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The proposed level set method by C-V is failed to control the local feature. In order to eliminate C-V method's defects, a novel segmentation model based on exponential boundary gradient speeding term is proposed, by incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented in less iteration. And the penalizing energy term eliminates the time-consuming re-initialization process. What's more, a termination criterion based on the length change of the evolving curve is proposed to ensure that the evolving curve can automatically stop on the true boundaries of objects. Large numbers of experiments indicate this model can not only selectively speed the segmentation of specific objects, but also can improve the segmentation accuracy of objects having weak boundaries.