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Old 04-23-2012, 12:02 AM
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mek42 mek42 is offline
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first attempt at computer aided color matching: success!

I'm using Golden acrylics for my miniatures wargaming hobby and have been struggling with color mixing to get reasonably close to historical colors for 20th century military vehicles and uniforms. After reading a bunch of threads here in color theory I tried something.

I copied the color I was aiming for into Adobe Illustrator (I have CS5.5 Master Collection in case a different Adobe program would be better for this) and put the document into CMYK color space. Then I started pasting in some Golden colors from their website (of colors I [thought] I owned).

Then I found this linear algebra equation solver website: http://mkaz.com/math/linear_algebra/...alculator.html This website will only calculate for CMY, no K, but I'll address this later.

I put in the Golden color CMY eyedropper tool results on the left of the equals sign and the CMY of the color I was trying to match to (1973 "Sinai grey" for IDF armored vehicles - CMYK: 33.33, 35.29, 44.31, 1.18 (%)) on the right of the equals sign and solved.

For most of my trials I had Titan Buff as the third color. Obviously, I rejected solutions where one of the variables was negative. My first viable solution came to Cobalt Green Titanate, Quinacridone Magenta and Titan Buff in about equal parts. This is when I learned that I did not own all three colors in the same format (heavy body, fluid, airbrush) and I didn't want to fool around with figuring how to measure proportions of heavy body to fluid. So I brought up some other reds that I had.

Then I had a realization. The color I was aiming for was closer in value to white than black*. In fact, I had started using Chromium Oxide Green, but ended up getting bunches of negative solutions until switching to the Cobalt Green Titanate. So I tried using Light Magenta as my "red" (I'm reading about CMY, but my default thinking is RBY and I have doubts about CMY not obtainable from RBY but that is not for this thread). The solution came up almost equal amounts green and red with a tiny bit Titan Buff.

This is when I looked at the K channel for the colors. The K for my target color was actually a bit higher than the average of my green and red, so I decided to omit the Titan Buff and hope that pigment mixing saturation (brightness?) loss would be my friend. Equal amounts of the two colors was a bit too pink, so I added a bit more green and got reasonably close to where I wanted to be. I think I then added too much Glazing and/or Airbrush Medium, but that isn't germane to color theory.

I mentioned the lack of K channel in the aforementioned equation solver. Ideally, one could solve for the four parameters or, as artists, just add some neutral grey as needed if the value was way off.

So, my idea was that using CMYK color definitions of colors with a little bit of linear algebra would get me to a good starting point for a color match. I then experienced success with this. I also learned some things about color while doing this, even if more mathematical / numerical than paint on substrate.

In fact, I just had a pigment thought. During this whole process I was concerned that using the CMYK color space intended for printing would not be very applicable to paint mixing as printing uses discrete dots of separate colors to achieve blending, similar to airbrushing (my only college art was airbrush so I tend to see everything as how it relates to airbrush). But, thinking about it, paints have discrete pigment particles and if the paint is thoroughly mixed, these pigment particles will be homogeneously (evenly) distributed, thus simulating a printer or airbrush putting down the various pigment particles that have been mixed as paint.

* I wonder if this is a chroma question rather than a value question, as most of my negative solutions seem to have been related to one of my mixing colors having 100% Y channel. I also wonder if the method I used will give better results for colors that do not have any channel at 100%. The intuition I have about this is that 100% for a given channel is akin to blowing out an individual color channel in digital photography.
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Old 04-25-2012, 09:42 AM
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xerula xerula is offline
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Re: first attempt at computer aided color matching: success!

As you say, real paints do not mix like ideal colors, but as a mathematically rigorous way of arriving at "a good starting point for a color match" this is an interesting approach.

It took me a while to figure out your rationale for representing your paint mixing problem as a system of equations in this format. If I understand you correctly, each equation (row) represents C, Y or M, and each column represents a different paint (CYM). The coefficients are actually the values you obtained in Illustrator, and thus the variables you are solving for (x1, x2, x3) are the relative quantities of each paint required to match your target paint color.

All this makes me wonder how mixes are already computed for highly multivariate scenarios like in giclée printing, and if what you are trying to do isn't already described in the technical literature somewhere... And I also wonder how useful these methods are for painters, compared to just building up lots of experience with mixing paints...

