Determining CIEDE2000 for Printing Conformance

Transcription

1 (A paper to be presented at the iarigai Research Conference, Sept , 211, Budapest, Hungary) Determining CIEDE for Printing Conformance Robert Chung and Ping-hsu Chen Keywords: CIELAB, E* ab, E, Optimized E Abstract ISO specifies tolerance of solid KCMY in CIELAB DE metric. Due to the fact that CIELAB lacks visual uniformity, ISO/TC13 decided to use CIEDE metric, where appropriate, for all new ISO/TC13 standards and revisions of existing standards. This study used a printing database of over printed samples to find out how solid conformance, determined by each metric, compared to each other. This research is not limited to finding CIEDE values that are backward compatible with CIELAB DE. More importantly, this study recommends tolerance of solid KCMY in CIEDE metric that are visually uniform. As a result, the value of 2.4 E is recommended for solid CMY and the value of 3.6 E is recommended as for black solid. These recommendations accommodate both visual uniformity and compatibility of the two E metrics. 1. Introduction CIE developed the CIELAB color space as an approximation of uniform color space in The Euclidean distance in CIELAB color space, i.e., E* ab, provides a quantitative way to define color difference. Several color difference metrics, such as CIE94, CMC, and CIEDE, have been proposed to provide a better correlation between the perceived color difference and instrumental color difference. There is no single ratio between E* ab metric and these newer color difference metrics. In Berns paper (1996) and textbook (), he described a method for setting color tolerance between color difference data and visual data. This research adopted the method to find optimized CIEDE tolerances values for ISO (4 and 7) solids of KCMY with a tolerance of 5 E* ab. 2. Research Question The Euclidian distance is not good enough to discern and describe perceived color difference for graphic arts industry. For example, equal color differences values E* ab of solids KCYM are perceived unequal in their visual color difference. The 24 th ISO/TC13 Plenary Meeting, Sao Paulo, Brazil (TC13 N1733, 21) resolved to use CIEDE for all new ISO/TC13 standards and revisions of existing standards, where appropriate. A difficulty in adopting E is that there is no single tolerance value in E metric that matches exactly the outcome with E* ab metric. For example, two samples with identical E* ab, as shown in Table 1, do not have the same E values, calculated according to CIEDE equations (ISO 13655, 9).

2 2 Table 1. Example of samples with identical E* ab but not identical E values ISO aim (L*,a*,b*) Samples (L*,a*,b*) E* ab E 59, -36, , -36, , -41, Using ISO aim for cyan (L*, a*, b* = 54, -36, -49) as an example, a tolerance of 5 E* ab encompasses a group of (L*, a*, b*) values on the circumference of a circle that have an Euclidean distance of 5 from the ISO aim. When calculating the E values between the ISO aim and the group of (L*, a*, b*) values, they do not produce a single CIEDE value. This issue can be further explored and expressed in Figure 1. The upper-center figure shows the ISO aim of cyan solid. There are 36 points, at an interval of 1 degree, on the circumference of the circle and they are all 5 E* ab away from the cyan ISO aim. 3 3 CIEDE CIEDE 3 3 CIEDE CIEDE Figure 1. Example of samples with identical E* ab but not identical E values The middle-left figure shows the histogram of E values for those points on the circumference of the circle compared to the histogram of E* ab that are 5 E* ab from the

3 3 cyan ISO aim. To elaborate, the E values of those equal E* ab points are (1) smaller in magnitude, (2) not converging, and (3) non-normal distributed. The middle-right, lower-left, and lower-right of Figure 1 show the cases for magenta, yellow, and black solids, respectively. By observing the E distributions of CMYK solid, we can further conclude that: (1) colors having equal E* ab convert to a range of E, (2) E magnitude of CMY solid is less than E* ab, and (3) E magnitude of black solid is similar to E* ab. In other words, there is no easy solution in determining a single value in CIEDE metric for each of the KCMY solids. This leads to the research question, How can we determine color tolerance as a single CIEDE metric for KCMY solids that represents the best compromise in E* ab? 3. Literature Review & Research Question There are three instances where converting color tolerance from E* ab into E numbers for KCMY solids were studied. Specifically, Andreas Kraushaar (21), Danny Rich (21), and David McDowell (211) discussed their approaches and findings at ISO/TC 13 meetings. Kraushaar used 112 CIELAB measurements of KCMY solids from the bvdm/fogra certification database, computed both E* ab and E between measurement and ISO colorimetric aims. Based on the CRF (cumulative relative frequency) of E* ab and E, he showed that the probability of passing at 5 E* ab for cyan solid is equivalent to the probability of passing at 2.6 E. Only cyan solid was documented in his case study. Rich took thousands of data points passing the ISO criteria around the printed solids. Ratios and their ranges between the two metrics, E* ab and E, were recommended based on those simulated pass data. Due to the fact that the magnitude of E is hue-, chroma-, and lightness-dependent, Rich was not able to recommend a single E, but a range of E that equate to 5 E* ab. McDowell took ratios between two metrics, E* ab and E, from colorimetric data measured from proofing samples of IT8.7/4 target, and tried to find the best ratios of tints and solids between E* ab and E. It was shown that the ratio is proportional to KCMY ink amount and there is no single ratio between the two metrics. The above literature review indicates that equal E* ab transforms into unequal E of less magnitude around KCMY solids, with the exception for K. But none can claim that there is a CIEDE metric for each of the KCMY solids. Thinking outside the box, this research used a printing database of over printed samples to find out how solid conformance, determined by each color difference metric, compared to each other. To state the research question differently, i.e, Is there a single E that will pass as many jobs that E* ab also passes and, at the same time, fail as many jobs that E* ab also fails? If such a value exists, we will call it, Optimized E.

