A novel scheme for color-correction using 2-D Tone Response Curves (TRCs)

1
A novel scheme for color-correction using 2-D
Tone Response Curves (TRCs)

• Vishal Monga
• ESPL Group Meeting,
• Nov. 14, 2003

2
Outline

• Device Calibration Characterization
• One-dimensional Calibration
• Typical Approaches
• Merits and Limitations
• Two-dimensional Color-Correction
• Basic Concept
• Applications
• calibration
• stability control
• device emulation

3
Why characterization calibration?

• Different devices capture and produce color
  differently

4
Why characterization calibration?

• Produce consistent color on different devices

5
Device Independent Paradigm
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Printer Calibration and Characterization

• Calibration
• Tune device to a desired color characteristic
• Typically done with 1-D TRCs
• Characterization
• Derive relationship between device dependent and
  device independent color
• Forward characterization given CMYK, predict
  CIELAB response (based on a printer model)
• Inverse characterization given an input CIELAB
  response, determine CMYK required to produce it

7
Partitioning the device-correction

• Motivation
• Some effects e.g. device drift may be addressed
  
• (almost) completely via calibration
• Calibration requires significantly lower
  measurement
• and computational effort

8
One-Dimensional Calibration

• Two major approaches
• Channel Independent
• Gray-Balanced Calibration
• Channel Independent
• Each of C, M, Y and K separately linearized to a
  metric e.g. Optical density or ?E from paper
• Ensures a visually linear response along the
  individual channels

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Channel wise linearization .
Device Raw Response
One-dimensional TRCs
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Channel wise Linearization . Testing
CMYK sweeps
Calibrated Printer response
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Gray-balance Calibration

• Goal CMY must produce gray/neutral
• search for CMY combinations producing a b0
• Also capable of handling user-specified aim
  curves

12
One-Dimensional Calibration Analysis

• Very efficient for real-time color processing
• For 8 bit processing just 256 bytes/channel
• Very fast 1-D lookup
• So whats the problem?
• Device gamut is 3-dimensional (excluding K)
• We only shape the response along a
  one-dimensional locus i.e. very limited control

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1-D Calibration Analysis ..

• Example 1-D TRCs can achieve gray-balance or
  channel-wise linearity but not both

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1-D Calibration Analysis ..

• Gray-balance lost with channelwise linearization

a vs CMYd
b vs CMYd
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Alternatives

• Use a complete characterization
• 3-D (or 4-D) look-up tables (LUTs) involve no
  compromises
• Expensive w.r.t storage and/or computation
• Require more measurement effort
• Explore an intermediate dimensionality
• 2-D color correction
• Requirements Must be relatively inexpensive
  w.r.t computation, storage measurement effort

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Two-Dimensional Color Correction

• 2-D TRCs instead of 1-D TRCs

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Example of 2-D Color Correction

• Cyan 2-D LUT

255
C
510
0
M Y

• Specify desired response along certain 1-D loci
• Interpolate to fill in the rest of the table
• LUT size 256 x 511 128 kB/channel

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Example of 2-D Color Correction
Linearization 1-D TRC
K
K
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Application to Device Calibration
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Application to Device Calibration

• Enables greater control in calibration
• e.g. linearization and gray-balance
  simultaneously
• More generally, arbitrary loci in 2-D space can
  be controlled to arbitrary aims
• A geometric comparison with 1-D
• 1-D An entire plane CC0 maps to same output C
• 2-D A line in 3-D space (intersection of planes
  CC0, MY S0) maps to same output C

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Visualization of 1-D Vs 2-D calibration
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Results

• Hardcopy Prints
• Fig. 1, 1D linearization TRC (deltaE from paper)
• Fig. 2, 1D gray-balance TRC
• Fig. 3, 2-D TRCs

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Application to Stability Control
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Experiment

• Build calibration characterization at time T0
• Print measure a CIELAB target, compute ?E
  between input and measured CIELAB values
• Repeat at time T1 (gtgt T0 ) for different
  calibrations (e.g. 1-D deltaE, gray-balance, 2-D)

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Results
 

• Printer Phaser 7700
• Times T0 Aug 1st T1 Aug 20th

   
 
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Application to Device Emulation
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Device Emulation

• Make a target device emulate a reference
• Reference could be another device
  printer/display
• Or a mathematical idealization (SWOP)

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SWOP emulation on Xerox CMYK

• Problem
• SWOP rich black requires high C,M,Y
• Xerox CMYK rich black requires low C,M,Y
• 1-D TRCs for emulation
• Monotonic ? cannot preserve rich black
• 4-D SWOP CMYK ? Xerox CMYK
• Accurate, but costly for high speed printing
• 2-D emulation
• A good tradeoff?

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Partial 2-D Emulation

• Use 4-D emulation as ground truth to derive 2-D
  TRCs
• 2-D Emulation LUTs are
• C vs. MY M vs. CY
• Y vs. CM K vs. min(C,M,Y)

SWOP CMYK
Xerox CMYK
K addition
4? 4 emulation LUT
CMY control point
Fill in C value
SWOP GCR
2D TRC for Cyan
C
M Y
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Visualization of emulation transform
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Emulation Results
1D 2D 4D
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Conclusions

• 2-D color correction
• Enables significantly greater control than 1-D
• Implementation cost gt 1-D but ltlt 3/4-D
• Addresses a variety of problems
• Calibration
• Stability Control
• Device Emulation
• References
• V. Monga, R. Bala and G. Sharma,
  Two-dimensional transforms for device color
  calibration'', Proc. SPIE/IST Conf. On Color
  Imaging, Jan. 18-22, 2004

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Back Up Slides
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2-D Calibration Response Shaping
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SWOP Emulation on iGen

• How to populate the 2-D table(s) ?
• Specify 1-D swop2igen type corrections along
  various axis (wherever possible) and interpolate?
• Experiments show interpolating gives a poor
  approximation to the response

Example
K
K is substantial
Almost no K
min(C,M,Y)
Interpolating between 1-D loci does not capture
this behavior
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SWOP Emulation on iGen

• Instead populate by brute force mimicking of
  the 4-dimensional response
• For the K table, treat min(C,M,Y) axis as CMY
  (approximately a measure of input black)
• Run equal CMY sweeps for each K through 4-D
  corrections fill the K table with the results
• C, M, Y tables are trickier
• Need to fold GCR into the table as well
• C (corrected Cyan) must be a function of (C,
  MY) as well as K

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SWOP Emulation on iGen
G,B
black
255
2
1
C
3
4
510
0
white
M,Y
Red
M Y
For each C i, i 0, 1, 255 (1) increase M
up to i, Y 0 (2) increase Y up to CMYi (3)
increase M from i 255 (4) increase Y from i
255, add K in sweeps according to a SWOP like
GCR
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SWOP Emulation on iGen - the K channel
255
K
K f (K, min(C,M,Y) )
0
255
min(C,M,Y)
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Implementation

• ALI scripts to derive 2-D TRCs
• Calibration
• Core routine get2DTRCs.ali
• Support routines stretchTRCs.ali,
  tuneGrayTRCs.ali, fittrc2maxgray.ali
• 2-D TRCs written as an ELFLIST of ELFOBJECTS (in
  this case CTK LUT objects)
• Emulation
• 2Demuln.ali, make2DTRCK.ali