基于安德森加速的快速 B 样条拟合算法

曲线拟合技术已被广泛地应用于图像处理、工程实验等领域。其中，B 样条曲线拟 合是曲线拟合中最常见的方法，它具有局部性好、连续性好等优点，但拟合精度一般较低。在实 际应用中，B 样条曲线拟合对于精度和速度的要求都较高。为了提升平面 B 样条曲线拟合速度， 将安德森加速的想法应用到曲线拟合的方法之中，提出一种基于安德森加速的拟牛顿方法。首先 设定一个初始形状，然后根据初始形状找到其每个数据点的投影点的位置参数，然后利用安德森 加速计算出控制点的相应位置，迭代进行以上 2 步，直到结果收敛。实验结果表明，该方法在收 敛速度和迭代时间上均优于其他方法。

Anderson acceleration for B-spline curve fitting

In recent years, curve fitting technology has been widely used in image processing, engineering experiments and other fields. Among them, B-spline curve fitting is the most common method in curve fitting, the method of B-spline curve fitting has the advantages of locality, continuity but the fitting precision is relatively low. In practical application, B-spline curve fitting requires higher accuracy and speed. In order to increase the speed of planar B-spline curve fitting, Anderson acceleration is applied to the method of planar B-spline curve fitting. And then a quasi-Newton method based on Anderson acceleration is proposed. Firstly, an initial shape is set, and then the position parameters of the projection point of each data point are found according to the initial shape. Then, the corresponding position of control points is calculated by Anderson acceleration, and the above two steps are iterated until the result converges. The experimental results show that the proposed method in this paper outperforms other methods with respect to convergence speed and iteration time.