Optimal Color-Optimized Calibration Method in the New ISO 10128 Standard for Inkjet Printing

Optimal Color-Optimized Calibration Method in the New ISO 10128 Standard for Inkjet Printing

Introduction

When discussing color calibration in printing processes, it is impossible not to mention the international standard ISO/TS 10128. Several years ago, the author published a dedicated article, “Revisiting Three Color Calibration Methods”, to share insights with the industry. Let us first review the historical context:

01

With the release and widespread adoption of ISO 12647-2:2004 for offset printing process control, six dot gain (TVI) target curves—later reduced to five in the 2013 revision—were clearly defined. These curves became objective standards followed by offset printing and other printing processes. Meanwhile, the coated paper characterization datasets Fogra39 / Fogra51, introduced by Germany’s Fogra, became the “gold standard” for sheet-fed offset printing on coated paper for most printing companies.

From a technical standpoint, this approach is understandable. However, the existence of multiple dot gain standards inevitably requires separate CMYK curve adjustments under different printing conditions. This leads to inconsistent color appearances—for example, differences between coated and uncoated paper, between AM and FM screening—and makes gray balance difficult to control. Yet consumers and print buyers expect consistent color appearance, not variability.

02

As a result, the G7 methodology, originating in the United States, was developed in 2006 and rapidly gained widespread adoption. G7 controls color by independently adjusting three-color overprint gray scales and single black tonal scales. This approach produces gray balance that aligns with human visual adaptation and defines a relatively unified NPDC (Neutral Print Density Curve). As a result, highlight and midtone consistency can be achieved across different printing conditions, delivering a more uniform shared visual appearance in curve-based calibration.

Nevertheless, curve-based calibration remains an indirect solution. The ultimate goal is to calibrate color, not curves. Whether TVI or G7, color control is achieved indirectly by adjusting key process parameters. While effective in most cases, these methods can fall short under extreme conditions—especially in highlight and shadow regions—where paper color and ink overprint behavior pose persistent challenges.

03

CMYK-to-CMYK transformation algorithms, such as DeviceLink profiles, overcome the limitations of single-channel curve adjustments. By directly mapping a target printing condition to a reference printing standard, they enable true color calibration through direct gamut comparison and optimization. This approach often delivers superior results.

Currently, digital proofing and digital printing widely adopt DeviceLink calibration. Under stable printing conditions, average color differences can be reduced to ∆E00 < 1, making this the most precise calibration method available.

In traditional offset printing, however, the complexity of process control and tool implementation limits DeviceLink adoption. As a result, simpler curve-based methods remain preferred.

This has long presented a dilemma: no method seemed capable of delivering both high accuracy and operational simplicity.

That changed with the release of ISO/TS 10128:2023, which replaced the 2009 version and introduced a new calibration concept: color-optimised correction, also known as the Optimal method. This approach directly compares measured colors with target colors and iteratively computes correction curves.

 

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Origin of the Optimal Method

Although officially adopted in ISO/TS 10128:2023, the Optimal method was originally developed in 2009 by William B. Birkett and Charles Spontelli, affiliated with Doppelganger LLC and Bowling Green State University, respectively.

Notably, both researchers are also the developers of the SCTV spot color calibration method standardized in ISO 20654. The resulting CTV calibration was later incorporated into ISO 10128 as a branch of TVI—an impressive demonstration of their long-term commitment to research and innovation.

After extensive calibration practice and proven success since 2009, their work was publicly presented in the 2018 TAGA Proceedings, where the method was formally named OPTIMAL Color-Optimized Calibration. In 2023, it was officially recognized as the fourth color calibration method in ISO 10128.

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Technical References

ISO 10128:2023 provides only a brief description of the Optimal method. To fully understand its principles and workflow, one must consult the 2018 TAGA Proceedings (www.taga.org), where detailed explanations are available.

The Technical Association of the Graphic Arts (TAGA) is an international organization composed of industry professionals, academics, and students, dedicated to scientific research and technological innovation in graphic communications.

 

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Mathematical Foundation

Both TVI curves defined by ISO 12647 and NPDC curves defined by G7 are smooth, idealized curves described by precise polynomial functions.

Tone Value Increase (TVI):

TVI(x)=100×(ax4+bx3+cx2+dx)\mathrm{TVI}(x) = 100 \times \left( a x^4 + b x^3 + c x^2 + d x \right)TVI(x)=100×(ax4+bx3+cx2+dx)

Where:

• TVI = tone value increase (%)
  
  

• a, b, c, d = polynomial coefficients
  
  

• x = normalized tone value, x=TV/100x = \mathrm{TV}/100x=TV/100
  
  

• TV = tone value (%) ranging from 0 to 100

Table 10 — Polynomial Coefficients for Tone Value Increase Curves

(ISO 12647-2:2013, Figure 3)

• Figure: Polynomial expression of ISO TVI curves

(CGATS/IDEAlliance TR 015-2015)

The relationship of the NPD of the black tone and its input tone value is defined by computations similar to those of 5.3 as follows.

