Comparison between two images

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Angela
Angela on 8 Dec 2018
Edited: Walter Roberson on 10 Dec 2018
I have an image that includes artifacts that i have removed through different processes.
I want to show that the final image is better in quality than the original with a quantitative way (not just visually).
I know there are some metrics that are used to show that two images might be different, for example cross correlation
but such calculation will only show that the two images are different. The goal is to show that the new image is smoother (i.e. better) than the previous one.
Is anyone familiar with such metric?

Answers (2)

Walter Roberson
Walter Roberson on 8 Dec 2018
  1. replace entire image with a constant value
  2. measure variation in constant image and see that it is 0 everywhere
  3. an image with no variation is perfectly smooth
  4. new (constant ) image is smoother (i.e. better) than the original
  5. no other non-constant image could possibly be smoother (i.e. better)
  6. conclude that the constant image is the best possible version of the original image .
  2 Comments
Walter Roberson
Walter Roberson on 8 Dec 2018
Edited: Walter Roberson on 9 Dec 2018
Assign 0 to all pixel components leaving an all black image . The all black image will be perfectly smooth . You have defined smoother as better , therefore the all black image is the best possible version of your original image .
It does not matter that there is structure in the original image . Removing the structure leaves a smoother image and you have defined smoother as better .
Imagine that you have an image that is all white on the left and all black on the right . It has a sharp transition from white to black. Now take another image which is all white on the left third and all black on the right third and fades from white to black across the middle third . It does not have any sharp transition so it is smoother than the first image . Therefore an algorithm that blurs edges priduces smoother images and by your definition those are better images . Therefore aa processing algorithm that blurs the image completely into a single value produces aa smooth image which is by your definition the best image .
We can then optimise the algorithm to simply replacing the entire image with 0 and we would be confident that the smoothness could not be surpassed .

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Image Analyst
Image Analyst on 8 Dec 2018
  8 Comments
Walter Roberson
Walter Roberson on 10 Dec 2018
It is from the middle of the three references Image Analyst posted, http://perso.lcpc.fr/hautiere.nicolas/pdf/2010/hautiere-jei10.pdf

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