4 4 4. Methodology In order to determine Optimized E, we need a database with a large amount of printed samples, including jobs that pass and jobs that fail the criterion of 5 E* ab. We also need an optimization strategy. Once Optimized E is determined, we need to realize that finding CIEDE values that are backward compatible with CIELAB DE, is not the endgame. More importantly, we need to recommend tolerance of solid KCMY in CIEDE metric that are visually uniform while backward compatible. This section describes (1) an example of color tolerance optimization, (2) how to derive Optimized E tolerances from database. The result of Optimized E tolerances are discussed before the determination of E tolerances for ISO solid conformance. An Example of Color Tolerance Optimization In his textbook, Berns describes an optimization routine that derives color tolerances between instrumental and visual data. Below is a step-by-step adoption of the optimization routine used in this research: Step 1. Given a database with 35 L* a* b* measurements for cyan solids. Their E* ab values and conformance compared to ISO tolerance (5 E* ab ) are listed in Table 2. Table 2. E* ab values and conformances of 35 cyan samples Sample E*ab Conformance Sample E*ab Conformance Sample E*ab Conformance #1 5.1 Fail # Pass # Pass #2 2.5 Pass # Pass # Pass #3 1.7 Pass # Fail # Fail #4 6.1 Fail # Pass #28 3. Pass #5 3.5 Pass # Pass # Pass #6 1.3 Pass # Pass #3 1.9 Pass #7 1.4 Pass # Fail # Fail #8 2.7 Pass #2 1.3 Fail # Pass #9 3.7 Pass #21 7. Fail # Pass #1 3.2 Pass # Fail # Fail # Pass #23 4. Pass # Pass # Pass # Pass Step 2. The data in the Table 2 are then sorted into two groups: pass (5 E* ab or less) and fail (greater than 5 E* ab ). Step 3. The CIEDE values of 35 measurements can also be calculated based on the measurements and the ISO aim. Two groups (pass and fail) data are listed in Table 3 with corresponding CIEDE values and placed in ascending order.

5 5 Table 3. Data of pass & fail groups with CIEDE values in ascending order (Table 3). Table 3. CIEDE values in ascending order Pass CIED Pass CIED Fail CIEDE Step 4. The cumulative percentages (also known as CRF or cumulative relative frequency) for pass and fail groups are then calculated as follows: CRF pass,i =(i /n p ) CRF fail,i = (i /n f ) where n p and n f represent the numbers of samples passed and failed, respectively, and i represents sample ID, which is 1 to 25 for pass group and 1 to 1 for fail group in this example. Step 5. The CRF percentages (%CRF) with corresponding CIEDE values are listed in Table 4. Table 4. CRF of pass and fail groups with CIEDE values Pass CRF % CIED Pass CRF % CIED Fail CRF % CIEDE

6 6 Step 6. The %CRFs are plotted as a function of CIEDE values (Figure 2). Figure 2. %CRF of pass and fail groups If only the CRF of passed samples are plotted (colored in cyan) in Figure 2, one might conclude that the equivalent tolerance is the maximum E of the pass group. This is what Kraushaar did. On the other hand, if only the CRF of failed samples are plotted (colored in blue), then the equivalent tolerance is the minimum E of the fail group. When both CRF curves are plotted, the intersection of the pass and the fail groups provides Optimized E tolerance that maximizing the agreement between two metrics. In this case, below the intersection (2.4 E & 81% ), the CRF curve (colored in cyan) represents the case that data pass with E* ab metric also pass with E metric, and the CRF curve (colored in blue) represents the case that data fail with E* ab metric also fail with E metric. This points out the importance of having a large database with both pass and fail samples when determining Optimized E. Deriving Optimized E Tolerances from Database In this research, a total of 28 jobs from three databases, PSA, PSO, and G7, as shown in Table 5, were used. PSA (211) database (n = 35) is unfiltered, thus, containing failed samples according to ISO criteria. On the other hand, PSO database (n = 88) is filtered, i.e., it only contains passed samples according to ISO criteria. G7 database (n = 85) is filtered where only samples that pass G7 Grayscale requirements are included. In addition, G7 database is not filtered according to ISO criteria for solid conformance, and hence it also provides data failed 5 E* ab. These three databases were all used in the optimization routine, as described in the previous section. Table 5. Three databases used in this research Database Number of Jobs Filtered/Unfiltered Remark PSA 35 Unfiltered 21 PSA survey PSO 88 Filtered by solid & Courtesy of bvdm/fogra TVI G7 85 Filtered by greyscale Courtesy of IDEAlliance

