This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Differential Earth Mover's Distance with Its Applications to Visual Tracking
February 2010 (vol. 32 no. 2)
pp. 274-287
Qi Zhao, University of California, Santa Cruz, Santa Cruz
Zhi Yang, University of California, Santa Cruz, Santa Cruz
Hai Tao, University of California, Santa Cruz, Santa Cruz
The Earth Mover's Distance (EMD) is a similarity measure that captures perceptual difference between two distributions. Its computational complexity, however, prevents a direct use in many applications. This paper proposes a novel Differential EMD (DEMD) algorithm based on the sensitivity analysis of the simplex method and offers a speedup at orders of magnitude compared with its brute-force counterparts. The DEMD algorithm is discussed and empirically verified in the visual tracking context. The deformations of the distributions for objects at different time instances are accommodated well by the EMD, and the differential algorithm makes the use of EMD in real-time tracking possible. To further reduce the computation, signatures, i.e., variable-size descriptions of distributions, are employed as an object representation. The new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way. Extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard Mean Shift tracker is demonstrated.

[1] P. Indyk and N. Thaper, “Fast Image Retrieval via Embeddings,” Proc. Third Int'l Workshop Statistical and Computational Theories of Vision, 2003.
[2] K. Grauman and T. Darrell, “Fast Contour Matching Using Approximate Earth Mover's Distance,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. I-220-I-227, 2004.
[3] D. Forsyth, “A Novel Approach to Color Constancy,” Int'l J. Computer Vision, vol. 5, no. 1, pp. 5-36, Aug. 1990.
[4] B. Funt and G. Finlayson, “Color Constant Color Indexing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp.522-529, May 1995.
[5] E. Land and J. McCann, “Lightness and Retinex Theory,” J. Optical Soc. of Am., vol. 61, no. 1, pp. 1-11, 1971.
[6] D. Freedman and M. Turek, “Illumination-Invariant Tracking via Graph Cuts,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 10-17, 2005.
[7] D. Comaniciu, V. Ramesh, and P. Meer, “Kernel-Based Object Tracking,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 5, pp. 564-577, May 2003.
[8] G. Hager, M. Dewan, and C. Stewart, “Multiple Kernel Tracking with SSD,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. I-790-I-797, 2004.
[9] Y. Rubner, “Perceptual Metrics for Image Database Navigation,” PhD dissertation, Stanford Univ., 1999.
[10] R. Collins, “Mean-Shift Blob Tracking through Scale Space,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 234-240, 2003.
[11] J. Bergen, P. Anandan, K. Hanna, and R. Hingorani, “Hierarchical Model-Based Motion Estimation,” Proc. European Conf. Computer Vision, pp. 237-252, 1992.
[12] S. Avidan, “Support Vector Tracking,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 1064-1072, Aug. 2004.
[13] S. Avidan, “Ensemble Tracking,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 2, pp. 261-271, Feb. 2007.
[14] R. Collins, Y. Liu, and M. Leordeanu, “Online Selection of Discriminative Tracking Features,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 10, pp. 1631-1643, Oct. 2005.
[15] G. Hager and P. Belhumeur, “Efficient Region Tracking with Parametric Models of Geometry and Illumination,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 10, pp. 1025-1039, Oct. 1998.
[16] M. Isard and A. Blake, “Condensation—Conditional Density Propagation for Visual Tracking,” Int'l J. Computer Vision, vol. 29, no. 1, pp. 5-28, 1998.
[17] J. Shi and C. Tomasi, “Good Features to Track,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 593-600, 1994.
[18] H. Tao, H. Sawhney, and R. Kumar, “Object Tracking with Bayesian Estimation of Dynamic Layer Representations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 1, pp.75-89, Jan. 2002.
[19] M. Swain and D. Ballard, “Color Indexing,” Int'l J. Computer Vision, vol. 7, no. 1, pp. 11-32, 1991.
[20] G. Bradski, “Computer Vision Face Tracking for Use in a Perceptual User Interface,” Proc. IEEE Workshop Applications of Computer Vision, pp. 214-219, 1998.
[21] S. Birchfield and R. Sriram, “Spatiograms versus Histograms for Region-Based Tracking,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 1158-1163, 2005.
[22] Q. Zhao and H. Tao, “Object Tracking Using Color Correlogram,” Proc. IEEE Workshop Performance Evaluation of Tracking and Surveillance, pp. 263-270, 2005.
[23] T. Cover and J. Thomas, Elements of Information Theory. John Wiley and Sons, 1991.
[24] J. Puzicha, T. Hofmann, and J. Buhmann, “Non-Parametric Similarity Measures for Unsupervised Texture Segmentation and Image Retrieval,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 267-272, 1997.
[25] W. Niblack et al., “Querying Images by Content, Using Color, Texture, and Shape,” Proc. SPIE Conf. Storage and Retrieval for Image and Video Databases, pp. 173-187, 1993.
[26] M. Werman, S. Peleg, and A. Rosenfeld, “A Distance Metric for Multi-Dimensional Histograms,” Computer, Vision, Graphics, and Image Processing, vol. 32, pp. 328-336, 1985.
[27] T. Kailath, “The Divergence and Bhattacharyya Distance Measures in Signal Selection,” IEEE Trans. Comm. Technology, vol. 15, no. 1, pp. 52-60, Feb. 1967.
[28] H. Ling and K. Okada, “An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 5, pp. 840-853, May 2007.
[29] S. Shirdhonkar and D. Jacobs, “Approximate Earth Mover's Distance in Linear Time,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.
[30] A. Adam, E. Rivlin, and I. Shimshoni, “Robust Fragments-Based Tracking Using the Integral Histogram,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 798-805, 2006.
[31] F. Hitchcock, “The Distribution of a Product from Several Sources to Numerous Localities,” J. Math. and Physics, vol. 20, pp. 224-230, 1941.
[32] C. Papageorgiou and T. Poggio, “Trainable Pedestrian Detection,” Proc. IEEE Int'l Conf. Image Processing, vol. 4, pp. 35-39, 1999.
[33] http://www.cse.ohio-state.eduotcbvs-bench /, 2009.
[34] http://www.cvg.rdg.ac.uk/slidespets.html , 2009.
[35] G. Dantzig and M. Thapa, Linear Programming: 1: Introduction. Springer, Jan. 1997.

Index Terms:
Earth mover's distance (EMD), gradient descent, real-time tracking.
Citation:
Qi Zhao, Zhi Yang, Hai Tao, "Differential Earth Mover's Distance with Its Applications to Visual Tracking," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 2, pp. 274-287, Feb. 2010, doi:10.1109/TPAMI.2008.299
Usage of this product signifies your acceptance of the Terms of Use.