基于二阶差商波动最小的坏点挑选及曲线光顺算法  

Bad Data Selecting and Curve Smoothing Arithmetic Based on Minimizing the Undulation of the Divided Difference

作　　者：高学峰[1] 田中旭[2] 褚伟波[1] 

机构地区：[1]上海大学机电工程与自动化学院,上海200072 [2]上海交通大学内燃机研究所,上海200030

出　　处：《中国图象图形学报》2007年第12期2184-2188,共5页Journal of Image and Graphics

基　　金：国家自然科学基金项目(50475182);上海市自然科学基金项目(04ZR14053);上海市重大科技攻关项目(04dz12011)

摘　　要：针对2维数据坏点挑选问题,以节点二阶中心差商的波动最小为基础,首先构造了表征节点Pi在提高样条曲线光顺度方面潜力大小的函数,然后给出了一种基于结点差商波动最小的坏点挑选算法。并将该算法利用一些实例与曲率极值法进行了对比分析,结果表明,该算法能有效标出坏点位置。另外,基于节点二阶中心差商波动最小的原则,还给出了一种通过将节点在允许范围内进行适当调整,以减小样条曲线二阶导函数波动的光顺处理算法。实例验证结果表明,此样条曲线光顺处理算法能够有效地控制三次样条曲线二阶导函数的波动,即能提高曲线的光顺程度。As to the selection of the 2D bad data, this paper used the method of minimizing the undulation of the divided difference of 2D data and presented an algorithm that begins with constructing a function that can compute each knot＇ s potential on improving spline curve＇ s smoothness. After analyzing some examples that using the extreme curvature-value method and the method stated previously, it indicated that the algorithm this paper put forwards marked the positions of the bad data efficiently. Based on the method of minimizing the undulation of the divided difference of 2D data, this paper also gave a smoothing treatment for cubic spline curve to appropriately relocate the positions of the knots in the permissive scope. The numerical example at the last section demonstrated that this algorithm can effectively control the undulation of the cubic spline＇ s second-derivative function.

关 键 词：坏点 光顺处理 三次样条曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]