Image segmentation is one of the most important research contents in the field of image processing and is widely used in real life. Most of the involved models that are based on PDE or calculus of variations are non-convex

so they are easy to get into local minimums

and most of these experiment results which we get are not satisfactory. Besides

the calculation time of these models is too slow to meet the actual demand. Therefore

according to the background removal model and the regional fitting method

we proposed a new image segmentation model in this article. Firstly

following the principle of the background removal

we did some reforms to the original background removal model. With the application of region-scalable fitting method and Heaviside function we get a new region-scalable fitting background removal model. However

the improved model here is not a convex model

and cannot get the global minimum solution

so we make convex optimization to the improved model to get a convex model to solve this problem. Finally

by using the Split Bregman method and level set method

the global minimum solution of the model can be obtained. Comparing with ICV(improved Chan-Vese) model

LK(Li-Kim) model and CV(Chan-Vese) model

several numerical experiment results show that the proposed model in this article has a better performance on image segmentation. Meanwhile

the experiment also demonstrates that the proposed model in this article is more efficient than RSF(region-scalable fitting) model in the case of similar segmentation results. Finally the experiment results also show that different initial positions have little effect on image segmentation results which demonstrates that our model is low sensitive to initialize contour curve. When dealing with the MRI images and synthetic images

the model presents in this paper can not only obtain good segmentation results

but also has a high efficiency on segmentation. The experiment results also show that the model in this article is robust.