A global optimization SAR image segmentation model can be easily
  transformed to a general ROF denoising model
Guangming Liu Qi Liu Jing Liang
In this paper, we propose a novel locally statistical active contour model
(LACM) based on Aubert-Aujol (AA) denoising model and variational level set
method, which can be used for SAR images segmentation with intensity
inhomogeneity. Then we transform the proposed model into a global optimization
model by using convex relaxation technique. Firstly, we apply the Split Bregman
technique to transform the global optimization model into two alternating
optimization processes of Shrink operator and Laplace operator, which is called
SB_LACM model. Moreover, we propose two fast models to solve the global
optimization model , which are more efficient than the SB_LACM model. The first
model is: we add the proximal function to transform the global optimization
model to a general ROF model[29], which can be solved by a fast denoising
algorithm proposed by R.-Q.Jia, and H.Zhao; Thus we obtain a fast segmentation
algorithm with global optimization solver that does not involve partial
differential equations or difference equation, and only need simple difference
computation. The second model is: we use a different splitting approach than
one model to transform the global optimization model into a differentiable term
and a general ROF model term, which can be solved by the same technique as the
first model. Experiments using some challenging synthetic images and Envisat
SAR images demonstrate the superiority of our proposed models with respect to
the state-of-the-art models.