved. Selected numerical experiments demonstrate that the segmented images can cope with some sate of art segmentation results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo. Fast image recovery using variable splitting and constrained optimization. IEEE transactions on image processing, 19(9):2345–2356, 2010
K. A. Berdawood, A. Nachaoui, R. Saeed, M. Nachaoui, and F. Aboud. An alternating procedure with dynamic relaxation for cauchy problems governed by the modified helmholtz equation. Advanced Mathematical Models & Applications, 5(1), 131–139, 2020
L. Chen, Y. Li, and T. Zeng. Variational image restoration and segmentation with Rician noise. J. Sci. Comput., 78(3):1329–1352, 2019
W. Dong, X. Li, L. Zhang, G. Shi, Sparsity-based image denoising via dictionary learning and structural clustering. In: CVPR 2011, pp. 457–464. IEEE (2011)
P. Dvalishvili, A. Nachaoui, M. Nachaoui, T. Tadumadze, On the well-posedness of the cauchy problem for a class of differential equations with distributed delay and the continuous initial condition. volume 43, pp. 146–160. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan 9 B Vahabzdeh (2017)
E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson. Optimal parameter selection for the alternating direction method of multipliers (admm): quadratic problems. IEEE Transactions on Automatic Control, 60(3), 644–658, 2014
M. Hakim, A. Ghazdali, A. Laghrib. A multi-frame super-resolution based on new variational data fidelity term. Appl. Math. Model. (2020)
M. Hong and Z.-Q. Luo. On the linear convergence of the alternating direction method of multipliers. Mathematical Programming, 162(1–2), 165–199, 2017
M. Howard, M. C. Hock, B. T. Meehan, and L. E. Dresselhaus-Cooper. A locally adapting technique for edge detection using image segmentation. SIAM J. Sci. Comput., 40(4):B1161–B1179, 2018
M. Jung and M. Kang. Efficient nonsmooth nonconvex optimization for image restoration and segmentation. Journal of Scientific Computing, 62(2), 336–370, 2015
S.-H. Kim, K.-J. An, S.-W. Jang, and G.-Y. Kim. Texture feature-based text region segmentation in social multimedia data. Multimedia Tools and Applications, 75(20), 12815–12829, 2016
A. Laghrib, A. Ben-Loghfyry, A. Hadri, and A. Hakim. A nonconvex fractional order variational model for multi-frame image super-resolution. Signal Processing: Image Communication, 67:1–11, 2018
A. Laghrib, A. Chakib, A. Hadri, and A. Hakim. A nonlinear fourth-order pde for multi-frame image super-resolution enhancement. Discrete & Continuous Dynamical Systems-B, 25(1):415, 2020
A. Laghrib, M. Ezzaki, M. El Rhabi, A. Hakim, P. Monasse, and S. Raghay. Simultaneous deconvolution and denoising using a second order variational approach applied to image super resolution. Computer Vision and Image Understanding, 168:50–63, 2018
F. Li, C. Shen, and C. Li. Multiphase soft segmentation with total variation and \(H^1\) regularization. J. Math. Imaging Vision, 37(2), 98–111, 2010
S. Lu, S.V. Pereverzev. Regularization theory for ill-posed problems, volume 58 of Inverse and Ill-posed Problems Series. De Gruyter, Berlin, 2013. Selected topics
Z. Lu, X. Jiang, G. Huo, D. Ye, B. Wang, Z. Zheng, A fast T-spline fitting method based on efficient region segmentation. Comput. Appl. Math. 39(2) (2020)
A. Mitiche, I.B. Ayed, Variational and Level Set Methods in Image Segmentation, volume 5. Springer Science & Business Media (2010)
A. Nachaoui, M. Nachaoui, Iterative methods for forward and inverse bioelelectric field problem, in International Conference on Applied Mathematics, Modeling and Life Sciences, Icamls’ 18 (2018)
A. Nachaoui, M. Nachaoui, A. Chakib, M.A. Hilal, Some novel numerical techniques for an inverse Cauchy problem. J. Comput. Appl. Math. 381, 113030, 21 (2021)
M. Nachaoui. Parameter learning for combined first and second order total variation for image reconstruction. Advanced Mathematical Models & Applications, 5(1), 53–69, 2020
S. S. Ngambeki, X. Ding, and M. D. Nachipyangu. Real time face recognition using region-based segmentation algorithm. Int. J. Eng. Res. Technol, 4(4), 875–878, 2015
S. Pare, A.K. Bhandari, A. Kumar, G.K. Singh, S. Khare, Satellite image segmentation based on different objective functions using genetic algorithm: A comparative study. in 2015 IEEE International Conference on Digital Signal Processing (DSP), pp. 730–734 (2015)
C. Van Chung, J. De los Reyes, C. Schönlieb, Learning optimal spatially-dependent regularization parameters in total variation image denoising. Inverse Problems 33(7), 074005 (2017)
Y. Wang, J. Yang, W. Yin, and Y. Zhang. A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences, 1(3), 248–272, 2008
Y. Yuan and C. He. Variational level set methods for image segmentation based on both \(L^2\) and Sobolev gradients. Nonlinear Anal. Real World Appl., 13(2):959–966, 2012
T. Zhang, Analysis of multi-stage convex relaxation for sparse regularization. J. Mach. Learn. Res. 11(3) (2010)
F. Zhao and X. Xie. An overview of interactive medical image segmentation. Annals of the BMVA, 2013(7), 1–22, 2013
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Nachaoui, M., Laghrib, A., Hakim, M. (2021). A New Space-Variant Optimization Approach for Image Segmentation. In: Nachaoui, A., Hakim, A., Laghrib, A. (eds) Mathematical Control and Numerical Applications. JANO'13 2021. Springer Proceedings in Mathematics & Statistics, vol 372. Springer, Cham. https://doi.org/10.1007/978-3-030-83442-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-83442-5_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-83441-8
Online ISBN: 978-3-030-83442-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)