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THE REPRODUCTION OF COLORS AS A PROCESS OF LIGHT INTENSITY SCALING

ADRIEN LUCCA

The word “scale” can refer to phys-ical quantities for space, time or energy: a photographic print might for example reproduce the light-in-tensity values of a scene with low-er light levels than the original scene, by keeping similar relations between each element: “shadows” will be less light than highlights. The print “scales-down” the light values of the scene. It is in this sense of proportional transforma-tions that we will use the word “scale” in this article.

To quantify something, we need to find a way to measure it, and for measuring something units are re-quired. A unit should be a given fixed quantity of something. With units, we can count another quan-tity of the same thing as a cer-tain quantity of units, like in the sentence: “two inches is as long as the length of one inch plus the length of one inch”. The metric system pushes the abstraction a bit further: instead of human body-in-spired units such as inches or feet, the meter is defined relative-ly to the second and to the speed of light in vacuum [1].

Color is not electromagnetic ener-gy. It is not a property of the ma-terial substances around us, not a stimulation of the retina, neither a property of light. However, color is predetermined by all these fac-tors: (1) the type and intensity of electromagnetic energy that is (2) transformed by material substances that (3) ends-up in our eyes stimu-lating the retina.

Colors and sounds are sensations synthesized in our brains - how can we measure that?

Sensations have a triple ori-gin: physical (vibration of air for sounds, light-matter inter-actions for colors); physiologi-cal (the action of the stimulus on the ears or the eyes); mental (all the brain-business that builds the sensations in our minds). We can-not measure the effect of sound or color directly in the brain-cells. However, 20th Century color-scien-tists built a tool to give a double reference to the physical quanti-ties and to their physiological effects.

It was postulated in the 19th Century by Young, Maxwell, Helm-holtz, Graßmann and others that all colors could be described as the variation of three parameters – as a “tristimulus”. Standard-ized for the first time in 1931 by the CIE (Commission Internationale de l’Éclairage), modern colorime-try describes any color by counting the level of stimulation it produc-es on 3 distinct photoreceptors by counting the intensity of so-called “primary” Red, Green, Blue, colored lights that are required to visual-ly match a given color.

The algorithms for color measure-ments require an empirical basis: a model of a human observer’s sen-sitivity to light stimulation - we need a human-like automata with-in the computer. This model is called the standard observer by

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the CIE. The standard observer’s tables – or color matching func-tions – are the results of color matching experiments performed in the 1920’s-1930’s by William David Wright and John Guild.

To understand how the color-match-ing experiment links physical quan-tities with retinal responses, one should consider that at the lowest level the human retina responds to light stimuli by the action of three types of cells – the cones – that have a prominent sensibili-ty to electromagnetic radiation of Short, Medium and Long wavelengths, within a window of approximately one “octave” of electromagnetic ra-diation (mostly between 400 and 700 nanometers) [2].

What is important is that there is often a very large number of dif-ferent physical light spectra that will produce the exact same re-sponse of the retina. As a conse-quence, these stimuli will gener-ate equivalent color sensations: we call them metameric stimuli. There is almost an infinity of combina-tions of two monochromatic lights of complementary wavelengths that synthesize the sensation white, for ex.

Color metamerism is the foundation of the color matching experiment. A subject is placed in front of a box containing a bipartite white screen. On each side of the screen three dimmable “primary” RGB lights can be projected. On the left side of the screen only, a monochromator projects one after another a set of equal-energy monochromatic lights (laser-like lights made of a single wavelength) [3].

The subject has to match on the right side of the screen the color of the light projected on the left side, by changing the intensity of two of the three RGB light projec-tors.

Because monochromatic lights are too colorful to be matched with combinations of the RGB primaries, the third primary is added to the monochromatic light on the left to desaturate it until a perfect vi-sual match is found. When this op-eration has been performed on the entire set across the visible spec-trum, each monochromatic light has been matched with an equivalent mixture of (positive or negative values of) RGB primaries.

The resulting table contains the color matching functions which are used to compute the intensities of RGB primaries needed to match the visual appearance of any fur-ther light stimulus. The most wide-ly used CMFs today are the CIE 2° standard observer from 1931 and the CIE 10° from 1964.

