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基于Grassmann流形的仿射不变形状识别

DOI: 10.3724/SP.J.1004.2012.00248, PP. 248-258

Keywords: 形状识别,Grassmann流形,仿射不变,形状空间,形状均值

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Abstract:

?传统的Kendall形状空间理论仅适用于相似变换,然而成像过程中目标发生的几何变形在更多情形时应该用仿射变换来刻画.基于Grassmann流形理论,本文分析了仿射不变形状空间的非线性几何结构,提出了基于Grassmann流形的仿射不变形状识别算法.算法首先对训练集中的每类形状分别计算形状均值和方差,进而在形状均值附近的切空间构建多变量正态分布;最后,根据测试形状的观测和先验形状模型求解测试形状的最大似然类,对形状进行贝叶斯分类.MPEG7形状数据库的实验结果表明,与传统Kendall形状分析中的基于Procrustean度量识别算法相比,本文识别算法具有明显优势;真实场景中的目标识别结果进一步表明,本文算法对仿射变形有更好的适应能力,在复杂场景下能以较高的后验概率辨识出目标类别.

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