带方向信息的薄板样条插值函数及其应用  

Thin Plate Spline Interpolation Function with Orientation Information and Its Application

作　　者：吴敏 郭田德 韩丛英 WU Min;GUO Tiande;Han CONGYING(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Key Laboratory of Big Data Mining and KnowlttLyc Management,Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049 [2]中国科学院大学数学科学学院,中国科学院大数据挖掘与知识管理重点实验室,北京100049

出　　处：《应用数学学报》2021年第5期659-677,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11731013,11991022,U19B2040,11571014);中央高校基本科研业务费专项资金资助项目。

摘　　要：薄板样条(TPS)函数是一个很好的形变分析工具,常用于图像配准,传统的薄板样条函数只是利用特征点的坐标信息,而现实中很多特征点都带有方向信息,比如指纹细节点和sift特征点.为了在薄板样条函数中利用方向信息,本文在传统薄板样条目标函数基础上增加了方向平行惩罚项及方向一致性惩罚项,根据变分法的结论,目标函数的求解转换为求解一个微分方程,用格林函数法求解这个微分方程,从而得到带方向信息的薄板样条函数新形式.本文得到的薄板样条函数适合于任意维度的点集,在指纹图像配准和人造点集插值上的实验表明,和传统薄板样条函数相比,本文提出的薄板样条函数对于带方向信息的图像配准和点集插值更加准确.The thin-plate spline(TPS)function is a good deformation analysis tool,which is often used for image registration.The traditional TPS function only uses the coordinate information of feature points,but in reality,many feature points have orientation information,such as fingerprint minutiae and sift feature points.In order to use the orientation information,this paper adds a orientation parallel penalty item and a orientation consistency penalty item based on the traditional TPS objective function.According to the conclusion of the variational method,the solution of the objective function is transformed into solving a differential equation,which is solved by the Green function method,so that a new form of the TPS function with orientation information is obtained.The TPS function obtained in this paper is suitable for point sets of any dimension.Experiments on fingerprint image registration and artificial point set interpolation show that the TPS function proposed in this paper is more accurate for image registration and point set interpolation with orientation information.

关 键 词：薄板样条 点集插值 图像配准 变分法 

分 类 号：O212.7[理学—概率论与数理统计]