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Mathematical Problems in Engineering
Volume 2014, Article ID 406358, 9 pages
Research Article

A Linear Approximate Algorithm for Earth Mover's Distance with Thresholded Ground Distance

School of Information Science & Engineering, Lanzhou University, Lanzhou 730000, China

Received 16 July 2013; Accepted 27 November 2013; Published 16 January 2014

Academic Editor: Jian Li

Copyright © 2014 Longjie Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Effective and efficient image comparison plays a vital role in content-based image retrieval (CBIR). The earth mover’s distance (EMD) is an enticing measure for image comparison, offering intuitive geometric interpretation and modelling the human perceptions of similarity. Unfortunately, computing EMD, using the simplex method, has cubic complexity. FastEMD, based on min-cost flow, reduces the complexity to (O( )). Although both methods can obtain the optimal result, the high complexity prevents the application of EMD on large-scale image datasets. Thresholding the ground distance can make EMD faster and more robust, since it can decrease the impact of noise and reduce the range of transportation. In this paper, we present a new image distance metric, , which applies a threshold to the ground distance. To compute , the FastEMD approach can be employed. We also propose a novel linear approximation algorithm. Our algorithm achieves complexity with the benefit of qualified bins. Experimental results show that (1) our method is 2 to 3 orders of magnitude faster than EMD (computed by FastEMD) and 2 orders of magnitude faster than FastEMD and (2) the precision of our approximation algorithm is no less than the precision of FastEMD.