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Image segmentation using a multilayer level-set approach. (English) Zbl 1216.65024

Summary: We propose an efficient multilayer segmentation method based on implicit curve evolution and on variational approach. The proposed formulation uses the minimal partition problem as formulated by D. Mumford and J. Shah [Commun. Pure Appl. Math. 42, No. 5, 577–685 (1989; Zbl 0691.49036)], and can be seen as a more efficient extension of the segmentation models previously proposed in T. F. Chan and L. A. Vese [in: Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, Vol. 1682, 141–151 (1999); IEEE Trans. Image Process. 10, No. 2, 266–277 (2001; Zbl 1039.68779); Int. J. Comput. Vis. 50, No. 3, 271–293 (2002; Zbl 1012.68782)]. The set of unknown discontinuities is represented implicitly by several nested level lines of the same function, as inspired from prior work on island dynamics for epitaxial growth [R. E. Caflisch et al., Appl. Math. Lett. 12, No. 4, 13–22 (1999; Zbl 0937.35191); S. Chen et al., J. Comput. Phys. 167, No. 2, 475–500 (2001; Zbl 0993.74081)]. We present the Euler-Lagrange equations of the proposed minimizations together with theoretical results of energy decrease, existence of minimizers and approximations. We also discuss the choice of the curve regularization and conclude with several experimental results and comparisons for the piecewise-constant segmentation of gray-level and color images.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U10 Computing methodologies for image processing
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