More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework based Kernel Matrix Representation
This work addresses image set classification, an incremental improvement for computer vision applications.
The paper tackled improving covariance descriptors for image set classification by extending them to a Log-Euclidean framework on SPD manifolds, resulting in a lower-dimensional and more discriminative representation that achieved superior recognition accuracy compared to state-of-the-art methods.
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.