Bregman Divergences for Infinite Dimensional Covariance Matrices

TL;DR

This paper proposes a novel method for computing and comparing covariance descriptors in infinite-dimensional spaces using kernels and Bregman divergences, improving classification in computer vision tasks.

Contribution

It introduces a kernel-based approach to compute Bregman divergences between covariance descriptors in Hilbert spaces, enhancing their discriminative power.

Findings

Improved classification accuracy on material and texture recognition tasks.

Effective in person re-identification and action recognition from motion data.

Demonstrates advantages of high-dimensional covariance descriptors over traditional methods.

Abstract

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.