A multiphase level set framework for image segmentation using the Mumford and Shah model. (English) Zbl 1012.68782

Vese, Luminita A.; Chan, Tony F.

Int. J. Comput. Vis. 50, No. 3, 271-293 (2002).

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)

Keywords:

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