More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework based Kernel Matrix Representation

TL;DR

This paper introduces an improved covariance descriptor framework for image set classification using Log-Euclidean kernel matrix representations on SPD manifolds, resulting in more discriminative and accurate recognition.

Contribution

It extends covariance descriptors to the SPD manifold with Log-Euclidean kernels and combines multiple kernels via supervised learning for enhanced image set coding.

Findings

Superior recognition accuracy over state-of-the-art methods

Lower-dimensional, more discriminative data representations

Effective kernel combination via supervised learning

Abstract

We consider a family of structural descriptors for visual data, namely covariance descriptors (CovDs) that lie on a non-linear symmetric positive definite (SPD) manifold, a special type of Riemannian manifolds. We propose an improved version of CovDs for image set coding by extending the traditional CovDs from Euclidean space to the SPD manifold. Specifically, the manifold of SPD matrices is a complete inner product space with the operations of logarithmic multiplication and scalar logarithmic multiplication defined in the Log-Euclidean framework. In this framework, we characterise covariance structure in terms of the arc-cosine kernel which satisfies Mercer's condition and propose the operation of mean centralization on SPD matrices. Furthermore, we combine arc-cosine kernels of different orders using mixing parameters learnt by kernel alignment in a supervised manner. Our proposed framework provides a lower-dimensional and more discriminative data representation for the task of image set classification. The experimental results demonstrate its superior performance, measured in terms of recognition accuracy, as compared with the state-of-the-art methods.