  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.