It is interesting to remember that the data which is used in today’s color measurement devices and al-gorithms is the average physio-logical reaction to light stimuli of real human subjects that are not alive anymore (49 people for the 1964 set). All light stimuli can be coded as RGB equivalents because the recorded eye-print of 49 dead or nearly-dead people still func-tions.

When we measure surface colors, we measure the light that is reflected by a surface at a certain angle of observation.

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We have to choose the light that illuminates our material sample and calculate its color accordingly be-cause the color of the object de-pends on the spectrum of the light that lights it up.

We scale our RGB values by com-paring them to the calculated RGB values of an ideal model placed in similar conditions: the perfect light diffusor, a surface that re-flects 100% of incoming light even-ly in every direction. The perfect diffusor represents both physical-ly and perceptually the “perfect white”, every surface color mea-surement is calibrated on it, every colorimetric measurement is formu-lated relatively to this perfect white object.

In the color matching experiment RGB values were referring to real

lights of a given intensity seen and compared by real people. For surface colors, RGB values are ex-pressed in terms of percentages of the RGB values of the perfect dif-fuser illuminated by a given source of light.

When units are expressed in per-centages of a reference value, the scale is lost. We call this kind a “relative measurement”, as opposed to an absolute measurement ex-pressed by physical units like the candela by m² for luminance.

The high capacity of adaptation of the visual system to different lev-els of light intensity explains why scale-less color measurements work well as long as we stay in the do-main of validity of colorimetry: too weak or too powerful light lev-els will produce wrong results.

400 450 500 550 600 650 700

Wavelengths (nm)

Stiles and Burch functions (1955)

The Stiles & Burch 2-deg CMFs are based on measurements made in 10 observers. The data are referred to as pilot data, but probably repre-sent the best estimate of the 2 deg CMFs, since, unlike the CIE 2-deg functions (which were reconstructed from chromatic-ity data), they were measured directly. Source: http://www.cvrl.org/database/text/cmfs/sbrgb2.htm

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above:Georges de la TourMagdalen with the Smoking Flame 1638-1640Coll. Los Angeles County Museum of Art(C) Google Art Project

below:Georges de la TourJoseph the carpenter (detail)1645Coll. Musée du Louvre, Paris(C) RMN / Gérard Blot

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Across the history of painting we can see the traces of an idea: us-ing the optical and chromatic prop-erties of pigments under light, what the painters call their “val-ues”, to reproduce light and color values as they appear in the real world. This is what any “optically realistic” painting seems to do.

The project of “painting the light” existed long before colorimetry was standardized by the CIE and before photography was invented. Works by – among others – Latour, Rembrandt or Seurat point out well what I will call a fundamental problem of the figuration of light in material pictures. This problem is not lim-ited to the field of painting as it also appears in color photography.

If you take a close look at the idea of “painting the light”, there are many arguments in favor of its impossibility and of its absurdity:first of all, there is no defined limit for the intensity of light in the real world. A contrast ratio of 1:100000 in an outdoor scene is a common thing [4], while for example in tempera painting techniques the most white and the most black pig-ments (titanium white and iron-man-ganese spinel black) will make a contrast ratio of ± 1:40. A high-end inkjet printer will pro-duce similar results on matte paper and go as far as ± 1:100 on glossy media. Oil painting will also yield to better contrasts, but still many orders of magnitude behind outdoor scenes.

Second argument, the variety of the possible colors in a painting is determined by the optical proper-ties of the pigments used.

Their colored appearance is caused by the absorption of some parts of the light spectrum. However, no pigments will ever absorb 100% of a part of the light spectrum, as no black will ever absorb all light. Even the most colorful orange pig-ment (the DPP Orange, PO73) emits a less orange light under the sun-light at noon than the light coming from a piece of white paper at the end of sunset.

If we want to paint an optical or a colorimetric “copy” of the white paper as it is illuminated at sun-set, we’ll have a problem, we can simply not match it: it’s too dark, there’s no way to really duplicate the special combination of Pink and Orange plus lots of light that a nice sunset offers - among the colored materials used by artists, only colored glass for stained-glass windows can match this.

It’s unfortunate, but it’s true: light and color can be recorded or measured with much higher accura-cy than they can be reproduced by artistic media such as painting, printing or even most digital dis-plays. When we look at paintings from this perspective we realize that the history of the represen-tation of light in painting can be interpreted as a series of attempts at solving what I called a funda-mental problem of the figuration of light in material pictures.

