Earlier this week I wrote about color not being a physical phenomenon, but rather an illusion taking place in our mind. I also wrote about Hunt's problem of completing a wardrobe. Hunt's example is a motivation for colorimetry. When we can keep constant the illuminants and observers, we can use CIE colorimetry and a color management system to closely match color scenes involving ordinary dyes and pigments.
When we can control but not keep constant the illuminants, then we can still do a pretty good job at matching the appearance of colors in a reproduction by using a color appearance model. "Control the illuminant" means we have to know what it is, as Randall Munroe suggests in his xkcd cartoon on the dress.
When we do not know the illuminant, we can estimate it if there is an object in the scene whose color we know. In the dress picture sparking the Internet on 26 February, there is no reference object, no complexion is visible. In this sense, the xkcd cartoon is not a faithful abstraction of the problem at hand because it shows a lot of skin. We would need a second picture were the lady is not wearing the dress. Actually, a nude by itself is not sufficient and the lady should also hold a calibration target, at least the white side of a gray card.
Back in the late 80s and the 90s, Robert Hunt used to teach a course on color science at the RIT. After the course, Roy Berns used to take out Dr. Hunt for a dinner. One year, he took him to a fancy Italo-American restaurant. On the East coast, the fancier a restaurant was, the darker it was, because the cultural understanding was that for a romantic date people would be willing to pay a premium price, but would want a low light level.
As they entered the restaurant, they noticed that the light-bulbs were red and the whole restaurant was imbued in pink. When they sat down at the table, they felt extremely uncomfortable, because they were not able to decide whether the tablecloth was white or pink. After a long discussion and the desperate search for a reference white, Roy Berns finally remembered he had his business card in the wallet and he knew it was white. This allowed them to enjoy their dinner.
In their honor, we should introduce a so-called Hunt-Berns effect: Inability of the cognitive factor to decide on a set. Example: When in an environment with colored illumination the brightest object is not known a priori to be white, the cognitive part of chromatic adaptation fails because it is not possible to establish whether that object is white or has a hue similar to that of the illuminant. This is especially so, if the observer is knowledgeable about the Helson-Judd effect.
This would take care of the illuminant problem by having a second photograph of the lady, this time in the nude and with a white reference target. However, this would not necessarily explain the effect seen in the photograph.
It is pretty obvious from the photograph, that the dress is not Lambertian, therefore the geometric appearance has also to be measured. We would need a spectrogoniometer rather than a simple colorimetric device like a camera, whose white balancing algorithm can get completely duped when confronted with an unexpected target.
As everybody who ever tried to touch up a dent in a car with metallic paint knows, not all surfaces have a color made with a simple dye or pigment based colorant. If for example the color is based on pearlescence or iridescence, you cannot reproduce it on a photograph displayed on a screen. At the very least you need a movie. In this end, you have to examine the original.
Color reproduction is about reproducing an illusion. It will always be hard.