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.

(https://arxiv.org/pdf/2005.01338.pdf)

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:


$$  x\mapsto \frac{x}{1+x} $$
$$  x\mapsto \frac{x}{\sqrt{1+x^2}} $$
$$  x\mapsto \frac{2}{\pi}\arctan{x} $$


There are many more versions, since they are used a lot in statsitics, articial neural networks, etc.