B-Spline Curve Fitting Based on Gradient Vector Flow Deformable Models

In this paper, an algorithm for data points approximation with deformable models based on gradient vector flow is proposed. Firstly, the data points are projected onto an image plane to define the digital image composed of data points. The external force of data points is calculated as gradient vector flow. The kind of external force is a static force field, which calculated as a diffusion of the gradient vector, and the initial deformable contours are presented by B-spline curve. Then, the energy functional extremum problem of the B-spline deformable contour was addressed by finite element method. In this way, we get the deformable contours approximation to data points by the external force field. In the experimental results we verify this algorithm and demonstrate the utility of GVF deformable models on the curve fitting approach. The method presented in this paper needs not to parameterize the data points and can spend less computation time than the traditional fitting method. Furthermore, the method is more versatility for a variety of data points fitting, especially for complex convex-concave data points.