For example two “tricks” are ob-viously in action in the paint-ings of la Tour (1593-1652). First of all the light of the scene is “white balanced”: all the hues of the scene have been modified for the white pigment used by the painter

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to be associated to the white ob-jects on the picture, even if the light should be orange, it is not. The contrast of the scene is squeezed within the dimensions of the contrast available in the oil painting palette, in CG this is called “tone mapping”.

An attempt at avoiding white bal-ance can be seen in Bonnard’s or in impressionist paintings. How-ever the price for keeping closer hues is the loss of even more con-trast. Interesting solutions for locally increasing contrast were proposed in Seurat’s paintings by surrounding too light objects with dark-complementary colors, making the contrast appear visually higher than it actually is.

Another stunning solution for solv-ing the contrast problem is found in a detail of la Tour’s Joseph the carpenter (1645): a child’s hand which is hiding the brightest part of the scene makes it possible for the painter to use the white pig-ment for the skin of the characters instead of using it to depict the light source as in Magdalen with the Smoking Flame (1638-1640). Hiding the light source allows the entire picture ligtness to “jump” a step higher.

Both surface colors and geometric objects can be defined without any scale, but only by proportions or relations between their elements. If all the points of a closed line are at the same distance from one point which is not contained in the line, the line can only be a per-fect circle. There is no need to decide what the size of the radius is to define a circle.

But once we want to realize a cir-cle by tracing it, we have to choose a scale for it, and we can-not choose any scale: if it is too small, the thickness of the traced line will interfere with the shape and it will never represent a circle, but more likely a sin-gle point. The same is true for any object that materializes a geomet-rical model, and for pictures too: a Mona Lisa made of 10x15 pixels is not a Mona Lisa.

Geometric objects are perfect ab-stractions that do not require scale, and colorimetry has geomet-ricized color sensations in a sim-ilar way. However, when a material picture is made from such elements it has to deal with the real-world problems of contrast, of gamut (the gamut is the color-space of a giv-en color-production apparatus), and of metric dimension. The work of creating a picture becomes an ef-fort at tuning abstract geometrical parameters to fit the given con-straints of a media.

I recently made an album that pres-ents how I deal with these problems of scaling in my work. The album source refers to the physiological color vision, to the physical lim-its of a printing device, and to some laws of optics in the physical world. Each picture is a proposal at “printing light” in the domain of the possible. And the objects are visual equivalents of light phenomena defined geometrically and colorimetrically, tuned to fit the media.

To illustrate what I’m talking about I made a video that captured every step of one run of the com-

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Georges Seurat, Le chahut, 1889-1890Coll. Kröller-Müller Museum, Otterlo, NL(C) Google Art Project

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puter program that I wrote to make the pictures. It shows well how each element’s lightness is op-timized and maximized within the printer’s color-space, and then how the entire picture’s colors and brightness is set to the maximal possible level. The video is avail-able on Youtube at this address: https://youtu.be/NkRBJB9BqvI

I didn’t talk about the icono-graphic references of the pictures created (micro or macrocosmos), or described in detail what my al-gorithms do, for example how they use several layers of randomness to generate pictures. But I hope the questions will open new horizons for discussion.

Adrien LuccaMaquette algorithm visualizationYoutube video, 1:09May 8, 2015

NOTES

[1] One meter is the Length of the path trav-elled by light in a vacuum in 1/299,792,458 of a second.

[2] This is valid in photopic (i.e. “daylight”) conditions. At low illumination levels the col-or sensitivity to Red light drops and the peak sensitivity moves from about 555nm to about 500nm: this is called the Purkinje effect.

[3] A monochromator is an optical device that transmits a mechanically selectable narrow band of visible light.

[4] Bill Freeman & Frédo Durand (year unspeci-fied): Dynamic Range and Contrast Syllabus of the course 6.098 Digital and Compu-tational Photography and 6.882 Advanced Compu-tational Photography, MIT/EECSURL: http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/08_HDR_6.pdf

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Adrien LuccaAlbum Source Alpha version (detail)Colorimetric object: d. Light Spot - Red, 5000KBackground luminance 10.1%March 11, 2015