Comparing Colors and Measuring Statistics

[leeharper_admin]

Delta E (dE) is probably the statistic that is of the most general interest. It is shown with the unpinned skin tone sample at the bottom. It is a mathematical representation of how different two colors are. A dE of 3.0 is considered to be undetectable by the human eye - in this case the value is almost 20, which indicates a skin tone in need of help.

I am very interested in learning more about the Delta E and Standard Deviation information that CurveMeister can calculate. An application of the Delta E readings that would be very helpful to me would be the fine tuning of printing profiles. I have an X-Rite i1 for creating custom profiles, and I always have trouble discerning which media type to use to print my profile target. What I would usually do is to print an evaluation image (attached - available from colourconfidence.com) that shows me which media type offers the greatest saturation (without blocking up at values below 100%). I envision that CMs Delta E readings would allow me to measure the linearity of the step wedges produced with each media type setting.

Could you or Mike flesh out this aspect of CM for me, so that I can better understand how I could apply it to my profiling workflow? (My thinking is that if Delta E readings were to get larger as the step wedge got darker it would indicate that the media type chosen was causing the printer to lay down too much ink) Also, in the quoted text it mentions that Delta E readings can be used to check skintones, but I fail to see how this could be done. Some more information about this would also be great.

Cheers,
Lee.

[leeharper_admin]

I also wanted to ask about the following (again from this week's handout):

Standard Deviation (sd) is a mathematical representation of the amount of data variation in the sample. This can be used to gauge image quality and texture variation, and for calculations such as the Modulation Transfer Function, which characterizes the resolution of an optical system.

I'd really like to know more about this as well.

Cheers  :)
Lee.

[ggroess]

Lee,
I have posted this to Mike for further explanation. 
He is the Man behind the Stats...

Let me know if he does not contact you regarding this.
Greg

[leeharper_admin]

Thanks Greg ;) I think that I'll be able to put this to good use!

Lee.

[leeharper_admin]

Hi Greg,

Mike still hasn't been in touch about this - would you mind giving him a nudge ;)

From our Skype chat it seems as though the Delta E measurements won't help with printer profiling, but the course notes mention that the dE readouts can be used to check skin tones:

Delta E (dE) is probably the statistic that is of the most general interest. It is shown with the unpinned skin tone sample at the bottom. It is a mathematical representation of how different two colors are. A dE of 3.0 is considered to be undetectable by the human eye - in this case the value is almost 20, which indicates a skin tone in need of help.

I'd be very interested in knowing how dE can help with skin tones.

I'd also like to know more about the Standard Deviation measurement - particularly how it relates to texture variation.

Thanks so much,
Lee.

[ggroess]

I have nudged him again....

I'll call him if you do not get any response from him...sometimes he falls into the code machine and gets caught up in it...

Greg

[-default]

Sorry about the slow response.  I'm normally pretty quick on these things, but sometimes the automatic notification mechanism does not kick in when it should, and I need a nudge from Greg.

The deltaE concept is a very general one, and covers a wide range of issues.  It's the linear, or Euclidean, distance in Lab space between two colors.  In the manual I sort of prime the pump by mentioning some ways that deltaE could be used. 

Measuring skin tone is one - the larger the deltaE, the greater the change in skin tone, usually relative to a nominal value, or a value taken from another image whose skin tones need to be matched.  Since skin tones vary in brightness, the pin should be constrained only in the L channel, so that Curvemeister ignores variation in brightness, and displays what is called deltaE HS, or a variation in hue and saturation.

DeltaE is often used to characterize the accuracy of a printer profile by scanning test patches, and calculating the deltaE of the individual patches versus a set of target values.  The easiest way to do this would be to compare Lab readings from your own print, and a reference print, but this is not normally available, so the Lab values are compared with theoretical targeted values instead.  This turns out to be a non-trivial problem, and it is where profile calculation software earns its keep.

So, for example, if 100 percent black were actually printed as Lab(10, 0, 0), and white as Lab(90, 0, 0), you would expect the steps of a wedge that varies from Lab(0,0,0) to Lab(100,0,0) to fall more or less evenly between the two values.  The water gets deeper very quickly with color blends, however there is the added issue of trading brightness off against hue and saturation.

You also mentioned standard deviation.  This is basically a way to take a population of samples, in this case pixel values, and characterize the amount of variation in that sample.  This relates directly to noise, and can also be used for an interesting optical resolution calculation called the modulation transfer function, where an image is compared with pure noise to characterize the amount of information retained by an optical system.

I hope this is the type of answer you were looking for.

[mikemeister_admin]

I hope this is the type of answer you were looking for.

It's exactly the sort of answer I was hoping for - thank you so much for your reply :)

At work (where I profile printers) we currently have an X-Rite i1 spectrophotometer, and next year we will be getting a copy of X-Rite MeasureTool, so I will eventually be able to make these measurements directly. Obviously taking readings from a digital representation of the printout creates the problem of calibrating the scanner/camera used to digitise the printout. It sounds though that at a pinch I could use CM to get in the ball park, even if this process couldn't give me empirical results.

Thank you for expanding upon the skin tone correction example. Using dE in comparison with another image makes the concept make much more sense. Is dE HS the default behaviour within CM, or do you need to manually tell CM that HS is all you wish to compare (and by extension, if I was checking a grayscale step-wedge for linearity, could I have dE report only L* values?).

Thanks for your help :)
Lee.

[-default]

DeltaE HS is not the default behavior.  By pinning the L channel to a fixed value, you are essentially forcing Curvemeister to calculate deltaE using differences in the ab channels only,

I'd be inclined to convert the image to grayscale if all I were interested in was overall brightness.  One of the issues with profiles, though, is whether neutrals are represented accurately or not, so at some point, in judging the quality of a profile, some attention should be paid to the a and b values for nominally neutral colors.

You may be intrigued by the profile plotter action, which displays a neutral ramp as a plot.  It's located here. 
http://curvemeister.com/downloads/profileplotter/index.htm

If this is interesting, I also have an application that does the same thing, with some extra metrics to try to characterize banding and the accuracy of the AtoB tables.

[imported_BoydMac]

Mike,  You mention that Delta is the linear between two colors in linear space.  Is there a way to have CM calculate it in human perceptual space or is this what is actually done already?