基于黎曼流形的平面目标识别  

Planar Object Recognition Based on Riemannian Manifold

作　　者：李广伟[1,2,3] 刘云鹏[1,3] 尹健[4] 史泽林[1] 

机构地区：[1]中国科学院沈阳自动化研究所,沈阳110016 [2]青岛大学管理科学与工程系,青岛266071 [3]中国科学院研究生院,北京100049 [4]空军装备研究院总体所,北京100076

出　　处：《自动化学报》2010年第4期465-474,共10页Acta Automatica Sinica

基　　金：国家自然科学基金(60603097);中国科学院国防科技创新基金(CXJJ-65)资助~~

摘　　要：平面目标识别中的几何形变可用射影变换群描述.与紧致李群SO(n,R)不同,正则化的射影变换群,即非紧致李群SL(n,R)上由黎曼度量决定的黎曼指数映射不同于由单参数子群决定的李群指数映射.基于黎曼流形优化算法得到取值于特殊线性群SL(3,R)的样本的内蕴均值和协方差矩阵,并依此构建李群正态分布.利用此先验知识,根据贝叶斯定理进行简单背景下的平面目标的识别实验.结果表明,利用射影变换群的统计特性可有效提高平面目标识别的成功率.The geometric warps between planar objects can be represented by projective Lie groups. Compared with the compact Lie group SO（n, R）, the Riemannian exponential map on the noncompact Lie group SL（n, R） determined by a Riemannian metric is usually different from the Lie group exponential map determined by one-parameter subgroups. We compute the samples intrinsic means on the special linear group SL（3, R） based on the Riemannian manifold optimum algorithm and propose the Lie group norm distribution. The test results of the planar object recognition in the simple background, which is based on the full Bayes statistical rule, have shown that the proposed algorithm with the intrinsic statistical property of the projective group may improve the rate of recognition effectively.

关 键 词：黎曼流形 目标识别 射影变换 李群 流形优化 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]