Scaling of measures/ metrics

[richterallen]

Hi to all,

my problem is the following:
I have different different quality metrics which are able to assess image quality by investigating several parameters in an image.
The problem with those metrics is their scale. Some of them range from 1 to 10 (10-highest quality) some of them from 0 to 1, etc.

I want to figure out how well those metrics correlate with assessments done by human subjects who judged the images on a scale from 1 - 5. how can I compare between the various scales? how can I rescale the mathematic metrics so that all of them range from 1 to 5? (so i can compare it to human judgement).

Thanks a lot in advance

Allen

 

[phoenixthoth]

first, fix a universal metric (which is a term i just made up) that has a set range: 0-10 or 0-1 or 1-5. just pick one and then make the others conform to that via a formula that converts 0-10 to 1-5. these are all linear formulas of the form y=mx+b where x is the old scale and y is the new scale.

the case of transforming 0-10 to 1-5 or vice versa would go like this:
two points are (0,1) and (10,5). (first scale first coordinates--second scale second coordinates)

the slope is (5-1)/(10-0)=4/10=.4.
the y-intercept is 1 (this is because we're given the point (0,1)).

so the transformation is y=.4x+1.

for example, a 2 on the 1-10 scale is a .4(2)+1=1.8 on the 1-5 scale.
a 10 on the 0-10 scale is a .4(10)+1=5 of the 1-5 scale.

etc.

 

[tacman]

Hi Allen, thank you for sharing your problem with us. Scaling of measures and metrics can be challenging, especially when they have different ranges. In order to compare the different scales, you can use a statistical method called normalization. This involves transforming all the metrics to a common scale, such as a 0-1 scale, so that they can be compared. This can be achieved by dividing each metric by its maximum value and then multiplying by the desired range (in your case, 1-5). This will rescale all the metrics to the same range and make them comparable to the human judgement scale. Another approach could be to use a statistical technique called linear regression, where you can find the relationship between the different scales and use that to convert one scale to another. I hope this helps and good luck with your research!