梯度向量流的各向异性扩散分析

Anisotropic Diffusion Analysis of Gradient Vector Flow

为了解决梯度向量流力场(gradient vector flow,简称GVF)难以进入目标凹部的问题,提出了一种新的主动轮廓模型外力场——各向异性梯度向量流.GVF的扩散项是各向同性且光滑性强的拉普拉斯算子,它在各个方向的扩散速度相同.拉普拉斯算子根据图像的局部结构可分为沿边界法线和切线方向的扩散,沿切线方向的扩散具有增强边界的作用,而法线方向扩散具有去除噪音、扩散力场的作用.基于分析二者在扩散过程中的作用,提出了一种各向异性梯度向量流扩散方法,切线和法线方向的扩散速度可以根据图像的局部结构自适应地选择.实验结果表明,与GVF相比,所提出的方法考虑了扩散过程中法线和切线方向的不同作用,能够进入细长的凹部,并改进了分割结果.

A new external force field for active contour model, called anisotropic gradient vector flow, is presented to solve the problem that gradient vector flow （GVF） is difficult to enter the indentation. The diffusion term of GVF is the isotropic and highly smooth Laplacian operator with the same diffusion speed along tangent and normal directions. The diffusion of Laplacian operator is actually decomposed into the tangent and normal directions by the local image structures. Diffusion along the tangent direction enhances the edge, while diffusion along the normal direction removes noise and propagates the force field. This paper develops an anisotropic gradient vector flow based on the analysis of diffusion process of GVF along tangent and normal directions. In the proposed method, the diffusion speeds along the normal and tangent directions are adaptively obtained by the local structure of the image. The experimental results show that compared with GVF, the proposed method considering these two diffusion actions can enter long, thin indentation and improve the segmentation.