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A multiphase level set framework for image segmentation using the Mumford and Shah model. (English) Zbl 1012.68782
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:
 68U99 Computing methodologies and applications 68T45 Machine vision and scene understanding 68U10 Computing methodologies for image processing 68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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