镜像等距不变量的构造及其应用  

Construction Method for Mirror Isometric Invariant and Its Applications

作　　者：胡平[1,2] 李海洋[1,2] 曹伟国[1,2] 李华[1,2] 

机构地区：[1]中国科学院计算技术研究所计算机应用研究中心,北京100190 [2]中国科学院大学,北京100190

出　　处：《计算机辅助设计与图形学学报》2013年第7期1005-1011,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家"九七三"重点基础研究发展计划项目(2004cb318000);国家自然科学基金重点项目(60873164);国家自然科学基金(60533090)

摘　　要：提出一种镜像等距不变量的构造方法.在可定向曲面上找到2条相交的测地线,并在交点处计算2个切向量以及它们的叉积,记录叉积的方向;再利用方向和曲面的定向情况判断叉积的符号,利用带符号的叉积的模构造积分核,以此扩展等距不变量的构造框架,得到了一组新的不变量.这种不变量既有等距不变性,又能根据符号反映两者是否有镜像关系.通过在人手模型上进行了大量实验的结果表明,该方法对镜像等距的物体具有良好的识别和区分效果.We present a method of constructing mirror isometric invariant. Firstly, we look for two intersecting geodesics on the orientable Surface and two tangent vectors at the intersecting point. Then the cross product of two tangent vectors is calculated, and the direction of cross product is recorded. In the following step, the sign of the cross product is determined via the direction of cross product and the surface, and a new integral kernel is constructed through this cross product. Thus, the framework of isometric invariants is extended by this new kernel, and a new set of invariants can be obtained. All invariants are isometric, and can reflect the mirror relationship of the two objects as well. Several experiments are done on the human hand models. The results show that objects can be recognized and distinguished using these mirror isometric invariants with high efficiency.

关 键 词：非刚体 镜像变换 等距变换 不变量 目标识别 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]