Abstract: The Local Image Fitting (LIF) model is sensitive to the size, shape and position of initial contour. In order to solve the problem, a local image intensity fitting model combined with global information was proposed. Firstly, a global term based on global image information was constructed. Secondly, the global term was linearly combined with the local term of LIF model. Finally, an image segmentation model in the form of partial differential equation was obtained. Finite difference method was used in numerical implementation, simultaneously, a level set function was regularized by a Gaussian filter to ensure the smoothness of the level set function. In the segmentation experiments, when different initial contours are selected, the proposed model can get the correct segmentation results, and its segmentation time is only 20% to 50% of LIF model. The experimental results show that, the proposed model is not sensitive to the size, shape and position of the initial contour of evolutionary curve, it can effectively segment images with intensity inhomogeneity, and its segmentation speed is faster. In addition, the proposed model can segment some real and synthetic images quickly without initial contours.

Key words: image segmentation, Local Image Fitting (LIF) model, level set function, image with intensity inhomogeneity, initial contour

摘要： 针对局部图像拟合（LIF）模型对初始轮廓大小、形状和位置敏感的问题，提出一个结合全局信息的局部图像灰度拟合模型。首先，构造了一个基于全局图像信息的全局项；其次，将该全局项与LIF模型中的局部项线性组合；最后，得到了一个以偏微分方程形式存在的图像分割模型。数值实现采用有限差分法，同时采用高斯滤波器正则化水平集函数以确保水平集函数的光滑作用。在分割实验中，当选取不同的初始轮廓时，该模型均能得到正确的分割结果，且分割时间仅为LIF模型的20%到50%。实验结果表明，所提模型既对演化曲线初始轮廓的大小、形状和位置都不敏感，又能够有效地分割灰度不均图像，且分割速度较快。此外，在无初始轮廓的情形下，该模型能快速分割一些真实图像和人造图像。

关键词: 图像分割, 局部图像拟合模型, 水平集函数, 灰度不均图像, 初始轮廓