Thursday, November 14, 2013

What Color is an Orange?

Thomas E. Phipps has recently written: “The secret of doing physics lies in the finding of harmless idealizations---those that reveal more than they conceal. There is no formula for it. It is an art…but also a matter of taste, guided by experience.” [1] Not only do I agree, but I see different “harmless idealizations” in different parts of physics.
In the above quote, I could have replaced “doing physics” by “writing nonfiction books for children” and offended fewer people.  With this substitution, author Tristan Boyer Binns seems to have applied Phipps’s philosophy in her little book, What Color is an Orange? [2]
In the space of 32 picture-studded pages (including title page and table of contents), and using simple declarative sentences, Binns has captured a surprising amount of color science. We learn that oranges don’t have to be orange (e.g., no light—no orange; and an orange in blue light looks black). Also, we learn that rods and cones trap the light from an orange, that a prism disperses light into different colors, and a lens re-unites the colors. We even learn about mixtures of paint, ink, and light using three primaries each. The light mixtures reveal their red, green, and blue components when the orange is shown on TV and we see a raster-image detail. In each case, photographs and illustrations (in color) carry much of the message, well beyond the text. For example, in describing the action of a prism the text says “Each colour of light bends a little more than the colour next to it.” Binns doesn’t say which rays refract the most, but it is clear from the picture of a prism refracting light on the opposite page.
There are lots of idealizations. When describing light reflection from an orange, Binns says, “White light falls on an orange. The orange reflects back only the orange light. It traps, or absorbs, all the other colours in the white light.” Another idealization: the colors in a rainbow are exhausted by ROYGBIV. Another: you can get any color by admixing red, green, and blue lights. One can object at every turn. But the picture is intelligible and consistent. It avoids graphs and formulas. And I believe the only numbers in the book are the page numbers. 
Binns is addressing children age nine and over. Could I do better than she did in conveying the subject to this audience? I don’t think so. And she has written many other books whose topics are far from color science---indeed, far from any science. The target audience, however, is probably the same.
I came upon Binns’s book because a Datacolor visitor from China gave it to me during a stay in Lawrenceville. It looked rather strange and not entirely inviting to see all the Chinese text crowding out the feng shui of the page layout. But that just showed something else: within 32 pages, you can even explain the concepts in two languages.
Whenever we teach, we must deal in “harmless idealizations”---in this case, pictures that retain their basic integrity when refinements are introduced. Deciding which idealizations are harmless is no mean feat. It is a matter of taste, guided by experience…

1. T. E. Phipps, Jr., Old Physics for New: a worldview alternative to Einstein’s relativity theory, 2nd ed.  (Apeiron, Montreal, 2012), p. 47.
2. T. B. Binns, What Color is an Orange? Raintree, 2006 (Republished 2007 by Harbin Inst of Tech. Press, as What Colour is an Orange? with inter-line Chinese translation.)

Michael H. Brill

Tuesday, August 27, 2013

Anatomy of a "Hue Angles" column

This column marks the seven-year anniversary of Hue Angles. Perhaps it is time to review the premise of the column: what is and what is not a Hue Angles. The charter defines the column as “tidbits of interesting lore shared by ISCC members in short-essay form.” The task is harder than it looks, yet also intrinsically fun. Not only should there be a hint of color education, but some of the writer’s personal experience is an important ingredient. Terry Benzschawel’s color-science mind in the job of a Wall-Street quant was a great example. So was Hugh Fairman’s essay on Henry Hemmendinger and colored M.C. Escher prints. Of course, Ralph Stanziola’s personal journey in selling color-measurement instruments was such a piece. I could mention others---they’re in the archives.

We need more such essays. I’m sure many readers could craft a story or two, taking off from a meeting trip or a sales foray, or even a journey to an art museum. Please let me hear from you.

Now, having reviewed what is (in my opinion) a Hue Angles column, let me talk about what is not in the charter. I was given the helpful suggestion to write about the color of fireworks, based on my having seen three separate fireworks displays simultaneously from a small island off the coast of Cape Ann in Massachusetts. As a lead off base, the person who suggested this topic provided an essay from the Konica-Minolta website ( Upon reading that essay, I found it said all I could ever think of saying about firework color---and much that I had not known. Sparks cast by strontium salts produce red, sodium produces yellow (in moderation, please), barium produces green, and copper produces blue. Predictably, a mixture of strontium and copper produces purple. Although fireworks have been around for thousands of years, the use of metal salts to control color dates only from the 1830s. What was missing from this piece was another sort of spark---that of originality and personal investment. This essay was already written, and not a Hue Angles waiting to be born. It might be part of someone else’s testimonial, but not of mine.

So that is why I need your inputs.

Well, there is one twist to the firework story. Ever notice that firework displays that are shown in movies tend to be all washed out in color? In great part that is because the points of light saturate the photographic medium in all three channels. I wonder why movie makers aren’t more attentive to this problem. Maybe they want the dark parts of the image to show up, and are willing to sacrifice the firework display. But many people ignore such effects, which is why color management has a way to go before it is used widely and enthusiastically. John McCann could probably write a great Hue Angles on his experience with such effects and how they are remedied by high-dynamic-range images. He literally wrote the book on HDR [1].