 

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Conditional Definition

If YR(TV)>YCY_R(TV) > Y_CYR(TV)>YC

Then:

NPD(TV)=−log⁡10(YR(TV))(11)\mathrm{NPD}(TV) = -\log_{10}\left(Y_R(TV)\right) \tag{11}NPD(TV)=−log10(YR(TV))(11)

Else:

NPD(TV)=−log⁡10[YR(TV)−(RA−RR)(YC−YR(TV)YC−1+RR)(RA2+1)](12)\mathrm{NPD}(TV) = -\log_{10} \left[ Y_R(TV) - (R_A - R_R) \left( \frac{Y_C - Y_R(TV)}{Y_C - 1 + R_R} \right)^{\left(\frac{R_A}{2}+1\right)} \right] \tag{12}NPD(TV)=−log10YR(TV)−(RA−RR)(YC−1+RRYC−YR(TV))(2RA+1)(12)

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Where

YR(TV)=1−RR×(TV+TVI100)(13)Y_R(TV) = 1 - R_R \times \left(\frac{TV + TVI}{100}\right) \tag{13}YR(TV)=1−RR×(100TV+TVI)(13) YC=(0.7+0.3×(YDYL)13)3(14)Y_C = \left( 0.7 + 0.3 \times \left(\frac{Y_D}{Y_L}\right)^{\frac{1}{3}} \right)^3 \tag{14}YC=(0.7+0.3×(YLYD)31)3(14) RA=1−YDYL(15)R_A = 1 - \frac{Y_D}{Y_L} \tag{15}RA=1−YLYD(15) RR=0.978223R_R = 0.978223RR=0.978223 TVI(TV)=0.967175 TV−1.525445×10−2TV2+9.1347×10−5TV3−3.552×10−7TV4(16)TVI(TV) = 0.967175\,TV - 1.525445 \times 10^{-2} TV^2 + 9.1347 \times 10^{-5} TV^3 - 3.552 \times 10^{-7} TV^4 \tag{16}TVI(TV)=0.967175TV−1.525445×10−2TV2+9.1347×10−5TV3−3.552×10−7TV4(16)

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Definitions

• YDY_DYD
  Luminous reflectance factor of the dark end of the black scale, in the range of 0 to 1.
  
  

• YLY_LYL
  Luminous reflectance factor of the substrate, in the range of 0 to 1.
  
  

• YR(TV)Y_R(TV)YR(TV)
  Luminous reflectance factor corresponding to the reference NPD curve.
  
  

• YCY_CYC
  Control point along the NPD curve at which the scaling of YRY_RYR is initiated.
  
  

• RAR_ARA
  Actual reflectance range based on the light and dark ends of the tone scale.
  
  

• RRR_RRR
  Defined reflectance ratio used to adjust the subsequent scaling of the data.

• Figure: Polynomial expression of G7 NPDC curves defined in TR015

G7 gray balance curves are linear by definition, but practical printing conditions rarely achieve perfect linearity. Real-world data always contain fluctuations, making these curves approximations rather than exact ideals.

Similarly, the Optimal method also employs polynomial modeling—but specifically uses Bernstein polynomials. For offset printing, polynomial orders between 3rd and 6th degree typically yield optimal results. Higher degrees improve precision but reduce curve smoothness.

• Figure: Bernstein polynomial with parameters [0, 0.5, 0.2, 1.5]

Unlike TVI (dot percentage) or NPDC (density), the resulting Optimal curves have no direct physical meaning. They represent neither dot area nor density, but rather a purely mathematical solution optimized for color difference minimization.

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Principle of Operation

The entire calibration process involves identifying the polynomial parameters that minimize color differences between the measured dataset and the target dataset. The final output is a set of Optimal correction curves.

Because target curves are nonlinear, the optimization is typically solved using nonlinear least squares, specifically the Gauss–Newton method based on matrix mathematics.

The workflow is as follows:

1. Print a baseline chart using linear curves

2. Measure the chart to obtain Lab values

3. Compare measured Lab values with target ICC Lab values

4. Solve the normal equations to determine curve parameters

5. Iterate the process (typically ~5 iterations) until ∆E is minimized

Despite the mathematical complexity, modern software completes this optimization in 1–2 seconds. Weighting factors can be introduced to adapt the method to different printing processes.

