The document discusses the numerical stability of color transformations when using lookup tables (LUTs) for printers. It notes that while printers are not truly linear, LUT-based interpolation is commonly used but can result in lost monotonicity if too many measurements are taken, potentially causing artifacts. The document speculates on experiments that could help determine the optimal number of measurements for maintaining monotonicity with different printer types and ink combinations.
There is a very long tradition in designing color palettes for various applications. Although color palettes have been influenced by the available colorants, starting with the advent of aniline dyes there have been few physical limits on the choice of individual colors. This abundance of choices exacerbates the problem of limiting the number of colors in a palette.
The traditional solution is that of "color forecasting." Color consultants assess the sentiment or affective state of a target customer class and compare it with new colorants offered by the industry. They assemble a limited color palette, name the colors according to the sentiment, and publish their result.
The color forecasting business is very labor intensive and difficult, thus for years computer engineers have tried to come up with algorithms to design harmonious color palettes, alas with little commercial success. Contrary to the auditory sense, there is no known physiological mechanism sustaining harmony and the term "harmonious" just has the informal meaning of "going well together."
We argue that the intellectual flaw resides in the belief that a masterful individual can devise a "perfect methodology" that the engineer can then reduce to practice in a computer program. We suggest that the correct approach is to consider color forecasting as an act of distillation, where a palette is digested from the sentiment of a very large number of people. We describe how this approach can be reduced to an algorithm by replacing the subjective process with a data analytic process.
As an increasing portion of manuscripts submitted to American journals is from Asian scientists, increasing a journal impact factor is becoming more critical
There is a very long tradition in designing color palettes for various applications. Although color palettes have been influenced by the available colorants, starting with the advent of aniline dyes there have been few physical limits on the choice of individual colors. This abundance of choices exacerbates the problem of limiting the number of colors in a palette.
The traditional solution is that of "color forecasting." Color consultants assess the sentiment or affective state of a target customer class and compare it with new colorants offered by the industry. They assemble a limited color palette, name the colors according to the sentiment, and publish their result.
The color forecasting business is very labor intensive and difficult, thus for years computer engineers have tried to come up with algorithms to design harmonious color palettes, alas with little commercial success. Contrary to the auditory sense, there is no known physiological mechanism sustaining harmony and the term "harmonious" just has the informal meaning of "going well together."
We argue that the intellectual flaw resides in the belief that a masterful individual can devise a "perfect methodology" that the engineer can then reduce to practice in a computer program. We suggest that the correct approach is to consider color forecasting as an act of distillation, where a palette is digested from the sentiment of a very large number of people. We describe how this approach can be reduced to an algorithm by replacing the subjective process with a data analytic process.
As an increasing portion of manuscripts submitted to American journals is from Asian scientists, increasing a journal impact factor is becoming more critical
The enormous possibilities and widespread connectivity offered by the Internet and the World Wide Web has spawned multiple ways of exchanging and communicating color images. The Internet is an evolving communication system, where uses, technologies, and applications are continuously introduced by a plethora of players. Its functionality, reliability, scaling properties, and performance limits are largely unknown—albeit they span wide gamuts from optic fiber to wireless connections and from game consoles to palmtop devices, etc. To be successful in Internet imaging, users and developers must design systems in a top-down approach. The goal of this tutorial is to sort out the available standard methods so that attendees will become familiar with the different possibilities for Internet imaging; the trade-offs, issues and dependencies of each; how and when each is used; and their system implications. To this end, we systematically present the standard methods for color encoding, image compression, file formatting, protocols, and applications.
Color is a perceptual phenomenon that can be explored through psychometrics and modeling of attribute correlates. Color is also a cognitive phenomenon that can be researched through color naming and categorization. We begin with a review of previous research, with an emphasis on the challenges and applications of this work. Building on a large unconstrained color naming corpus collected online from over 4,000 volunteers we demonstrate the long-tail of color naming and derive an online color tool based on the thesaurus model of synonyms and antonyms.
To further improve the quality and quantity of the underlying naming corpus, we introduce two novel feedback mechanisms to the Italian version of the online color thesaurus: instance based harvesting of missing names and optional user ranking of included names. This allows a more efficient creation of a higher quality color naming corpus.
