We derived a new nonlinear governing partial differential equation (PDE) for calculating the gradient vector fields (GVFs) based on the variational method. By using the topolo-gical analysis of GVFs, the skeleton curves of an image were obtained. The main advantage of this method is simplicity. It works directly on the gray-scale images without the segmentation processing. We tested the proposed method on the Newton-ring interference fringe pattern, and compared it with the well-studied and widely-used block thresholding method and fringe extreme tracking method. The experimental results demonstrated the good performance of the proposed method.%基于变分法提出用于计算灰度图像梯度矢量场的非线性偏微分控制方程,利用图像梯度矢量场的拓扑性,可实现骨架线的提取.该方法的主要优点是它的简单性,可直接应用于灰度图像,不需要任何的分割处理.把提出的方法应用于牛顿环干涉条纹中,并与广泛使用的分块二值化细化算法和极值跟踪法进行了比较,实验结果表明了本方法的良好性能.
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