Abstract
Based on the expression of a open surface on which images are defined as intersection of zero level set of a signed distance function and a binary label function and by making use of concepts of intrinsic gradient and divergence, the partitioning strategy of regions on a surface via m binary label functions for 2m regions, a general varaitional model for multiphase image segmentation on an implicit open surface is proposed. Based on techniques of convex relaxation and thresholding, the gradient descent method, dual method, Split Bregman method, augmented Lagrange method are designed, where, the last three methods are fast ones. In order to improve its efficiency and make it implement easily, we propose another new method based on dual method without convex relaxation and thresholding of binary label functions, which is referred as direct dual method. Finally, numerical examples validate the model and its fast algorithms proposed in this paper.
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References
Bertalmio, M., Cheng, L., Osher, S., Sapiro, G.: Variational problems and partial differential equations on implicit surface. J. of Com. Phy. 174(2), 759–780 (2001)
Li, J.-G., Pan, Z.-K., Wei, W.-B., Li, C.-F.: A variational level set method for image segmentation on implicit surfaces. Journal of Image and Graphics 15(5), 808–813 (2010)
Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Tran. on Image Processing 10(2), 266–277 (2001)
Osher, S., Fedkiw, R.: The level set method and dynamic implicit surfaces. Springer (2002)
Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the mumford and shah model. Int. J. of Com. Vis. 50(3), 271–293 (2002)
Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20(1), 89–97 (2004)
Goldstein, T., Osher, S.: The Split Bregman algorithm for L1 regularized problems. SIAM Journal on Imaging Sciences 2(2), 323–343 (2009)
Wu, C., Tai, X.-C.: Augmented Lagrangian method, dual methods, and Split Bregman iteration for ROF, vectorial TV, and high order models. SIAM J. Ima. Sci. 3(3), 300–339
Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J.-P., Osher, S.: Fast global minimization of the active contour/snake model. Journal of Mathematical Imaging and Vision 28(2), 151–167 (2007)
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Duan, J., Pan, Z., Wei, W., Liu, C., Wang, G. (2013). A Variational Model for Multiphase Image Segmentation on an Implicit Open Surface and Its Fast Algorithms. In: Yang, J., Fang, F., Sun, C. (eds) Intelligent Science and Intelligent Data Engineering. IScIDE 2012. Lecture Notes in Computer Science, vol 7751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36669-7_97
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DOI: https://doi.org/10.1007/978-3-642-36669-7_97
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