Abstract
We derive mathematically a class of metrics for signals and images, considered as elements of R N, 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 R N.
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Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index (preprint). (March 2011), http://www.math.uwaterloo.ca/~dbrunet/
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Brunet, D., Vrscay, E.R., Wang, Z. (2011). A Class of Image Metrics Based on the Structural Similarity Quality Index. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2011. Lecture Notes in Computer Science, vol 6753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21593-3_11
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DOI: https://doi.org/10.1007/978-3-642-21593-3_11
Publisher Name: Springer, Berlin, Heidelberg
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