Abstract: 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 topological 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.