关键词: 格拉斯曼流形, 线性子空间, 黎曼优化, 图像集识别, 流形学习

Abstract:

In recent years， image set recognition methods for characterizing image sets in linear subspace based on Riemannian manifolds have good results. Aiming at the problems of high computational cost and limited applicability of the existing image set recognition methods based on Riemannian manifolds due to the high dimensionality of the image linear subspace existing in this field， an image set recognition method based on Grassmann manifold was proposed. Firstly， starting from the geometry of the linear subspace， the linear subspace was modeled by using the Grassmann manifold to obtain the joint Riemannian metric based on the Grassmann manifold. Then， with this joint Riemannian metric， a low-dimensional Grassmann manifold was learned from a high-dimensional Grassmann manifold. Finally， image set recognition was performed on the image set data on the low-dimensional manifold obtained by learning. The experimental results show that the recognition accuracy of the proposed method on the ETH（Eidgen?ssische Technische Hochschule）-80 dataset is improved by 2.5 percentage points compared with Projection Metric Learning （PML） and Graph embedding Glassmann Discriminant Analysis （GGDA）. It is proved that on the low-dimensional manifold learned by the proposed metric and method， the image set data has a better classification structure， thereby reducing the calculation cost of image set recognition， increasing the scope of application， and improving the recognition accuracy.

Key words: Grassmann manifold, linear subspace, Riemannian optimization, image set recognition, manifold learning