We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purposes. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.

本文介绍了一种利用无穷维空间中的Covariance Descriptors（CovDs）进行计算和比较的方法，并通过利用核函数计算Hilbert空间中的CovDs之间的多种Bregman散度，克服了CovDs只保留测量二阶统计值的局限性，从而利用这些散度在物料和纹理识别、人员重新识别和从动作捕捉数据中识别动作等多个领域展示了该方法的优势。

无限维协方差矩阵的布雷格曼散度