1. 1 A novel scheme for color-correction using 2-D Tone Response Curves (TRCs) Vishal Monga ESPL Group Meeting, Nov. 14, 2003

2. 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. 3 Why characterization & calibration? Different devices capture and produce color differently

4. 4 Why characterization & calibration? Produce consistent color on different devices

5. 5 Device Independent Paradigm

6. 6 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. 7 Partitioning the device-correction Characterization Calibration Output Device Calib.CMYK Archival/ Fast Re-print Path Device Independent Color “Calibrated” CMYK Device CMYK 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

8. 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

9. 9 Channel wise linearization ………. Device Raw Response One-dimensional TRCs

10. 10 Channel wise Linearization …. Testing CMYK sweeps Calibrated Printer response

11. 11 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

12. 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 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

13. 13 1-D Calibration : Analysis …….. Example: 1-D TRCs can achieve gray-balance or channel-wise linearity but not both

14. 14 1-D Calibration : Analysis …….. Gray-balance lost with channelwise linearization a* vs C=M=Y=db* vs C=M=Y=d

15. 15 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

16. 16 Two-Dimensional Color Correction 2-D TRCs instead of 1-D TRCs 2D TRC Calibration determined 2D TRCs C M Y Calibration Transform C’ 2D TRC v i1 (C,M,Y) M’ v i2 (C,M,Y) Y’ v i3 (C,M,Y) Fixed Transforms 2D TRC

17. 17 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

18. 18 Example of 2-D Color Correction C M Y Calibration Transform C’ M + Y v i1 (C,M,Y) M’ v i2 (C,M,Y) Y’ v i3 (C,M,Y) Fixed Transforms Calibration determined 2D TRCs C C + Y M C + M Y Linearization 1-D TRC K’K

19. 19 Application to Device Calibration

20. 20 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=C 0 maps to same output C’ – 2-D: A line in 3-D space (intersection of planes C=C 0, M+Y = S 0 ) maps to same output C’

21. 21 Visualization of 1-D Vs 2-D calibration

22. 22 Results Hardcopy Prints – Fig. 1, 1D linearization TRC (deltaE from paper) – Fig. 2, 1D gray-balance TRC – Fig. 3, 2-D TRCs

23. 23 Application to Stability Control

24. 24 Experiment Build calibration & characterization at time T 0 – Print & measure a CIELAB target, compute  E between input and measured CIELAB values – Repeat at time T 1 (>> T 0 ) 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

25. 25 Results Printer : Phaser 7700 Times: T 0 = Aug 1 st T 1 = Aug 20 th Correction Derived at Measured at Average  E 94 error 95%  E 94 error 1-D gray-balance + characterization T0 T0 T0 T0 2.21 4.08 1-D channel independent T1 T1 T1 T1 5.78 7.51 1-D gray-balance T1 T1 T1 T1 4.73 8.02 2-D T1 T1 T1 T1 2.66 4.59 No recalibration T0 T0 T1 T1 6.83 10.67

26. 26 Application to Device Emulation

27. 27 Device Emulation Make a target device ``emulate” a reference – Reference could be another device – printer/display – Or a mathematical idealization (SWOP)

28. 28 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?

29. 29 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 addition 4  4 emulation LUT CMY control point C M + Y SWOP CMYK 2D TRC for Cyan Xerox CMYK Fill in C value SWOP GCR

30. 30 Visualization of emulation transform

31. 31 Emulation : Results 1D2D 4D

32. 32 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

33. 33 Back Up Slides

34. 34 2-D Calibration : Response Shaping

35. 35 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

36. 36 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

37. 37 SWOP Emulation on iGen 510 G,B M + Y 0 255 1 2 3 4 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

38. 38 K min(C,M,Y) K’ = f (K, min(C,M,Y) ) 0 255 SWOP Emulation on iGen - the K channel

39. 39 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