This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Normalized Kemeny and Snell Distance: A Novel Metric for Quantitative Evaluation of Rank-Order Similarity of Images
August 2002 (vol. 24 no. 8)
pp. 1147-1151

There are needs for evaluating rank order-based similarity between images. Region importance maps from image understanding algorithms or human observer studies are ordered rankings of the pixel locations. We address three problems with Kemeny and Snell's distance (d_{KS}), an existing measure from ordinal ranking theory, when applied to images: its high-computational cost, its bias in favor of images with sparse histograms, and its image-size dependent range of values. We present a novel computationally efficient algorithm for computing d_{KS} between two images and we derive a normalized form \hat{d}_{KS} with no bias whose range is independent of image size. For evaluating similarity between images that can be considered as ordered rankings of pixels, \hat{d}_{KS} is subjectively superior to cross correlation.

[1] S. Etz and J. Luo, “Ground Truth for Training and Evaluation of Automatic Main Subject Detection,” Human Vision and Electronic Imaging, 2000.
[2] C.M. Privitera and L.W. Stark, “Algorithms for Defining Visual Regions-of-Interest: Comparison with Eye Fixations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 9, pp. 970-982, Sept. 2000.
[3] J. Luo, A. Savakis, S. Etz, and A. Singhal, “On the Application of Bayes Networks to Semantic Understanding of Consumer Photographs,” Proc. IEEE Int'l Conf. Image Processing, 2000.
[4] J. Zhao, Y. Shimazu, K. Ohta, R. Hayasaka, and Y. Matsushita, “An Outstandingness Oriented Image Segmentation and its Applications,” Proc. Int'l Symp. Signal Processing and Its Applications, 1996.
[5] X. Marichal, T. Delmot, C.D. Vleeschouwer, V. Warscotte, and B. Macq, “Automatic Detection of Interest Areas of an Image or of a Sequence of Images,” Proc. IEEE Int'l Conf. Image Processing, 1996.
[6] J. Luo and A. Singhal, “On Measuring Low-Level Saliency in Photographic Images,” Proc. IEEE Int'l Conf. Computer Vision Pattern Recognition, 2000.
[7] W.D. Cook and M. Kress, Ordinal Information and Preference Structures: Decision Models and Applications. Englewood Cliffs, NJ.: Prentice Hall, 1992.
[8] J.G. Kemeny and L.J. Snell, “Preference Ranking: An Axiomatic Approach,” Math. Models in the Social Sciences, MIT Press, 1978.

Index Terms:
Image similarity, rank ordering, spatial layout, Kemeny and Snell distance.
Citation:
Jiebo Luo, Stephen P. Etz, Robert T. Gray, "Normalized Kemeny and Snell Distance: A Novel Metric for Quantitative Evaluation of Rank-Order Similarity of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 8, pp. 1147-1151, Aug. 2002, doi:10.1109/TPAMI.2002.1023811
Usage of this product signifies your acceptance of the Terms of Use.