In any case, if you want to explore this further, and solve larger systems of equations, with more mixing colors, including K channel data, I can recommend the free statistical computing language & environment R: http://www.r-project.org/

The relevant R function is "solve". This way, you could also automate the combinatoric aspect of choosing and comparing mixes limited to two to four paints at a time, from a much larger library of characterized paints. You could reject nonsensical solutions and also explore using other color spaces. You could also sample data on actual mixes, model the deviation from idealized mixes, incorporate this into your predictive system and see just how accurate a matching tool it is possible to create. I'd been thinking along similar lines for watercolors, but incorporating even more parameters...

This is the sort of project that appeals to the geek in me (and which would absolutely horrify my painting teacher), so I can write the code if you like, if you feed me data. But again, it might be both reinventing the wheel and a waste of time... After all, I think my local DIY store has a similar system set up for housepaints.
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Old 04-26-2012, 02:44 AM
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Re: first attempt at computer aided color matching: success!

Thank you for replying. I'd started thinking I might have out-Geeked the forum. I might use different words than you, but yes, you understand exactly how it works.

I'm a chemist professionally, but with a very strong math background (master degree chemistry, 1 class short of master degree math).

This idea actually stemmed from Einion suggesting to use software to read what kind of color something is from CMY code in a different thread here. I have no experience actually mixing beyond the elementary school B + Y = G sort of thing. What little mixing I've tried in the past has been abysmally wrong. Doing it this way actually helped to direct my experiment, and then, by doing the experiment, I learned quite a bit about the mixing. Without this approach I may well have wallowed in my frustration at not being able to mix and not tried again. (I'm realizing I have some pretty severe emotional hangups to this art thing.)

In fact, after doing this, I've gone on to make a brown by mixing red and black, which for me is a big thing.

I think it comes down to using ones individual strengths to solve problems. So, don't be afraid to use your inner geek now and then even for art.

I'm sure there are other sites out there already setup to do different number of variable equations - I could have done it by hand too, but wanted to get moving while I had the mood to actually use the paints. But thank you very much for the offer!
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Old 04-26-2012, 10:58 AM
joe publik joe publik is offline
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Re: first attempt at computer aided color matching: success!

Hi mek42.

No, you haven't out-geeked the forum. Mathematician and laser physics PhD here!

This is a forum for artists, some of them clearly very good, and most with mix-and-match skills based on years of long experience. Einion, the Moderator, is clearly a knowledgeable guy/gal. They all have their own ways of getting the reults they want.

The issues you raise have fascinated me for 20 years - since Photoshop first appeared. And I have finally cracked it - I think. I don't want to dredge up old posts and arguments, just check out some of the posts under my nom-de-plume. As far as "amateur" math formulations are concerned you will find nothing better than the work of Zsolt Kovacs which I reference. This, I believe, represents many years of work by Zsolt and uses Matlab to carry out the matrix transformations you allude to. It's brilliant.

As far as matching paints for models and miniatures is concerned there was a short discussion about 6 months ago. I came across a website where the color coordinates of all the major brands were listed together with a simple web app to match to your needs. Look for it.

Color matching is fiendishly difficult at an amateur level. Clearly not so for the big players - think auto body matching and paint formulation at Lowes. I'm surprised you are achieving the success you appear to be having. The variables include - nature of illumination, calibration of computer monitor, paint batch variation and so on. In the end I splurged on a Gretag XRite spectrophotometer which allows all of these factors to be measured and corrected for. Everything in the workflow is calibrated - camera to computer to monitor to printer to paint. It amuses me but it is strictly a minority interest.

An interesting and low cost addendum to your own chosen workflow might be the purchase of a Pantone swatch book. You should pick one up on eBay at a reasonable price. This will allow you a visual match in real world conditions. You can then plug the values into Adobe. For what it's worth I prefer to use Lab over other coordinates.

Enjoy yourself but be warned that such techniques are a minority interest here.

Joe.
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Old 04-26-2012, 03:09 PM
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Re: first attempt at computer aided color matching: success!

