计算射影与排列不变量的新方法  

New derivation of projective and permutation invariants

作　　者：王元斌[1] 

机构地区：[1]东北大学计算机应用技术研究所,辽宁沈阳110004

出　　处：《计算机工程与设计》2008年第20期5388-5390,5393,共4页Computer Engineering and Design

基　　金：国家科技部十五科技攻关基金项目(2004BA721A05)

摘　　要：给出了一种表示和计算离散有限点集的射影与排列不变量的简单有效方法。该不变量在计算机视觉、模式识别中有重要应用。首先导出了射影直线上4个点的基于一种对称函数的射影与排列不变量,该不变量等于这4个点的某个原始交比值,具有计算量低,不丢失分辨力等优点。然后根据这个简单的对称函数,结合基本的多项式对称函数,推导出了平面上5个点的两个函数无关的射影与排列不变量,以及空间中6个点的3个函数无关的射影与排列不变量。A simple and effective method for the representation and computation of the projective and permutation invariants of point sets is presented. These invariants are important in computer vision and pattern recognition. The projective and permutation invariant of four distinct points on a projective line based on a simple symmetric function is derived first. This projective and permutation invariant takes one of the six raw cross ratios of the four points as its value. The computational complexity is low and the discriminating power is retained. Then two functional independent projective and permutation invariants of five points on the projective plane and three functional independent projective and permutation invariants of six points in the space are derived based on the proposed simple symmetric function and the elementary symmetric polynomials.

关 键 词：模式识别 计算机视觉 射影不变量 排列不变量 交比 对称函数 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]