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:

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

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

  • $\begingroup$ Thanks for the response. I have used them as activation functions. In this case, The MAD gives the difference between the two images. Whereas, SSIM gives a similarity between the images. For example, more MSE means less similarity. But when we convert it to PSNR, more PSNR indicates more similarity. $\endgroup$ May 30 '20 at 16:35
  • $\begingroup$ Once you converted the result to $[0,1]$, you can take one minus the result. Or incorporte it in the sigmoid: $1-\frac{1}{1+x}$ $\endgroup$ Oct 27 '20 at 17:33

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