 

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Sample Selection

All calibration methods depend critically on sample (chart) selection:

• TVI: CMYK single-channel tonal ramps (0–100%)

• G7 Grayscale: CMY overprint grays + K tonal scale (P2P chart)

• G7 ColorSpace: TC1617 chart

• PressSIGN: Control strip patches

• OPTIMAL: User-defined samples (recommended: actual production colors)

PressCal software recommends its own PressCalPTS chart.

⚠️ Sample choice directly determines calibration outcomes and evaluation validity.

For example, if the goal is to obtain PSO certification, then we should choose CMYK single-channel tones as samples; if it is to obtain G7 certification, we should choose CMY three-color gray and K color tones as samples; if it is digital proofing and calibration, we should choose ECI2002 or IT8.7-4/5 color charts as samples.

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Calibration Workflow (PressCal)

Currently, PressCal (https://www.optimalmethod.org/) is the only known tool supporting Optimal calibration. It is a macOS-only, command-line, Perl-based application resembling a developer-oriented curve engine.

Steps:

1. Define target ICC profile
   Use profiler_path (built-in or custom ICC)

2. Load measurement data
   Use press_path (MXF or TXT formats)

3. Select sample set and method
   Use select (e.g., all, g7, k, nosub)

4. Generate curves
   Use output (text, CGATS, DeviceLink, Photoshop curves, Prinergy)
   Execute with Command + R

 

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Example

Calibrating 220g Uncoated_M1.txt to GRACoL2013UNC_CRPC3.icc using Optimal:

• Processing time: 4.9 seconds

• Average ∆E reduced from 1.98 → 1.08

• Maximum ∆E reduced from 5.67 → 1.91

• Figure: Cumulative ∆E distribution before calibration

• Figure: Cumulative ∆E distribution after calibration

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Applications and Comparison

PressCal functions similarly to Curve4 / Curve+, but supports more calibration methods: OPTIMAL, TVI, SCTV (CTV), G7, and custom targets.

Limitations include:

• Command-line operation (not beginner-friendly)

• macOS only

• VPR output maintains Lab but modifies CMYK, complicating evaluation

Sample Selection Tokens

 

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Comparison Summary

Theoretically, Optimal's calibration results are better than TVI and G7, but since it is still a curve calibration method, the results are not better than Device-Link. It is a method that is not good enough but not bad either.

Our actual testing verified this conclusion, but unlike the official claims, the calibration results were not significantly different from G7. After all, the design of the P2P25/51 chart is very scientific, based on actual gray balance printing data. Calibration based on actual data is unlikely to be inferior to theoretical mathematical optimization methods. Our use of the Optimal method for curve calibration and VPR simulation of actual offset printing data also passed G7 certification because we used the GRACoL ICC based on G7 technology as the target, so this is not surprising. However, the verification that the OPTIMAL method is practically feasible is why it was accepted by ISO 10128.

 

Table 1: Comparison of results between Optimal and G7 calibrations (coated paper)

Method Comparison Results (G7 Evaluation)

Printing conditions: Offset coated paper (Lab: 92, 1.3, -5.5), Target ICC: GRACoL2013

Table 2: Comparison of results between Optimal and G7 calibrations (offset paper)

Method Comparison Results (G7 Evaluation)

Printing conditions: Offset printing on CCNB grey-backed white cardboard (Lab: 88, 0.36, -4), target ICC: GRACoL2006_SCCA

Theoretically, Optimal outperforms TVI and G7, but remains inferior to DeviceLink. It serves as an intermediate solution between curve-based calibration and full DeviceLink optimization.

The OPTIMAL method is a good approach, recognized by the ISO committee. Its calibration principle is similar to Device-Link, both aiming to minimize color difference. However, unlike Device-Link, it employs a four-dimensional cyclic calculation, yet the output remains a traditional curve. Since four curves can approximate the results of iterative optimization, Optimal can be considered a method between previous curve adjustments and Device-Link.

• Table 3: Comparison of four ISO 10128 calibration methods

Comparison of Calibration Methods

 

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Conclusion

The Optimal method offers:

• High flexibility

• Any process, any ink set, any gray balance

• Any sample set, any error metric

• Adjustable curve complexity

• Robust handling of measurement noise and outliers

• Open-source, standards-based, royalty-free implementation

In practice:

• TVI remains simplest and well-supported by Fogra

• G7/G7+ benefits from IDEAlliance promotion and brand backing

• DeviceLink dominates digital proofing and printing

• Optimal, newly standardized, still awaits broader industry adoption

With proper tooling and advocacy, Optimal has the potential to fill a crucial gap between simplicity and precision in color calibration.