A class of image metrics based on the structural similarity quality index

Authors:
Dominique Brunet;Edward R. Vrscay;Zhou Wang
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada;Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada;Department of Electrical and Computer Engineering, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada
Venue:
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part I
Year:
2011

Citing 2
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Abstract

We derive mathematically a class of metrics for signals and images, considered as elements of RN, that are based upon the structural similarity (SSIM) index. The important feature of our construction is that we consider the two terms of the SSIM index, which are normally multiplied together to produce a scalar, as components of an ordered pair. Each of these terms is then used to produce a normalized metric, one of which operates on the means of the signals and the other of which operates on their zero-mean components. We then show that a suitable norm of an ordered pair of metrics defines a metric in RN.