An improved hybrid gradient variation level set method for image segmentation and bias correction

References

• T.F. Chan and L.A. Vese, Active contours without edges, IEEE Trans. Image Process. 10(2) (2001), pp. 266–277.
   PubMed Web of Science ®Google Scholar
• Q. Ge, L. Xiao, H. Huang, and Z. Wei, An active contour model driven by anisotropic region fitting energy for image segmentation, Digit. Signal Process. 23 (2013), pp. 238–243.
   Web of Science ®Google Scholar
• E. Gocei and E.D. Martinez, A level set method with Sobolev gradient and Haralick edge dection, Glob. J. Technol. 5 (2014), pp. 131–140.
   Google Scholar
• R.K. Goodrich, A Riesz representation theorem, Proc. Amer. Math. Soc. 24(3) (1970), pp. 629–636.
   Google Scholar
• C. He, Y. Wang, and Q Chen, Active contours driven by weighted region-scalable fitting energy based on local entropy, Signal Process. 92 (2012), pp. 587–600.
   Web of Science ®Google Scholar
• C. Li, C. Kao, J. Gore, and Z. Ding, Implicit active contours driven by local binary fitting energy, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition(CVPR), IEEE Computer Society, Washington, DC, 2007, pp. 1–7.
   Google Scholar
• C. Li, C. Xu, C. Gui, and M.D. Fox, Level set evolution without re-initialization: A new variational formulation, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vol. 1, 2005, pp. 430–436.
   Google Scholar
• C. Li, C. Xu, C. Gui, and M. D. Fox, Distance regularized level set evolution and its application to image segmentation, IEEE Trans. Image Process. 19(12) (2010), pp. 3243–3254.
   PubMed Web of Science ®Google Scholar
• C. Li, R. Huang, Z. Ding, C. Gatenby, D.N. Metaxas, and 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) (2011), pp. 2007–2016.
   PubMed Web of Science ®Google Scholar
• D. Li, W. Li, and Q. Liao, Active contours driven by local and global probability distributions, J. Vis. Commun. Image Represent. 24 (2013), pp. 522–533.
   Web of Science ®Google Scholar
• L. Liu, L. Zeng, K. Shen, and X. Luan, Exploiting local intensity information in Chan–Vese model for noisy image segmentation, Signal Process. 93 (2013), pp. 2709–2721.
   Web of Science ®Google Scholar
• L. Liu, Q. Zhang, M. Wu, W. Li, and F. Shang, Adaptive segmentation of magnetic resonance images with intensity inhomogeneity using level set method, Magn. Reson. Imaging. 31 (2013), pp. 567–574.
   PubMed Web of Science ®Google Scholar
• B.S. Morse and D. Schwartzwald, Image magnification using level-set reconstruction, Comput. Vis. Pattern Recognit. 1 (2001), pp. 1–8.
   Google Scholar
• J.W. Neuberger, Sobolev gradients and differential equations, in Springer Lecture Notes in Mathematics, Vol. 1670, Springer-Verlag, Berlin, Heidelberg, 1997.
   Google Scholar
• S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys. 79(1) (1988), pp. 12–49.
   Web of Science ®Google Scholar
• R.J. Renka, Image segmentation with a Sobolev gradient method, Nonlinear Anal. 71(12) (2009), pp. 774–780.
   Web of Science ®Google Scholar
• W.B. Richardson, Steepest descent using smoothed gradients, Appl. Math. Comput. 112 (2000), pp. 241–254.
   Web of Science ®Google Scholar
• H. Schaeffer and L. Vese, Active contours with free endpoints, J. Math. Imaging Vision 49 (2014), pp. 20–36.
   Web of Science ®Google Scholar
• G. Sundaramoorthi and A. Yezzi, Sobolev active contours, Int. J. Comput. Vis. 73(3) (2007), pp. 345–366.
   Web of Science ®Google Scholar
• Y. Tian, F. Duan, M. Zhou, and Z. Wu, Active contour model combining region and edge information, Mach. Vis. Appl. 24 (2013), pp. 47–61.
   Web of Science ®Google Scholar
• L.A. Vese and T.F. Chan, A multiphase level set framework for image segmentation using the Mumford and Shah model, Int. J. Comput. Vis. 50 (2002), pp. 271–293.
   Web of Science ®Google Scholar
• L. Wang, C. Li, Q. Sun, D. Xia, and C.-Y. Kao, Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation, Comput. Med. Imaging Graph. 33 (2009), pp. 520–531.
   PubMed Web of Science ®Google Scholar
• X.-F. Wang, D.-S. Huang, and H. Xu, An efficient local Chan–Vese model for image segmentation, Pattern Recognit. 43(3) (2010), pp. 603–618.
   Web of Science ®Google Scholar
• C.-Y. Yu, W.-S. Zhang, Y.-Y. Yu, and Y. Li, A novel active contour model for image segmentation using distance regularization term, Comput. Math. Appl. 65 (2013), pp. 1746–1759.
   Web of Science ®Google Scholar
• Y. Yuan and C. He, Variational level set methods for image segmentation based on both L2 and Sobolev gradients, Nonlinear Anal., Real World Appl. 13 (2012), pp. 959–966.
   Web of Science ®Google Scholar
• K. Zhang, H. Song, and L. Zhang, Active contour driven by local image fitting energy, Pattern Recognit. 43(4) (2009), pp. 1199–1206.
   Web of Science ®Google Scholar