Abstract: The similarity or distance measure between Gaussian mixture models (GMMs) plays a crucial role in content based 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 first present a sparse representation based EMD called SR-EMD by exploiting the sparse property of the underlying problem. SR-EMD is more efficient 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 entropy- or divergence-based ones. Furthermore, motivated by the success of distance metric learning of vector data, we make the first 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 specific classification tasks. The proposed method is evaluated on both simulated data and benchmark real databases and achieves very promising performance.

Paper:

Peihua Li and Qilong Wang and Lei Zhang. A Novel Earth Mover's Distance Methodology for Image Matching with Gaussian Mixture Models. In: IEEE International Conference on Computer Vision (ICCV), 2013.

Demo Matlab Code:

Image retrieval using proposed SR-EMD.  [CODE]

L²ECM Descriptors and GMM in the Corel-Wang

Other Supplement Resources:

Matlab code for L²ECM features here

Matlab code for building GMMs in our paper here

Color descriptors software used in our paper here

Texture datasets used in this paper: [KTH-TIPS] [CUReT] [UMD]

Retrieval datasets used in this paper: [Corel-Wang] [Coil-100]