基于Grassmann流形的仿射不变形状识别  

Affine-invariant Shape Recognition Using Grassmann Manifold

作　　者：刘云鹏[1,2,3,4] 李广伟[5] 史泽林[1,2,3] 

机构地区：[1]中国科学院沈阳自动化研究所,沈阳110016 [2]中国科学院光电信息处理重点实验室,沈阳110016 [3]辽宁省图像理解与视觉计算重点实验室,沈阳110016 [4]中国科学院研究生院,北京100049 [5]青岛大学管理科学与工程系,青岛266071

出　　处：《自动化学报》2012年第2期248-258,共11页Acta Automatica Sinica

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

摘　　要：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.Traditional Kendall shape space theory is only applied to similar transform. However, geometric transforms of the object in the imaging process should be represented by affine transform at most situations. We analyze the nonlinear geometry structure of the affine invariant shape space and propose an affine-invariant shape recognition algorithm based on Grassmann manifold geometry. Firstly, we compute the mean shape and covariance for every shape class in the train sets. Then, we construct their norm probability models on the tangent space at each mean shape. Finally, we compute the maximum likelihood class according to the measured object and prior learned shape models. We use the proposed algorithm to recognize shapes in standard shape dataset and real images. Experiment results on MPEG-7 shape dataset show that our recognition algorithm outperforms the algorithm based on Procrustean metric in traditional Kendall shape space theory. Experiment results on real images also show that the proposed algorithm exhibits higher capacity to affine transform than the Procrustean metric based algorithm and can recognize object classes with higher posterior probability.

关 键 词：形状识别 GRASSMANN流形 仿射不变 形状空间 形状均值 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术] O186.12[自动化与计算机技术—计算机科学与技术]