基于遗传算法的B样条曲线拟合改进算法

Improved B-spline curve fitting algorithm based on genetic algorithm

B样条曲线拟合应用于绘制离散数据点的变化趋势,一般采用数据逼近或者迭代的方法得到,是图像处理和逆向工程中的重要内容。针对待拟合曲线存在多峰值、尖点、间断等问题,提出一种基于遗传算法的B样条曲线拟合算法。首先利用惩罚函数将带约束的曲线优化问题转换为无约束问题,然后利用改进的遗传算法来选择合适的适应度函数,再结合模拟退火算法自适应调整节点的数量和位置,在寻优的过程中找到最优的节点向量,持续迭代直到产生最终的优良重建曲线为止。实验结果表明,该算法有效地提高了精度并加快了收敛速度。

B-spline curve fitting is applied to draw the changing trend of discrete data points,which usually obtains by data approximation or iterative method.It plays an important part in image processing and reverse engineering.Aiming at the situations where multi-peak,cuspidal point or discontinuity exists in the curve to fit,this paper proposed a B-spline curve fitting algorithm based on genetic algorithm.Firstly it used the penalty function to transform the constrained optimization problem into an unconstrained problem.Then it used an improved genetic algorithm to select an adaptive fitness function,and adjusted the number and positions of nodes adaptively by combining the simulated annealing algorithm to find the optimal node vector.The iterations continued until generating the final good reconstruction curve.Experimental results show that the algorithm improves accuracy and speeds up convergence effectively.