Bregman Divergences for Infinite Dimensional Covariance Matrices

Mehrtash Harandi, Mathieu Salzmann, Fatih Porikli; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014, pp. 1003-1010

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 purpose. 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.

Related Material


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[bibtex]
@InProceedings{Harandi_2014_CVPR,
author = {Harandi, Mehrtash and Salzmann, Mathieu and Porikli, Fatih},
title = {Bregman Divergences for Infinite Dimensional Covariance Matrices},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2014}
}