Many of you have effectively written the book on other corners of our world. Let’s explore those corners together in the next seven years.

1. J. J McCann and A. Rizzi, The Art and Science of HDR Imaging. Wiley, 2011.

Michael H. Brill

Thursday, May 2, 2013

What the Dichromat's Eye Tells the Trichromat's Brain

At last February’s SPIE Electronic Imaging Symposium in Burlingame, CA, I posed the question, “Can trichromats really know what dichromats see?” I did this as a mini-paper in a session called “The Dark Side of Color” in which the goal is to ask controversial questions but not to answer them. I will re-express my argument here, because Hue Angles is also a place for controversial questions.

One would think trichromats do know what dichromats see, judging from several algorithms and software applications that simulate the appearance to a dichromat of any given trichromatic image [1-4]. But my SPIE talk challenged that presumption.

We do know what sets of tristimuli are matches for each kind of dichromat (protanope, deuteranope, or tritanope according to which cone system the dichromat lacks). The confusion loci define parallel lines through tristimulus space. In the central-perspective view that is chromaticity space, the parallel lines converge to a vanishing point, called a co-punctal point, that is different for each kind of dichromat.

Although useful, confusion loci and copunctal points don’t define how to map the appearance of a dichromatic color on the appearance from a trichromatic space. It is not even necessary for the dichromatic appearance of a light to match the trichromatic appearance of one of the lights on a confusion locus.  So how can one make the map?

Formally, the problem is as follows: Find a light Q that looks the same to a trichromat as a light P looks to a particular dichromat. If you could find a light Q for each light P, you could present such lights Q in an image as a simulation of the dichromat’s perception.

One is helped in this task by the theoretical assumption that a dichromat’s visual system is the same as a trichromat’s, except the dichromat lacks one kind of cones. One replaces the missing-cone input channel with one of the non-missing cone types. At a post-receptoral stage in the model (say, at an opponent-color stage), the theory chooses a channel and then either nulls it or substitutes one of the remaining channels. There are many color-vision models (ranging from Guth’s ATD model to CIECAM02), and the above algorithm allows several choices for implementation in each model. 

Having chosen a color-vision model and a way to “dichromatize” it, Capilla et al. [2]  predict Q’s from P’s by borrowing the asymmetric-matching idea from chromatic-adaptation studies.  They call their approach the “corresponding pair” idea: Map XYZ of light P to the dichromat’s model output, and then send that model output through the inverse of the trichromat’s model to arrive at Q.

Using this model structure, Capilla et al. compare images transformed using different color-vision models and “dichromatizing” options. The results are quite diverse, showing the impact of the choice that remains even after the assumed simplifications. Only experiment can decide which choice (if any) is right.  What experiment shall that be?

Even the existence of an experiment is problematic. On one level, my SPIE question devolves to the classic philosophical conundrum of my not being able to know if I see the same blue that you do.  The situation is saved to some extent by the existence of unilateral dichromats. There the appearance matches between the dichromatic eye and the trichromatic eye promise to be a legitimate “Rosetta Stone.” Indeed, unilateral dichromats depose the na├»ve model of a dichromat’s color always having the appearance of one of its confusion aliases in trichromatic vision. But to be trustworthy, color-appearance matches must be made cetera paribus---that is, all other variables being equal. The spatial context of a scene always affects the appearance of a color in that scene, and the contexts themselves cannot be equated between a dichromat and a trichromat. You would have to ask the unilateral dichromat to match all the colors in all the possible scenes in your universe to be sure that you had a good simulation. An additional complication is that unilateral dichromats are so rare that we cannot be too fussy about assuring that the trichromatic eye is really “normal.” Finally, the colors dichromats see can be as unstable as Gestalt effects like the Necker cube. One dichromat I know reported the following experience: At a distance, red roses look achromatic to him. When he gets nearer to the roses, they suddenly look red. Then, they stay red as he backs away from them, reverting to their previous achromatic appearance only when he looks away from them and back.

In my SPIE talk, I concluded that, if you still want to predict and simulate what dichromats see, you have truly passed…to the Dark Side of Color. Do you agree?

1. H. Brettel, F. Vienot, and J. D. Mollon, Computerized simulation of color appearance for dichromats, J. Opt. Soc. Am. A 14, 2647-2655 (1997).
2. P. Capilla, M. A. Diez-Ajenjo, M. J. Luque and J Malo, Corresponding-pair procedure: a new approach to simulation of dichromatic color perception. J. Opt. Soc. Am A 21, 176-186 (2004).
3. H. Kotera, A study on spectral response for dichromatic vision, Proc. 19th IS&T Color & Imaging Conference, pp. 8-13 (2011).

Michael H. Brill

Monday, March 4, 2013

Solution to Cryptogram

And the answer [1]  is…

"Within your lifetime will, perhaps,
As souvenirs from distant suns
Be carried back to earth some maps
Of planets and you'll find that one's
So hard to color that you've got
To use five crayons. Maybe, not."

