Bregman Divergences for Infinite Dimensional Covariance Matrices
This addresses classification problems in computer vision by improving CovDs, but it is incremental as it builds on existing kernel and divergence methods.
The authors tackled the limitation of Covariance Descriptors (CovDs) discarding information by only using second-order statistics, by mapping data to a high-dimensional Hilbert space before computing CovDs and using Bregman divergences for classification. Their experiments showed benefits on material/texture recognition, person re-identification, and action recognition tasks.
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.