What question did this study set out to answer?

This research aims to analyze the mathematical properties of the structural similarity (SSIM) index to enhance its application in image processing.

On the Mathematical Properties of the Structural Similarity Index

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Theoretical analysis of structural similarity index metrics reveals significant properties for optimization applications.

This research aims to analyze the mathematical properties of the structural similarity (SSIM) index to enhance its application in image processing.
Constructed a series of normalized and generalized vector-valued metrics based on SSIM ingredients.
Examined properties such as convexity, quasi-convexity, and distance preservation under transformations.
Modified SSIM metrics showed quasi-convexity, enhancing optimization applications.
Regions of convexity around minimizers were identified.
Established that the modified metrics preserve distances under orthogonal transformations.

Brunet et al. (2011) studied this question.

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