## A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model (2002)

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Venue: | International Journal of Computer Vision |

Citations: | 319 - 21 self |

### BibTeX

@ARTICLE{Vese02amultiphase,

author = {Luminita A. Vese and Tony F. Chan and Tony and F. Chan},

title = {A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model},

journal = {International Journal of Computer Vision},

year = {2002},

volume = {50},

pages = {271--293}

}

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### Abstract

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141--151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266--277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.