一种基于Grassmann流形的图像集分类算法研究

Research on Image Set Classification Algorithm Based on Grassmann Manifolds

当前基于多模型的图像集分类方法通过对每个图像集进行单次聚类来提取局部模型,与其他图像集进行匹配时使用固定的聚类。然而,如果环境条件不佳,则可能导致两个最近邻聚类表示同一对象的不同特征。针对这一问题,首先,根据重建误差,在Grassmann流形上定义两个子空间间的Frobenius范数距离。然后,通过稀疏表示从画廊图像集中提取局部线性子空间。对每个局部线性子空间,通过联合稀疏表示,利用探测图像集的样本来自适应构建相应的最近邻子空间。基于Honda、ETH-80和Cambridge-Gesture数据集的实验结果表明,与基于仿射包的图像集距离(AHISD)、稀疏近似最近邻点(SANP)和流形判别分析(MDA)等其他算法相比,算法的性能更优。

Existing multi-model approaches for image set classification extract local models by clustering each image set individually only once, with fixed clusters used for matching with other image sets. However, this may result in the two closest clusters to represent different characteristics of an object, due to different undesirable environmental conditions. In response to this problem, this paper first defines a Frobenius norm distance between subspaces over Grassmann manifolds based on reconstruction error. It then extracts local linear subspaees from a gallery image set via sparse representation. For each local linear subspace, the paper adaptively constructs the corresponding closest subspace from the samples of a probe image set by joint sparse representation. Experiments on Honda, ETH-80 and Cambridge-Gesture datasets show that the proposed method consistently outperforms several other recent tech- niques, such as Affine Hull based Image Set Distance （AHISD）, Sparse Approximated Nearest Points （SANP） and Manifold Discri- minant Analysis （MDA）.