7 7 5. Results and Discussion Figure 3 shows the %CRF versus the ordered E values. The green lines help to locate the intersections, Optimized E, and the percentages of outcome equality. When using 5 E* ab tolerances, the intersections of KCMY are at 3.6, 2.4, 2.2, and 1.5 E, respectively. Figure 3. Optimized E derived from the combined databases Optimized E corresponding to 5 E* ab tolerances of printed solids are listed in Table 6. Optimized E tolerances keep equal outcome higher than 84% in this case. Considering the two CRF curves form the shape of X, the following observations apply to all four graphs: (A) The lower left of the X represents samples that pass both 5 E* ab and its Optimized E. (B) The lower right of the X represents samples that fail both 5 E* ab and its Optimized E. (C) The upper left of the X represents samples fail E* ab metric, but pass at its Optimized E. (D) The upper right of the X represents samples pass 5 E* ab metric, but fail at its Optimized E.

8 8 Table 6. Optimized E tolerances corresponding to 5 E*ab tolerances of solids E*ab E K ISO Solid Tolerances C M Y These four observations can also be described as Figure 4. In the figure, the circle indicates the E*ab tolerance, and the ellipse indicates E tolerance. Case A, B, C, and D correspond to the A, B, C, and D observations above, respectively. (A) (B) (C) (D) Figure 4. "Venn diagrams" between E*ab and E metrics Determining E Tolerances for ISO Solid Conformance The key motivator of this research is to replace E*ab by E that better aligns instrumental color difference with perceived color difference while backward compatible. This means that a single E tolerance for all KCMY solids would be most desirable. Optimized E tolerance, as shown in Table 6, only provides backward compatibility between the two color difference metrics. One possible solution for a single E tolerance is to consider the average of all four Optimized E, or Ave _ ΔE = = By using the average, i.e., 2.4 E, it will have minimum impact on cyan solid conformance and be more forgiving for magenta and yellow solid conformance. However, a single E will cause many jobs in the database to fail due to the tightened

9 9 tolerance in black solid. A more suitable solution is to use 2.4 E for CMY solids tolerance and to use 3.6 E for black solid tolerance. To further verify that the black solid distribution is different than CMY solid distributions in the E dimension, a simulation of color differences of 4 data points, evenly selected from the spherical surface of the 5 E* ab spheres with centers of ISO aims of KCMY solids, were computed in E* ab and E. As shown in Figure 5, the distribution of the black solid is different than distributions of CMY solids. The recommendation of 3.6 E for the black solid is necessary in order to provide backward compatibility CIEDE 3 CIEDE CIEDE 3 CIEDE Figure 5. Distributions of E values from the spherical surface of (5) E* ab value Based on the above analyses and reasoning, it is recommended that 2.4 E be used for CMY solids tolerance, and 3.6 E be used for K solid for ISO solid conformance. 6. Summary ISO/TC13 resolved to use CIEDE because it has better correlation to human visual perception. Previous researches for converting color tolerance from E* ab into E for KCMY solids are mainly based on filtered database or simulated data. Due to the fact that there is no single ratio between two metrics, they had difficulties in making their recommendations convincing.

10 1 In this research, Berns' method was adopted to find Optimized E tolerances corresponding to the tolerances of 5 E* ab. The combined databases, consisted of 28 real printed jobs, were used to better represent the capability of the printing process. While there is no obvious ratio between the two metrics, Optimized E tolerances keep the pass/fail outcome between two metrics as close as possible. Overall, the equality of outcome is close to 9%. It should be noted that Optimized E tolerances are mainly provided a starting point to determine the CIEDE tolerances for ISO solid conformance. It represents the best compromise between CIELAB DE and CIEDE, but it is not necessary the final recommendation. Because the CIEDE calculation of black solid behaves differently than CMY solids, this research recommends that a more suitable solution is to use 2.4 E for CMY solids tolerance and to use 3.6 E for black solid tolerance for ISO solid conformance. 7. References R. S. Berns, Billmeyer and Saltzman s Principles of Color Technology, Third Edition. Wiley & Sons, New York,, pg R. S. Berns, Deriving instrumental tolerances from pass-fail and colorimetric data, Color Res. Appl. 21, , 1996 ISO Graphic technology - Process control for the production of half-tone colour separations, proof and production prints - Part 2: Offset lithographic processes. 4 and 7 ISO/TC 13 (N1733), Resolutions 24th Plenary Meeting, , Sao Paulo ISO Graphic technology -- Spectral measurement and colorimetric computation for graphic arts images. 9 A. Kraushaar, Results on CIEDE, ISO/TC 13 (N5), 21 D. C. Rich, White paper on ISO tolerances, ISO/TC 13 (N994), 21 D. L. McDowell, CIEDE Draft 2, ISO/TC 13 (N153), 211 R. Chung and P. Chen, Statistical Analysis of PSA Press Sheet Check-up Database, RIT Printing Industry Center, Rochester, NY, PICRM- PICRM-211-8, 211