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The segmentation of weak boundary is still a difficult problem, especially sensitive to noise, which leads to the failure of segmentation. Based on the previous works, by adding the boundary indicator function with L2,1 norm, a new convergent variational model is proposed. A novel strategy for the weak boundary image is presented. The existence of the minimizer for our model is given, by using the alternating direction method of multipliers (ADMMs) to solve the model. The experiments show that our new method is robust in segmentation of objects in a range of images with noise, low contrast, and direction.