黎曼流形上的保局投影在图像集匹配中的应用

Locality preserving projection on Riemannian manifold for image set matching

目的提出了黎曼流形上局部结构特征保持的图像集匹配方法。方法该方法使用协方差矩阵建模图像集合,利用对称正定的非奇异协方差矩阵构成黎曼流形上的子空间,将图像集的匹配转化为流形上的点的匹配问题。通过基于协方差矩阵度量学习的核函数将黎曼流形上的协方差矩阵映射到欧几里德空间。不同于其他方法黎曼流形上的鉴别分析方法,考虑到样本分布的局部几何结构,引入了黎曼流形上局部保持的图像集鉴别分析方法,保持样本分布的局部邻域结构的同时提升样本的可分性。结果在基于图像集合的对象识别任务上测试了本文算法,在ETH80和YouTube Celebrities数据库分别进行了对象识别和人脸识别实验,分别达到91.5%和65.31%的识别率。结论实验结果表明,该方法取得了优于其他图像集匹配算法的效果。

Objective This paper addresses the problem of image set matching in kernel learning approach, and a locality geometry structure preserved discriminant analysis based on a Riemannian manifold is presented for image set matching. Ri- emannian manifolds have been an effective way to represent image sets, which are mapped as data points on the manifold. Then, recognition can be performed by applying the discriminant analysis on such manifolds. However, the local structure of the data points is not exposed in the discriminant analysis. In computer vision applications, the multi-view facial images are nonlinearly distributed, and features often lie on Riemannian manifolds with known geometry. Set-based matching meth- ods utilize a set of images as input and model the probe set and gallery set individually. Hence, these methods can fully uti- lize the information provided by multiple images to obtain better matching and recognition accuracy. However, the popular learning algorithms such as discriminant analysis and support vector machines, etc. , are not directly applicable to such fea- tures due to the non-Euclidean nature of the underlying spaces. To overcome this limitation, each image set is mapped into a high-dimensional feature space, e.g. a high dimensional Reproducing Kernel Hilbert Space （RKHS）, using a nonlinear mapping function, to which many Euclidean algorithms can be generalized. Method For set based image matching tech- niques, as mentioned above, the key issues can be categorized based on how to represent the image sets and how to measure the similarity between two image sets. We naturally formulate the problem of the image set matching as matching points ly- ing on the Riemannian manifold spanned by symmetric positive definite （SPD）, i.e. nonsingular covariance matrices. In general, the success of kernel-based methods is often determined by the choice of the kernel function. By exploring an effi-cient metric for the symmetric positive definie covariance matrices, i.e. Log-Euclidean distance, we derive a kernel func- tion that explicitly maps the nonsingular covariance matrix from the Riemannian manifold to a Euclidean space. Different from other methods on Riemannian manifold, the local structure of data is taking into account. With the explicit mapping, a kernel version of Locality Preserving Projection （LPP） is apphed to keep the local geometry structure of the image set and an image set-based matching method is proposed. Result The proposed method is evaluated on set-based object classifica- tion tasks and face recognition tasks. Extensive experimental results show that the proposed method outperforms other state of the art set-based object matching and face recognition methods. In this paper, according our experimental settings, it reaches 91.5% and 65.31% on recognition rate in the public ETH80 object database and YouTube Celebrities video data- base respectively. Conclusion In this paper, we have proposed an efficient image set matching method. This method respr- esents each image set with its covariance matrix and models the problem as matching points on the Riemannian manifold spanned by nonsingular covariance matrix. We derived a Mercer kernel function, which successfully bridges the gap be- tween traditional learning methods operating in vector space and the learning task on a manifold. Through comparison exper- iments, it is shown to be generally better than other image sets matching methods.