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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.Abstract: 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.
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Key words:
- Riemannian manifold /
- object recognition /
- projective transformation /
- Lie group /
- manifold optimization
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