改进的二阶总广义变分图像前后景分割模型

针对总变分TV图像前后景分割模型易导致阶梯效应的缺陷，提出了二阶总广义变分TGV图像前后景分割模型。为进一步提升图像分割质量，在TGV前后景分割模型的正则项中引入边缘指示函数，使其在图像边缘区域减弱扩散，较好地保护边缘；在图像平滑区域增强扩散，有效地消除噪声。为突出前景信息，用矩形框标出图像的前景信息，对框内部、外部和边缘的像素做距离映射，并根据能量最小化原则，在二阶TGV模型的数据项中引入此距离映射函数，使模型总能量更小。最后，提出了一种有效的原始对偶分割算法来求解模型。实验表明，新模型不但能够去除阶梯效应现象，保持图像的边缘信息，还使得模型总能量更小，分割得到的图像视觉效果更好。

An image foreground and background segmentation model based on improved second order total generalized variation

In order to segment an image into foreground and background and overcome the staircase effect often caused by the total variation (TV) segmentation model, we propose a new image foreground and background segmentation model based on the second order total generalized variation (TGV). To improve the quality of image segmentation, an edge indicator function is introduced to the regularization term of the second order TGV-based image foreground and background segmentation model, which can reduce the diffusion to preserve image edge features in image edge regions, and enhance the diffusion to remove impulse noise and overcome the staircase effect in image smooth regions. Then, in order to highlight the foreground information of the image, we mark the foreground information of the image with a rectangular frame and perform distance mapping on the pixels inside the frame, outside of the frame, and on the edges. In addition, according to the energy minimization principle, the distance mapping function is introduced into the data item of the second-order TGV model so that the total energy of the model can be smaller. Finally, we propose a primal-dual segmentation method to solve the proposed model effectively. Experimental results show that the proposed model can not only avoid staircase effect, but also keep the edge information of the image and reduce the total energy of the model. The segmented image has a better visual effect.