基于MAP的结合局部和全局统计正则的活动轮廓模型

Active Contour Model Based on MAP Combining Local and Global Statistical Regularization

摘要: 为分割灰度不均匀或者噪声污染的复杂图像，本文提出了一个基于最大后验概率准则(MAP)的结合局部和全局统计正则的活动轮廓模型。首先假设被灰度不均和噪声污染的观测图像服从局部高斯分布；而局部均值图像和局部方差图像在目标和背景区域分别服从全局高斯分布和均匀分布。然后利用3个假设分别构建局部和全局统计正则项，基于MAP准则建立变分活动轮廓模型，并在模型中引入水平集函数的弧长项和H−1正则项，使得水平集函数在演化过程中保持稳定和平滑。最后采用变分法和梯度下降算法对所提的多目标优化模型进行数值求解。数值实验以合成图像和自然图像为实验对象，验证了本文模型对灰度不均和复杂边界的图像具有良好的分割效果，此外还对初始轮廓和噪声鲁棒。并且和几个经典的变分活轮廓模型进行了对比实验，本文模型展示了最优的实验效果。

Abstract: To segment complex images with intensity inhomogeneity or noise pollution, an active contour model based on maximum a posteriori probability (MAP) criterion combining local and global statistical regularity is proposed in this paper. First, it is assumed that the real image obeys a global Gaussian distribution in the background and the object region respectively, while the observed image polluted by intensity inhomogeneity and noise obeys a local Gaussian distribution. Then, the local and global statistical regularization term is constructed using three assumptions, and the variational active contour model is established based on the MAP criterion. The length term and H−1 regularization term of the level set function are introduced into the model, so that the level set function is stable and smooth in the evolution process. Finally, variational method and gradient descent algorithm are used to solve the proposed multi-objective optimization model. Numerical experiments on synthetic and natural images show that the proposed model has good segmentation effect on images with intensity inhomogeneity and complex boundaries, and is robust to initial contour and noise. Compared with several classical variational active contour models, the proposed model has the optimal experimental results.