基于四阶偏微分方程平滑的图像分割新方法

在方向曲率模值描述图像平滑度的泛函基础上，推导出一种四阶偏微分方程(PDE)图像降噪模型，在有效降噪的同时，较好地保持了边缘。该方法处理结果为分段线性图像，且在目标边缘处梯度存在阶跃。利用降噪结果的这一特点，提出一种新测地线主动轮廓模型。实验表明，新模型不但稳定，轮廓提取能力强，而且收敛速度快。

New image segmentation method based on fourth-order partial differential equations for noise removal

A class of fourth-order partial differential equations (PDEs) was proposed to optimize the trade-off between noise removal and edge preservation. These PDEs can remove noise and preserve edges by approximating an observed image with a piecewise planar image, and the gradient of the processed image isn't continuous at the boundary. A novel scheme for the detection of object boundaries was presented. The technique is based on geodesic active contours evolving in time according to intrinsic geometric measures of the Laplacian of image, which is infinite at the boundary after being processed by our fourth-order partial differential equations. The previous models of geodesic active contours were improved, and could detect boundaries more stably and quickly.