Reading your (Joe's) post, my speculation that others would have already covered this territory seems to have been well-founded. I'll read your older posts with interest and look for that web app. I wonder how far these methods could be extended to deal with situations encountered especially with watercolor, e.g. if for a particular target color, multiple solutions could be returned for different paint application strategies - overlaying transparent glazes, mixing on the palette, taking into account the underlying support color, etc.

It's always interesting to see how different painters develop a mental model for practical color matching and paint mixing. It seems to me that there are many valid approaches, balanced between dry analysis/quantification, and letting your intuition guide you.

I'm a postdoc in evolutionary genetics, so it looks like between the three of us we have biology, chemistry and physics covered... I wonder if *what you paint, as well as *how you paint, has been affected by your scientific perspective? My initial route into art was traditional botanical and zoological illustration (hence my focus on watercolor), which I took up as a creatively unfulfilled MSc student. The connections between art and science at the level of aesthetic contemplation are fascinating to explore... David Rothenberg's book "Survival of the Beautiful" has many thought-provoking things to say about this.

Joe
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Old 04-27-2012, 04:11 AM
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Re: first attempt at computer aided color matching: success!

Wait a minute, you're both Joe?

I have contacted the Italian professor and will be looking into the software over the weekend.

It is interesting to see the phrase "letting your intuition guide you" as I'm an INTJ, but also very, very analytical. I think I want to learn a bit of theory and let that guide my experiments from which an intuition can be developed. It is hard for me to give myself permission to "play" with these paints I've spent a bit of money on, creating things that will likely be dumpstered just to learn how they work together. On the other hand, I know that is the best way to learn such a thing, reinforced by the learning I made actually doing the mixing that I setup in this thread. I guess I want to have an expectation of what will happen at the easel, as it were, before setting out - a hypothesis to test, if you will.

Regarding the biology, I'm kind of a full-time bio student right now, as I'm retraining into med tech to seek work in a hospital lab. I'm not very happy with undergrad bio, too much just remembering things.

My route to art is miniatures wargaming. I collected a bunch of Golden acrylic supplies and dabble with fine art application now and again. For that matter, I'm certainly not the world's most prolific minis painter either.
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Old 04-27-2012, 10:39 AM
joe publik joe publik is offline
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Re: first attempt at computer aided color matching: success!

xerula

Watercolo(u)r is about 3 steps too far. Zsolt is quite clear on this. I prepared a series of swatches for him based on Liquitex acrylics. He is quite specific that no trace of the substrate be visible. Some of the sample acrylics I did were layered up to 1mm thickness. It is not necessary to do this in any final work but it is necessary in calibration sample prep. I've played around with acrylic glazes for my own amusement and it is possible to build models but not to high accuracy.

Like most amateurs I find it very difficult to establish and maintain values - or L in Lab - across a painting. Some of the pros on this forum seem to be able to do it by eye. I can't. The XRite allows me to make constant checks across a work in progress and adjust as necessary. So, to that extent, watercolo(u)r work is possible.

The XRite is one of the most interesting pieces of kit I've ever bought. I've personally built spectrophotmeters the size of a small room. To have one to hold in your hand is genius. I constantly check it against Pantone swatches. Measure, plug the values into Adobe, the same swatch pops up in the checker window.

mek42

Zsolt is most helpful and informative. His little programs are sweet and hugely informative in their own right. You can do coordinate transformations, change color temperatures and pull up 3D visualisations. You can even transform into Munsell - and that's unusual. If you want to get serious you'll need to prepare swatches of your Golden paints and have Zsolt input them into his database.

It's fun.

Joe.
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Old 04-27-2012, 01:19 PM
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Re: first attempt at computer aided color matching: success!

mek42 - yes, I am also a Joe. I don't know about personality categories, but I agree that when developing artistic skill ideally there will be a positive feedback relationship between technical analysis and a freer, direct exploration of a medium. I've found this to be the case with everything from photography to playing the piano.

Undergrad bio can be a bit dull with all the rote learning of names and processes and obscure bits of anatomy you'll never need to know about again... My brain is still full of this stuff, and I've tried to make it relevant to making and appreciating art, wherever possible.

joe_publik - I've started reading through the earlier threads you've contributed to. Obviously I need to digest Zsolt's work more fully before speculating about how these techniques can or can't be extended. I'm quite new to even thinking about color, pigments and paint in a computational context.

What model of XRite spectrophotometer do you use?

Joe
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