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| Vectorial Color |
 Why are the dots on a TV
screen red, green, and blue? You could say "Well, the eye has red,
green and blue receptors, so there you are." That idea is correct as
far as it goes, but it skims over details, like the fact that red cones
are most sensitive in the yellow. Confronting the details leads to a
practical new formulation for the facts of color mixing. Traditional
textbook color deals with a color vector [X Y Z], but the XYZ system
impedes the use of vector concepts. One benefit of the new formulation
is that it makes the notion of color vectors more intuitive and
practical, so the new work can be called "Vectorial Color." It merges
ideas from
William A. Thornton, Jozef B. Cohen, Michael H. Brill, Sherman Lee
Guth, Tom N. Cornsweet, James A. Worthey and others into a set of 3
color-matching functions and related methods. The materials linked
below explain vectorial color, and include supplementary material for
formal publications appearing elsewhere.
Supplementary
Materials for Vectorial Color
1. Orthonormal
functions graph and VRML (virtual reality) presentation of the Locus of
Unit
Monochromats.
2. The results of a
color-matching experiment depend on the choice of primary wavelengths.
Nonetheless, the results---the color matching functions---tend to peak
at certain fixed wavelengths. To make this discovery for yourself, watch the animated color matching functions.
3. Animated version of
Figures 6 and 7 in "Vectorial Color."
4. An early concept of "Strength
of Action in Mixtures," published by MacAdam and Thornton, but now
presented in animated form.
5. Tabulation
of orthonormal color matching functions: Work
with them yourself!
Complete Papers
about Vectorial Color
1. New draft article "Vectorial Color" and the Figures to go with it. The whole story
(24 pages + 16 figures), but needs a reference list.
2. Self-contained paper Color
Matching with Amplitude not
Left Out,
as presented at Color
Imaging Conference 12, in Scottsdale, Arizona, USA, in 2004
November.
3. The graphical material for the oral
presentation in Scottsdale and the speech as it was read. The
graphical presentation is a long web page with animated and
3-dimensional materials. It should be stimulating even if it's not
totally self-explanatory.
4. Summary of a talk given at Lighting and Color Conference, Orlando,
Florida, 2006 Feb. 8: "How White
Light
Works."
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Lighting
Quality and Light Source Size.
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 How
do we see the
shape
of a shiny object? What causes the dappled sunlight in the shade of a
tree? Suppose it is a sunny afternoon and you stand outside a store or
school with fluorescent lighting. Looking in the window, you see that
the fluorescent-lit interior looks washed out. Why is that? No
mystery! It looks washed out because it is washed out. It is obvious that
some light sources are small and bright, while others are large and
comparatively dim. This variation has effects which are seldom
discussed in clear language. A 1990 article addresses these topics, and
now in 2005 January, the article
is available as a web page: "Lighting quality and
light source
size," Journal of the IES 19(2):142-148
(Summer 1990). |
| Color Rendering |
| Two color
rendering
articles have been published in Color
Research and Application, in the last issue of
2003 and the first issue of 2004. The pdf files below (for Adobe
Acrobat Reader ) contain the final versions as submitted. |
|
Introductory Article
If a source emits light
within a single narrow band of wavelengths, color vision is lost. An
example is low-pressure sodium vapor lights, which are occasionally
used to light streets or parking lots. Now suppose that a light would
emit in two narrow bands. There is no example of a familiar light with
two extremely narrow bands, but many lights tend in the direction of
two bands. They are rich in yellow and blue, but fall short in the red
and the green. The curious fact is that a light can be deficient in red
and green and yet have a white appearance—any shade of white that you
like. To give good color contrasts to objects, a light must contain red
and green and blue. This should not be a surprise, because a TV screen
has red, green and blue phosphors, the primary colors of the TV
palette. Dr. William Thornton calls the key wavelengths the Prime
Colors, and pins them down at 450 nm, 540 nm, and 610 nm.
