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A novel scheme for color-correction using 2-D Tone Response Curves (TRCs) . Vishal Monga ESPL Group Meeting, Nov. 14, 2003. Outline. Device Calibration & Characterization One-dimensional Calibration Typical Approaches Merits and Limitations Two-dimensional Color-Correction

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a novel scheme for color correction using 2 d tone response curves trcs

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

Vishal Monga

ESPL Group Meeting,

Nov. 14, 2003

outline
Outline
  • Device Calibration & Characterization
  • One-dimensional Calibration
    • Typical Approaches
    • Merits and Limitations
  • Two-dimensional Color-Correction
    • Basic Concept
    • Applications
      • calibration
      • stability control
      • device emulation
why characterization calibration
Why characterization & calibration?
  • Different devices capture and produce color differently
why characterization calibration4
Why characterization & calibration?
  • Produce consistent color on different devices
printer calibration and characterization
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
partitioning the device correction

Device-correction-function

“Calibrated”CMYK

Device

CMYK

Device Independent Color

Calibration

Characterization

Output

Device

“Calibrated Device”

Alternate CMYK (fast emulation)

Calib.CMYK Archival/ Fast Re-print Path

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
one dimensional calibration
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
channel wise linearization
Channel wise linearization ……….

Device Raw Response One-dimensional TRCs

channel wise linearization testing
Channel wise Linearization …. Testing

CMYK

sweeps

Calibrated

Printer response

gray balance calibration
Gray-balance Calibration
  • Goal: C=M=Y must produce gray/neutral
    • search for CMY combinations producing a*= b*=0
    • Also capable of handling user-specified aim curves
one dimensional calibration analysis
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 what’s the problem?
    • Device gamut is 3-dimensional (excluding K)
    • We only shape the response along a one-dimensional locus i.e. very limited control
1 d calibration analysis
1-D Calibration : Analysis ……..
  • Example: 1-D TRCs can achieve gray-balance or channel-wise linearity but not both
1 d calibration analysis14
1-D Calibration : Analysis ……..

Gray-balance lost with channelwise linearization

a* vs C=M=Y=d

b* vs C=M=Y=d

alternatives
Alternatives
  • Use acomplete 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
two dimensional color correction

Calibration Transform

C’

vi1(C,M,Y)

2D TRC

C

M’

M

vi2(C,M,Y)

Y

2D TRC

Y’

vi3(C,M,Y)

2D TRC

Fixed Transforms

Calibration determined

2D TRCs

Two-Dimensional Color Correction
  • 2-D TRCs instead of 1-D TRCs
example of 2 d color correction

Control along device secondary axis (e.g. C = M, Y = 0)

x

Control along device

Gray (C = M = Y)

Control along primary

Control along device secondary to black

Control along primary

to black

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
example of 2 d color correction18

Calibration Transform

C

C’

vi1(C,M,Y)

M + Y

M

C

M’

M

vi2(C,M,Y)

Y

C + Y

Y

Y’

vi3(C,M,Y)

C + M

Fixed Transforms

Calibration determined

2D TRCs

Example of 2-D Color Correction

K

Linearization 1-D TRC

K’

application to device calibration20
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 C=C0 maps to same output C’
    • 2-D: A line in 3-D space (intersection of planes C=C0, M+Y = S0) maps to same output C’
results
Results
  • Hardcopy Prints
    • Fig. 1, 1D linearization TRC (deltaE from paper)
    • Fig. 2, 1D gray-balance TRC
    • Fig. 3, 2-D TRCs
experiment

LAB target

within device gamut

Characterization

(static)

Calibration

(updated)

Print & measure

CMYK

LAB Values

Error metric

calculation

E

Experiment
  • Build calibration & characterization at time T0
    • Print & measure a CIELAB target, compute E between input and measured CIELAB values
    • Repeat at time T1 (>> T0 ) for different calibrations (e.g. 1-D deltaE, gray-balance, 2-D)
results25

Correction

Derived at

Measured at

Average DE94 error

95% DE94 error

1-D gray-balance

+ characterization

T0

T0

2.21

4.08

1-D channel independent

T1

T1

5.78

7.51

1-D gray-balance

T1

T1

4.73

8.02

2-D

T1

T1

2.66

4.59

No recalibration

T0

T1

6.83

10.67

Results
  • Printer : Phaser 7700
  • Times: T0 = Aug 1st T1 = Aug 20th
device emulation
Device Emulation
  • Make a target device ``emulate” a reference
    • Reference could be another device – printer/display
    • Or a mathematical idealization (SWOP)
swop emulation on xerox cmyk
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?
partial 2 d emulation
Partial 2-D Emulation
  • Use 4-D emulation as “ground truth” to derive 2-D TRCs
  • 2-D Emulation LUTs are:

C vs. M+Y M vs. C+Y

Y vs. C+M 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

conclusions
Conclusions
  • 2-D color correction
    • Enables significantly greater control than 1-D
    • Implementation cost > 1-D but << 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/IS&T Conf. On Color Imaging, Jan. 18-22, 2004
swop emulation on igen
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

swop emulation on igen36
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 C=M=Y (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, M+Y) as well as K
swop emulation on igen37
SWOP Emulation on iGen

G,B

black

255

2

C

1

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 C=M=Y=i (3) increase M from i … 255 & (4) increase Y from i … 255,
  • add K in sweeps according to a SWOP like GCR
swop emulation on igen the k channel
SWOP Emulation on iGen - the K channel

255

K

K’ = f (K, min(C,M,Y) )

0

255

min(C,M,Y)

slide39

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