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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.

68U99Computing methodologies
68T45Machine vision and scene understanding
68U10Image processing (computing aspects)
68U05Computer graphics; computational geometry
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