Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection |
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Authors: | Xue-Cheng Tai Oddvar Christiansen Ping Lin Inge SkjÆlaaen |
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Affiliation: | (1) Department of Mathematics, University of Bergen, Johannes Brunsgate 12, N-5007 Bergen, Norway;(2) Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543 |
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Abstract: | In this work, we are trying to propose fast algorithms for Mumford-Shah image segmentation using some recently proposed piecewise
constant level set methods (PCLSM). Two variants of the PCLSM will be considered in this work. The first variant, which we
call the binary level set method, needs a level set function which only takes values ±1 to identify the regions. The second
variant only needs to use one piecewise constant level set function to identify arbitrary number of regions. For the Mumford-Shah
image segmentation model with these new level set methods, one needs to minimize some smooth energy functionals under some
constrains. A penalty method will be used to deal with the constraint. AOS (additive operator splitting) and MOS (multiplicative
operator splitting) schemes will be used to solve the Euler-Lagrange equations for the minimization problems. By doing this,
we obtain some algorithms which are essentially applying the MBO scheme for our segmentation models. Advantages and disadvantages
are discussed for the proposed schemes.
We acknowledge support from the Norwegian Research Council and IMS of the National University of Singapore. |
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Keywords: | level set method image segmentation total variation regularization phase field model |
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