Supervised earth mover's distance learning and its computer vision applications

  • Authors:

  • Fan Wang;Leonidas J. Guibas

  • Affiliations:

  • Stanford University, CA, United States;Stanford University, CA, United States

  • Venue:
  • ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
  • Year:
  • 2012

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Abstract

The Earth Mover's Distance (EMD) is an intuitive and natural distance metric for comparing two histograms or probability distributions. It provides a distance value as well as a flow-network indicating how the probability mass is optimally transported between the bins. In traditional EMD, the ground distance between the bins is pre-defined. Instead, we propose to jointly optimize the ground distance matrix and the EMD flow-network based on a partial ordering of histogram distances in an optimization framework. Our method is further extended to accept information from general labeled pairs. The trained ground distance better reflects the cross-bin relationships, hence produces more accurate EMD values and flow-networks. Two computer vision applications are used to demonstrate the effectiveness of the algorithm: first, we apply the optimized EMD value to face verification, and achieve state-of-the-art performance on the PubFig and the LFW data sets; second, the learned EMD flow-network is used to analyze face attribute changes, obtaining consistent paths that demonstrate intuitive transitions on certain facial attributes.