The poet was Marlow Sholander. He was my freshman calculus professor at Western Reserve University (before it united with Case Institute of Technology). I don't know when he wrote it, or why. He was known for chain smoking and for phrases like, "There are no Gausses in this class"---proved by lofting epsilons and deltas over our heads. But he said not a word about the four-color-map theorem. It was only a conjecture and not a theorem when I knew Sholander.  The proof would come in 1976 and be published in 1977 [2,3]. Even then, the proof was questioned because it required a computer. In fact, it was the first major theorem that was proved using a computer.

For new initiates: The four-color map theorem says that, no matter how you carve up a plane into connected (contiguous) areas, to assure that no two abutting regions have the same color, you don’t need more than four colors. “Abutting” means sharing a boundary of at least two points, so, e.g., Arizona and Colorado (which share only one point) could have the same color on a U.S. map.

You won’t find the theorem bandied about by geographers. The maps are entirely in the minds of mathematicians, e.g. the following from Wikipedia (

Why spend a career trying to prove (or disprove) something about four-color maps? To put it abstractly, I think it allows you to hold (and maybe control) certainty in the palm of your hand.  The intoxication of knowing exactly what could not have come from a distant planet---no matter how far away---is the essence of Sholander’s poem.

I would not have guessed he had it in him, and it was not he who got me excited about what was then the four-color conjecture.  Years before, my tiny sixth-grade class trooped across the soccer field to Brentwood High School, invited to partake in a flight of fancy led by a 12th-grade prodigy. This prodigy inundated us with fun and challenges from constructing flexagons and polyhedra to reading Fantasia Mathematica---which contains a story about an impossible five-color map. We made three visits after school, as I recall.
The others in my class returned and made flexagons. I spent every boring class moment for the next six years trying to disprove various “easy” truths like the four-color-map problem. And math classes didn’t have boring moments anymore.

The name of the prodigy? Jef Raskin, who started the MacIntosh project at Apple Computer. The rest is history, as Wikipedia will attest (in a different article). Some years after our visits, I chanced to meet him again, and he said he’d outgrown the childish pursuits he had started me on.

How strange that it was the dry, hierarchy-obsessed professor who carried the wonder to distant planets through his poem!

Michael H. Brill

1. The only solver was Paul Centore.
2. Appel, Kenneth; Haken, Wolfgang (1977), "Every Planar Map is Four Colorable Part I. Discharging", Illinois Journal of Mathematics 21: 429–490
3. Appel, Kenneth; Haken, Wolfgang; Koch, John (1977), "Every Planar Map is Four Colorable Part II. Reducibility", Illinois Journal of Mathematics 21: 491–567

Tuesday, February 12, 2013

Poem commemorating 25 years of SPIE Human Vision and Electronic Imaging

Last week I attended the 25th anniversary SPIE conference on Human Vision and Electronic Imaging (HVEI), chaired or co-chaired all this time by Bernice Rogowitz. Rather than give a theme paper, I opted to read the following poem at the banquet. Some have told me it might have more general appeal, so I post it here. (The answer to the cryptogram will appear in the next post.)

HVEI at 25

At 25 a backward look
Of HVEI undertook
Some witnesses and workers to
Prepare a retrospective through
Theme papers, strong, heroic and
A poem long as you can stand.

At year one we had elements
Of vision model elegance
And spatio-tempo-color dance
And tasks that put us in a trance.
I think the dance steps weren’t aligned---
We needed Arthur Murray’s kind.

Some years went by; we marched ahead
Leaving behind us in our stead
Cosines, Gabors, and patterns square,
Our tracks too faint to follow there.
At year ten it was time to rest
And say with one voice which way’s best.
With all one voice? You speak in jest.
And then along came ModelFest.

To tariff TV quality
VQEG took no holiday.
I think they’re speaking to this day;
Perhaps they’ll come to San Jose,
 Rate reference-free mosquito noise.
(Oops. It’s Burlingame now, guys.)

More years, and HVEI grew
And with it applications flew.
Coded images subtract
Each blur-, block-, fuzzy artifact,
While letting through a gentle “Hark!
You’re pirating my watermark!”
Salience maps and known eye motion
Might guide our plane across the ocean.
Safety, fun, and self-reliance
Promised by the vision science.

Finally at 25
We made our models more alive
In  human-vision camera bots
That see dim blurs instead of dots.
More camera bots are now prepared
To see your insides---are you scared?
The doctors in an instant know
By shades of green your entrails glow.
Plenoptic cameras let a sot
Be Ansel Adams—who’d-a-thot?
And Tangi-books will let you play
With lights and fingerpainting.  Hey!
The 3D TVs now abound
With headaches part of sensurround.
(They toasted 3D’s job as done,
Said buy one and enjoy the fun.)

In such a world can there be more
For HVEI to explore?
I’ll guess there’s room for knowledge new,
And surely Bernice thinks so too.

     Michael H. Brill

Saturday, January 12, 2013

A Color-Related Cryptogram

In preparation for the next post, which will contain the answer, here is a puzzle (from ISCC News #460):


In case you are not a cryptogram expert, here is a hint: X stands for L. A second clue: the poet was a mathematics professor at Case Western Reserve University.

Michael H. Brill