The enormous possibilities and widespread connectivity offered by the Internet and the World Wide Web has spawned multiple ways of exchanging and communicating color images. The Internet is an evolving communication system, where uses, technologies, and applications are continuously introduced by a plethora of players. Its functionality, reliability, scaling properties, and performance limits are largely unknown—albeit they span wide gamuts from optic fiber to wireless connections and from game consoles to palmtop devices, etc. To be successful in Internet imaging, users and developers must design systems in a top-down approach. The goal of this tutorial is to sort out the available standard methods so that attendees will become familiar with the different possibilities for Internet imaging; the trade-offs, issues and dependencies of each; how and when each is used; and their system implications. To this end, we systematically present the standard methods for color encoding, image compression, file formatting, protocols, and applications.
Color is a perceptual phenomenon that can be explored through psychometrics and modeling of attribute correlates. Color is also a cognitive phenomenon that can be researched through color naming and categorization. We begin with a review of previous research, with an emphasis on the challenges and applications of this work. Building on a large unconstrained color naming corpus collected online from over 4,000 volunteers we demonstrate the long-tail of color naming and derive an online color tool based on the thesaurus model of synonyms and antonyms.
To further improve the quality and quantity of the underlying naming corpus, we introduce two novel feedback mechanisms to the Italian version of the online color thesaurus: instance based harvesting of missing names and optional user ranking of included names. This allows a more efficient creation of a higher quality color naming corpus.
The numerical stability of LUT-based color transformations
1. The numerical stability of LUT-based color
transformations
Giordano B. Beretta
Print Production Automation Lab
Hewlett-Packard Laboratories
Palo Alto, California
1 April 2010
G. Beretta (HP Labs) speculative 1 April 2010 1 / 20
2. Disclaimer
For the following I have neither data nor an authoritative reference
This presentation is purely speculative
G. Beretta (HP Labs) speculative 1 April 2010 2 / 20
3. The ideal black & white printer
L*
paper
toner counts
0 31 63 95 127 159 191 213 255
G. Beretta (HP Labs) speculative 1 April 2010 3 / 20
4. The real black & white printer
L*
paper measure
a te
r pol
inte
toner measure counts
0 31 63 95 127 159 191 213 255
G. Beretta (HP Labs) speculative 1 April 2010 4 / 20
5. Halftoning
Gray tones are interpolated through halftoning
Simplest case: spatial (printer) or temporal (display) dithering
Example: 8 × 8 cell for 32 gray values (Bayer)
1 17 5 21 2 18 6 22
25 9 29 13 26 10 30 14
7 23 3 19 8 24 4 20
31 15 27 11 32 16 28 12
2 18 6 22 1 17 5 21
26 10 30 14 25 9 29 13
8 24 4 20 7 23 3 19
32 16 28 12 31 15 27 11
To achieve a given gray level L = 1 , use the interpolation line to
find the inverse of the number of pixels in the required dither
matrix
G. Beretta (HP Labs) speculative 1 April 2010 5 / 20
6. Determining the dither cell
L*
paper
ℓ1
toner counts
0 31 63 95 127 159 191 213 255
(increments of 8)
G. Beretta (HP Labs) speculative 1 April 2010 6 / 20
7. Printing is not linear
Printers are not linear
Dot gain, tribo-electric effects, etc.
There is actually no simple model
Solution: printer characterization:
print swatches for the various counts
measure each swatch
invert the lookup table
Question: How many measurements do we need?
