A Novel Earth Mover's Distance Methodology for Image Matching with Gaussian Mixture Models

Abstract

The similarity or distance measure between Gaussian mixture models (GMMs) plays a crucial role in contentbased image matching. Though the Earth Mover's Distance (EMD) has shown its advantages in matching histogram features, its potentials in matching GMMs remain unclear and are not fully explored. To address this problem, we propose a novel EMD methodology for GMM matching. We srst present a sparse representation based EMD called SR-EMD by exploiting the sparse property of the underlying problem. SR-EMD is more efscient and robust than the conventional EMD. Second, we present two novel ground distances between component Gaussians based on the information geometry. The perspective from the Riemannian geometry distinguishes the proposed ground distances from the classical entropyor divergence-based ones. Furthermore, motivated by the success of distance metric learning of vector data, we make the srst attempt to learn the EMD distance metrics between GMMs by using a simple yet effective supervised pair-wise based method. It can adapt the distance metrics between GMMs to specisc classiscation tasks. The proposed method is evaluated on both simulated data and benchmark real databases and achieves very promising performance.