Comparision between SSIM and MAD Image Quality Assessment Algorithms

I have been working with Most Apparent Distortion(MAD) tool to evaluate the quality of images. I have read a paper that compares SSIM, PSNR, FSIM, etc. with MAD. I am uncertain about some calculations done in the paper.

The output of MAD gives the distance between two images between [0, infinity). How do you convert this value in the similarity of range [0,1], so that it can be compared with other metrics (ssim, ms-ssim)?

A natural practice to convert, in a monotonous way, data in $$[0\,\infty)$$ to $$[0\,1)$$ is an increasing function, like those called sigmoid functions. They behave like $$x\mapsto x$$ close to $$0$$, and flatten to $$1$$ when $$x\to \infty$$. Classical examples are:
• $$x\mapsto \frac{x}{1+x}$$
• $$x\mapsto \frac{x}{\sqrt{1+x^2}}$$
• $$x\mapsto \frac{2}{\pi}\arctan{x}$$
• Once you converted the result to $[0,1]$, you can take one minus the result. Or incorporte it in the sigmoid: $1-\frac{1}{1+x}$ Oct 27 '20 at 17:33