EMD-L1: An Efficient and Robust Algorithm for Comparing Histogram-Based Descriptors

We propose a fast algorithm, EMD-L1, for computing the Earth Mover's Distance (EMD) between a pair of histograms. Compared to the original formulation, EMD-L1 has a largely simplified structure. The number of unknown variables in EMD-L1 is O(N) that is significantly less than O(N2 ) of the original EMD for a histogram with N bins. In addition, the number of constraints is reduced by half and the objective function is also simplified. We prove that the EMD-L1 is formally equivalent to the original EMD with L1 ground distance without approximation. Exploiting the L1 metric structure, an efficient tree-based algorithm is designed to solve the EMD-L1 computation. An empirical study demonstrates that the new algorithm has the time complexity of O(N2 ), which is much faster than previously reported algorithms with super-cubic complexities. The proposed algorithm thus allows the EMD to be applied for comparing histogram-based features, which is practically impossible with previous algori...

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Haibin Ling, Kazunori Okada
• Keywords: Computer Vision, ECCV 2006, Efficient Tree-based Algorithm, Fast Algorithm, Original Emd, Shape Dataset, SIFT Image Descriptors