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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: | 492 - 22 self |
BibTeX
@ARTICLE{Vese02amultiphase,
author = {Luminita A. Vese and Tony 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},
number = {3},
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.
Keyphrases
image segmentation shah model multiphase level set framework piecewise constant complex topology log level image denoising numerical result piecewise constant case 2-phase segmentation smooth optimal approximation triple junction four-color theorem piecewise smooth case sethian level new multiphase level multiphase level active contour model
