Approximate infinite-dimensional Region Covariance Descriptors for image classification

• Main Authors: Faraki, Masoud, Harandi, Mehrtash T., Porikli, Fatih
• Format: Conference Proceeding
• Language: English
• Subjects: Computer vision; Conferences; Geometry; Kernel; Least squares approximations; Manifolds; Region Covariance Descriptor; Reproducing Kernel Hilbert Space; Riemannian Geometry
• ISSN: 1520-6149; 2379-190X
• DOI: 10.1109/ICASSP.2015.7178193

We introduce methods to estimate infinite-dimensional Region Covariance Descriptors (RCovDs) by exploiting two feature mappings, namely random Fourier features and the Nyström method. In general, infinite-dimensional RCovDs offer better discriminatory power over their low-dimensional counterparts. However, the underlying Riemannian structure, i.e., the manifold of Symmetric Positive Definite (SPD) matrices, is out of reach to great extent for infinite-dimensional RCovDs. To overcome this difficulty, we propose to approximate the infinite-dimensional RCovDs by making use of the aforementioned explicit mappings. We will empirically show that the proposed finite-dimensional approximations of infinite-dimensional RCovDs consistently outperform the low-dimensional RCovDs for image classification task, while enjoying the Riemannian structure of the SPD manifolds. Moreover, our methods achieve the state-of-the-art performance on three different image classification tasks.