Comparison between two images

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?

Answer 1

[Walter Roberson]

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 .

[Angela]

Thank you for the answer. Unfortunately i am not sure i understand the steps.

You said replace with a constant value, do you mean replace the original image and the processed image with a random constant value? What do you mean variation? The difference between neighboring pixels? There is a structure in the image so it would not be zero even if there are no artifacts.

If you can explain to me with an algorithm i would appreciate it.

[Walter Roberson]

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 .

Answer 2

[Image Analyst]

See these links:

Image Quality Metrics

Vision Models for image quality assessment

Wikipedia Image Quality

[Angela]

Thank you for the answer. Many of these metrics imply that you have a reference image and they compute how close the reference image is to the processed image (the one we have removed the artifacts). I am looking for a non-reference metric, that i can use to show that the new processed image (the one we have removed the artifacts) is better than the original (with the artifacts) without having a reference image to compare to.

[Image Analyst]

How can you say that your processed image is better than the original reference image if you don't even HAVE the original reference image from which to make a measurement of???

[Angela]

The original image had many artifacts and noise which were very clearly seen which now have been removed. The new processed image does not have artifacts or noise anymore so the only way i can say that it is better is visual inspection but i want to find a quantitative metric too that does not need a reference image.

[Image Analyst]

But you have the reference image so why not use it to gauge the improvement your processing did?

Anyway there are ways to get metrics like the histogram that don't require reference images directly. But if you were to compare something like the standard deviation of image gray levels, then you just get a number. But to know if that number is any good, you have to see what the numbers are for other images, right? Including the reference image. So although the reference image is not used in the computation of the number for that test image, you still had to compute it for the other (ref) image to know if your number is any good or not.

[Walter Roberson]

I believe the situation is that Angela has a noisy image without having access to a non-noisy original, and wants to process the image to remove noise, and then wants to quantitatively measure how "good" the cleaned up image is.

So the task is to remove "bad" content but keep "good" content, and to somehow measure how well you do at that task.

In general, this is not something that can be done without prior knowledge of what the image is "supposed to" look like. For example if I provide a raw astronomical image, what looks at first like noise might in fact be signal, even if not the signal that was originally intended to be recorded -- it might, for example, give information about the Microwave Background Radiation, or might provide information about a large intergalactic dust cloud whose existence was not realized for decades after the image was taken, or might (somehow) provide evidence of what Dark Matter is (again, perhaps decades after the image was taken.)

A few days ago someone posted a image with what looked like a lot of salt and pepper noise, and which obviously had two cats. Cleaning up that image would involve removing irrelevant blobs. But it looked to me as if at the bottom front of the image there might be two pet mice -- difficult to tell with all of the image noise. Metrics that assume that the mice are not there would favour removing that blob from the image; Metrics that assume that the mice are there would favour keeping them. But if you do not know whether they are really there or if it is an artifact, then which of the two metrics would be proper to use?

[Image Analyst]

Yes, in fact the paper says, in the conclusion:

"Some recommendations emerge. First, a universal image

quality metric seems beyond the range of current knowledge,

and possibly unavailable because of the various (and

weakly correlated) components of the human visual behavior.

Although specific applications of image quality assessment

may select a visionmodel as being more relevant, itmay help

to check if, for instance, an image processing tuned with respect

to this vision model (e.g., visual performance) leads,

or not, to drawbacks for alternative quality indexes (visual

appearance and visual attention)."

[Angela]

I do not have an original without noise and artifacts to compare so i guess i am left with just visual inspection. Can you give me the reference of the above paper that you are quoting?

[Walter Roberson]

It is from the middle of the three references Image Analyst posted, http://perso.lcpc.fr/hautiere.nicolas/pdf/2010/hautiere-jei10.pdf