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

(TRCs)

Vishal MongaESPL Group Meeting,

Nov. 14, 2003

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Outline

Device Calibration & Characterization

One-dimensional Calibration– Typical Approaches– Merits and Limitations

Two-dimensional Color-Correction– Basic Concept– Applications

– calibration– stability control – device emulation

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Why characterization & calibration?

Different devices capture and produce color differently

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Why characterization & calibration?

Produce consistent color on different devices

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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

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Partitioning the device-correction

Characterization CalibrationOutputDevice

Calib.CMYK Archival/ Fast Re-print Path

Device Independent

Color

“Calibrated”CMYK

DeviceCMYK

Device-correction-function

“Calibrated Device”Alternate CMYK (fast emulation)

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

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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: C=M=Y must produce gray/neutral – search for CMY combinations producing a*= b*=0

– Also capable of handling user-specified aim curves

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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

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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 C=M=Y=d

b* vs C=M=Y=d

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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

2D TRC

Calibration determined2D TRCs

C

M

Y

Calibration Transform

C’

2D TRC

vi1(C,M,Y)

M’vi2(C,M,Y)

Y’vi3(C,M,Y)

Fixed Transforms

2D TRC

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Example of 2-D Color Correction

Cyan 2-D LUT:

–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

0

x

Control along device

Gray (C = M = Y)

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

Control along primary

Control along device secondary to black

255

510

C

M + Y

Control along primary

to black

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Example of 2-D Color Correction

CM

Y

Calibration Transform

C’

M + Y

vi1(C,M,Y)

M’vi2(C,M,Y)

Y’vi3(C,M,Y)

Fixed Transforms

Calibration determined2D TRCs

C

C + Y

M

C + M

Y

Linearization 1-D TRCK’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 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’

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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 (>> T0 ) for different calibrations (e.g. 1-D deltaE, gray-balance, 2-D)

Calibration(updated)

Characterization(static)

Print & measure

LAB target within device gamut

Error metric calculation

E

LAB Values

CMYK

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Results Printer : Phaser 7700 Times: T0 = Aug 1st T1 = Aug 20th

 Correction

 Derived at

 Measured at

 Average E94

error

 95% E94 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

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Application to Device Emulation

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Device Emulation

forward response g( vs ) of

emulated device Control Values

vs

Response Values

rs correction function h( rs ) of

emulating device

Emulation Control Values

ve

Complete Emulation Transform

fe( vs )=h(g(vs))

Calibration Transform

fc( vs ) (Partial Emulation)

Partial Emulation Control Values

Vc

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. M+Y M vs. C+Y Y vs. C+M K vs. min(C,M,Y)

K addition4 4

emulation LUTCMY

control point

C

M + Y

SWOP CMYK

2D TRC for Cyan

Xerox CMYK

Fill in C value

SWOP GCR

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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 > 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

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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

K

min(C,M,Y)

Example

K’ is substantial

Almost no K’

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

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

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SWOP Emulation on iGen

510

G,B

M + Y

0

255

1 2

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C

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

Red

black

white

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K

min(C,M,Y)

K’ = f (K, min(C,M,Y) )

0

255

255

SWOP Emulation on iGen - the K channel

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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