After printer linearization, simple linear interpolation is sufficient
G. Beretta (HP Labs) speculative 1 April 2010 7 / 20
8. Piecewise linear interpolation
L*
paper measure
measure
measure
measure
toner measure counts
0 31 63 95 127 159 191 213 255
G. Beretta (HP Labs) speculative 1 April 2010 8 / 20
9. Error sources
intra-instrument
8
7
inter-instrument
6
ICC maker 5
4
3
2
1
proof vs. press press drift
color transform proofer drift
G. Beretta (HP Labs) speculative 1 April 2010 9 / 20
10. Do not forget your error bars
Printer characterization is a physics experiment
Many sources of error (source: Ing. Rainer Wagner):
short term measurement repeatability: ∆E ∈ [0.02, 0.34]
long term measurement repeatability: ∆E ∈ [0.07, 0.62]
2 hour drift after calibration: ∆E ∈ [0.15, 2.04]
difference between instruments: ∆E ∈ [1.38, 4.90]
difference between sheets in an offset run: ∆E ∈ [0.26, 1.51]
difference between proofs over days: ∆E ∈ [0.62, 1.85]
maximal difference in 70% of an offset run: ∆E ∈ [3.20, 3.60]
error introduced by separation software: ∆E ∈ [2.37, 4.82]
difference between proof and print if technologies are different, ICC
workflow: ∆E ∈ [2.52, 5.33]
difference between proof and print if technologies and ICC
producers are different: ∆E ∈ [3.08, 6.64]
It is important to keep the error bars in mind
The interpolated values will be in an interval
G. Beretta (HP Labs) speculative 1 April 2010 10 / 20
11. Tolerance
L*
paper
toner counts
0 31 63 95 127 159 191 213 255
Note the tolerances are not constant!
G. Beretta (HP Labs) speculative 1 April 2010 11 / 20
12. How many measurements do we need?
To avoid artifacts, tone reproduction must be strictly monotonic
Naïve thought: because the printer is far from linear, the more
measurements we perform, the better the LUT
However:
if the error bars overlap, monotonicity is no longer guaranteed
increasing measurements can backfire
to improve print quality, increase printer accuracy first, then more
measurements are useful
G. Beretta (HP Labs) speculative 1 April 2010 12 / 20
13. Loss of monotonicity
L*
paper
non-monotonic
non-monotonic
toner counts
0 31 63 95 127 159 191 213 255
On the coarser grid, this function is unchanged!
G. Beretta (HP Labs) speculative 1 April 2010 13 / 20
14. What are the consequences?
Are too many measurements damaging?
In practice, the artifacts from loss of monotonicity are small relative
to the printer instability, so they do not make things much worse
There is no change on the coarser grid
There is no benefit having more measurements when
monotonicity is lost
G. Beretta (HP Labs) speculative 1 April 2010 14 / 20
15. Possible experiment 1
Determine the tolerance for an actual monochrome printer and
calculate the recommended maximal number of measurements for
strict monotonicity
G. Beretta (HP Labs) speculative 1 April 2010 15 / 20
16. Possible experiment 2
Separations introduce additional variance because the mapping is
non-injective (different ink combinations have the same CIELAB
value)
Example: add a gray ink
Typically, in the mid-tones there are multiple options for the
separations (Marc Mahy patent)
Determine the maximum number of meaningful measurements
when a gray separation is added
G. Beretta (HP Labs) speculative 1 April 2010 16 / 20
17. Possible experiment 3
Consider a gray image printed on a color printer
Example: add cyan, magenta, and yellow inks
Printer characterization is iterative
1 perform gray balancing
2 determine 3-dimensional lookup table for color correction
3 rebalance the grays
4 determine a new color correction table
5 usually print quality does not improve after 2 iterations
Determine the maximum number of measurements for which the
tone scale is monotonic when a color printer is used for grayscale
printing
G. Beretta (HP Labs) speculative 1 April 2010 17 / 20
18. From grayscale to full color
Tessellation of the printer’s color space
Failure of monotonicity becomes incorrect tessellation
in one or more dimensions a vertex has a non-monotonic
coordinate value and the tetrahedron is “is folded over”
there can be holes
tetrahedra can intersect
How is the argument scaled from grayscale to full color?
G. Beretta (HP Labs) speculative 1 April 2010 18 / 20
19. Scaling to n inks
There is order only in a 1-dimensional space
There is no order in a higher dimensional space
Heuristic method: print thousands of color scales and examine
them for transposed colors
More formally:
consider a sequence or family F = (xi )i∈I where the xi are byte
counts in n dimensions (separations)
consider the set {Fj } of all families that are monotonic in all
dimensions
let T be the color transformation
then the condition is that all T (Fj ) must be monotonic
G. Beretta (HP Labs) speculative 1 April 2010 19 / 20
20. My ignorance
I do not remember the math of all this
An intelligent paper should use a theorem of the underlying math
to declare a corollary that proves something non-obvious that
cannot be gleaned from studying the tessellation problem by itself
An opportunity for a small investigation
G. Beretta (HP Labs) speculative 1 April 2010 20 / 20