Journal of Biomedical Imaging
On the Length and Area Regularization for Multiphase Level Set Segmentation
International Journal of Computer Vision
A Multiphase Image Segmentation Method Based on Fuzzy Region Competition
SIAM Journal on Imaging Sciences
Multiphase image segmentation using a phase-field model
Computers & Mathematics with Applications
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
Statistical Density Estimation Using Threshold Dynamics for Geometric Motion
Journal of Scientific Computing
Active Contours with Free Endpoints
Journal of Mathematical Imaging and Vision
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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, and can be seen as a more efficient extension of the segmentation models previously proposed in Chan and Vese (Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, Vol. 1682, pp. 141–151, 1999, IEEE Trans Image Process 10(2):266–277, 2001), and Vese and Chan (Int J Comput Vis 50(3):271–293, 2002). 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 (Caflisch et al. in Appl Math Lett 12(4):13, 1999; Chen et al. in J Comput Phys 167:475, 2001). 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 piecewise-constant segmentation of gray-level and color images.