目的 图像分割是图像处理领域的重要研究内容之一,且应用广泛。在基于PDE和变分法的图像分割方法中,大部分图像分割模型的能量泛函均为非凸性,较容易陷入局部极小解,因而分割结果往往不尽如人意,且运算时间较慢。为此,本文根据背景去除模型的思想结合区域拟合的方法,提出了一种区域拟合的背景去除图像分割模型。方法 首先对背景去除模型进行改造;再结合区域拟合的方法对模型进行改进,并对改进模型进行凸优化处理;最后结合水平集和Split Bregman法对改进模型进行快速求解,获得全局最小值解。结果 针对改进模型在分割效果、计算效率及初始化位置对实验结果的影响这3个方面了进行数值实验,相较于ICV(improved Chan-Vese)模型、LK(Li-Kim)模型及CV(Chan-Vese)模型,本文模型能得到更优的分割效果,且在分割效果相似的情况下,本文模型较RSF(region-scalable fitting)模型耗时更短,同时当实验初始化位置不同时,实验亦能取得良好的分割效果。结论 在对于MRI(magnetic resonance imaging)图像以及合成图像等进行处理时,本文所给出的模型不仅能获得良好的分割效果,并且效率较高,而且从实验结果来看,本文模型具有一定的鲁棒性。

Objective 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. Method 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. Result 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. Conclusion 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.