This introductory article
asks:
"How does color rendering arise as a practical problem?" and "How do
Prime Colors relate to other ideas, such as Matrix R, and Opponent
Colors?" Detailed graphical examples are presented.
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New
calculation
for color rendering
An opponent method is
appropriate
to the color-rendering discussion because it brings to the surface the
notion of chromatic color, meaning actual departure from white or gray.
In this article, an opponent method expresses the predictability of
object colors, and leads to a matrix formulation that serves two
purposes. The effects of replacing a light L1 by another L2 are
estimated with a 3x3 “rendering matrix” P. Given an object’s
tristimulus vector under L1, the method makes an approximate prediction
of the new tristimulus vector under L2. Thanks to the opponent
formulation, matrix element P22 quantifies the gain or loss of redness
and greenness, while P33 expresses gain or loss of blueness and
yellowness. These in fact are major effects, so the method predicts
color changes item by item, and also in more general terms.
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| 30
(approximately) New
Ideas in the 2 Articles Above |
| The discussion of
lighting is
often burdened with preconceived ideas and hidden assumptions. In the
two articles above, I use prior research, but throw out the hidden
assumptions in favor of more rational ideas. In the 2 articles are
about 30 new ideas, which are now listed
on a web page of new ideas. Most of these are not entirely new, but are
old ideas often overlooked in the discussion of lighting and applied
color. |
| Linear
Models and the
Mean Vector |
It is often desired to
represent
object colors or lights by a linear model with only a few terms,
perhaps 3 or 4 terms. For example, the color rendering article above
uses a 3-term model to model all object spectral reflectances. To get
such a model from data, it is convenient to use so-called Principal
Components Analysis. Such an analysis expresses a population of data as
a mean vector plus a set of basis vectors, each times a coefficient.
This new research by Michael Brill and me discusses the role of the
mean vector and shows that it can sometimes be left out of the model.
This article has been accepted for publication in Color Research
and Application.
| Read
the preprint of Linear
Models and the Mean Vector: |
download
article - PDF (259 KB) |
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| Basic
Facts, New
Ideas,
etc. |
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Render
Asking:
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Color
rendering: asking the question
download
text - PDF (77 KB)
download
figures - PDF (210 KB)
This is a preprint of an article published in Color Research and
Application © 2003 Wiley Periodicals, Inc. James A. Worthey,
"Color Rendering: Asking the Question," Color Research and
Application 28(6):403-412,
December 2003. The article as published
is available for a fee at http://www.interscience.wiley.com
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| Render
Calc: |
Color
rendering, a new calculation that estimates colorimetric shifts
download text
- PDF (244 KB)
download
figures - PDF (139 KB)
This is a preprint of an article published in Color Research and
Application © 2004 Wiley Periodicals, Inc. James A. Worthey,
"Color Rendering, a new calculation that estimates colorimetric
shifts," Color Research and Application 29(1):43-56, February
2004. The article as published is available for a fee at http://www.interscience.wiley.com
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| Linear
Models and the Mean Vector: |
Principal
Components Applied to Modeling: Dealing with the Mean Vector
download
article - PDF (259 KB)
This is a
preprint of an article published in Color Research and
Application © 2004 Wiley Periodicals, Inc. James A. Worthey
and
Michael H. Brill, "Principal components applied to modeling: dealing
with the mean vector," Color
Research and Application 29(4):261-266,
August 2004. |
| Problems
viewing these articles? |
| Some users have
had
trouble in displaying and printing the pdf files. I believe that I have
resolved these problems as of 2003 April 16. Still I would be happy to
hear from you about color rendering or pdf files or anything. Please
email jim@jimworthey.com |
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How do
you feel
about logic?
Try a couple brain
teasers
Who is
Nick
Worthey?
My son, Nick J. Worthey, is an
illustrator and animator. You may enjoy his web page, http://www.nickworthey.com. I
enjoy Nick's black and white cartoons and his new prize-winning
animated movie.
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