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Zbl 1012.68782
Vese, Luminita A.; Chan, Tony F.
A multiphase level set framework for image segmentation using the Mumford and Shah model. (English)
[J] Int. J. Comput. Vis. 50, No.3, 271-293 (2002). ISSN 0920-5691; ISSN 1573-1405/e

Summary: 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. 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.

MSC 2000:: *68U99 Computing methodologies
68T45 Machine vision and scene understanding
68U10 Image processing
68U05 Computational geometry, etc.

Keywords: energy minimization; multi-phase motion; image segmentation; level sets; curvature; PDE's; denoising; edge detection; active contours

Cited in: Zbl 1216.65024 Zbl 1195.49036

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