计算机科学

计算机科学 ›› 2017, Vol. 44 ›› Issue (7): 318-323.doi: 10.11896/j.issn.1002-137X.2017.07.058

• 图形图像与模式识别 • 上一篇    

格拉斯曼流形降维及应用研究

曾青松,黄晓宇,钟闰禄   

  1. 广州番禺职业技术学院信息工程学院 广州511483,华南理工大学经济与贸易学院 广州510006,广州番禺职业技术学院信息工程学院 广州511483
  • 出版日期:2018-11-13 发布日期:2018-11-13
  • 基金资助:
    本文受广东省自然科学基金(2015A030313807),广东省科技计划项目(2016ZC0039),广州市属高校科研项目(1201610059),广东省公益研究与能力建设项目(2015A030402003),广州市教育系统创新团队建设计划(1201610034),广州番禺职业技术学院“十三五”科研项目(2016X002),华南理工大学中央高校基本科研业务项目(2015QNXM20),第二批广州市教育系统创新学术团队(13C18)资助

Study on Grassmann Manifold Dimension Reduction and Its Application

ZENG Qing-song, HUANG Xiao-yu and ZHONG Run-lu   

  • Online:2018-11-13 Published:2018-11-13

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摘要： 视频人脸识别的核心问题是如何准确、高效地构建人脸模型并度量模型的相似性,为此提出一种维数约减的格拉斯曼流形鉴别分析方法以提高集合匹配的性能。首先通过子空间建模图像集合,引入投影映射将格拉斯曼流形上的基本元素表示成对应的投影矩阵。然后,为解决高维矩阵计算开销大以及在小样本条件下不能有效描述样本分布的缺陷,引入二维主成分分析方法对子空间的正交基矩阵降维。通过QR分解正则化降维后的矩阵,得到一个低维、紧致的格拉斯曼流形以获得图像集更好的表达。最后将其投影到高维核空间中进行分类。在公开的视频数据库中的实验结果证明,提出的方法在降低计算开销的同时能够获得较高的正确率,是一种有效的基于集合的对象匹配和人脸识别方法。

关键词: 子空间,集合匹配,格拉斯曼流形,投影度量,二维主成分分析

Abstract: The key issues of video based face recognition is how to model facial images and measure the similarity between two models.To this end,a dimension reduction method in the Grassmann manifold was proposed to improve the performance of set matching.Firstly,an image set is modeled with a subspace,and the basic element of the Grassmann manifold is presented as the projection matrix by projection mapping.Then,to solve the problem of computational overhead with high dimension matrix,while the model cannot strictly describe the distribution with fewer samples,a two dimensional principal component analysis is implemented to reduce the dimension of the orthogonal basis matrix.By applying QR decomposition on the matrix,a lower dimension and tighten Grassmann manifold is obtained,which can be better to model the image set.Finally,a kernel function that mapped the orthogonal basis matrix from a Grassmann manifold to Euclidean space is used to classify image sets.Extensive experimental results on shared video based dataset show that the proposed method is an effective object matching and face recognition method based on set-to-set matching,and it outperforms other state of the art set-based matching methods with lower computational cost.

Key words: Subspace,Set matching,Grassmann manifold,Projection metric,2DPCA

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