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International, Inc. W. K. E. Analysis of Experimental Data Used for Development of CIE DE 2000 Color Difference Formula. Pavel Bourov , UniqueIC’s , Saratov, Russia Sergey Bezryadin , KWE International Inc , San Francisco, USA. Introduction.
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International, Inc. W K E Analysis of Experimental DataUsed for Development of CIE DE 2000 Color Difference Formula Pavel Bourov, UniqueIC’s, Saratov, Russia Sergey Bezryadin, KWE International Inc, San Francisco, USA
Introduction • For Printing Technology, accuracy of color reproduction is important. • When we talk about precision of color reproduction, there is a need for numerical evaluationof error. • To evaluate an error, we have to calculate color difference, a difference between original color and reproduced color. • CIE DE 2000 and its modifications are based on experimental data recorded by DONG-HO KIM, KLAUS WITT, M. R. LUO andROY S. BERNS. • This datashould be used in testing Color Difference Formula quality.
Introduction • In this presentation, we will… • Show that experimental data received by DONG-HO KIM, KLAUS WITT, M. R. LUO andROY S. BERNS should be additionally processed prior to its use for evaluation of Color Difference Formula quality. • Discuss experiment’s potential errors that were found as a result of testing experimental data for reproducibility. • Show that experimentalists used different scales for Visual Difference measuring. • Show that a methodical error of the experiment exists: dV ≠ 0for concurrentstandard and batch.
Array data description • The array of experimental data consists of 3813 pairs: • First element in a pair is stimulus called standard (or color center). • Second element is difference between first (standard) and second (batch) stimulus. • For each pair the following data is available: • Number and name of the pair. • Tristimulus values of the standard, XYZ. • Color difference between batch and standard, dx, dy and dY. • Visual Difference dV.
Array data description • The experimentally measured valueVisual DifferencedVmay be described by a function of six variables:dV = f(X, Y, Z, dx, dy, dY) • For a group of pairs with same standard (X, Y, Zare fixed) and negligibly small chromatic coordinates change (dx = dy = 0), a Visual Difference dV might be represented by a function of only one variable:dV=fX, Y, Z, dx=0, dy=0 (dY) • When dY values are small, fX, Y, Z, dx=0, dy=0 (dY) may be approximated by a linear function with Tailor formula and graphically represented by a straight line. • The function is equal to zero when dY=0. In this case a batch coincide with a standard of a pair.
Description of the method • To test reproducibility of data, we chose pairs for which the following conditions are met: • An angle between a vector representing the standard of a pair and a vector representing color difference is less than 5˚. • Here and further lengths and angles are in Cohen metric.
Analysis of Grey stimuli • We start our analysis with gray stimuli. An angle between standard of a pair and Day Light D65 does not exceed 5°. • The vertical axis D is Day Light D65. D Day Light D65 5˚
Analysis of Grey stimuli • KLAUS WITT experimental data has 13 pairs satisfying stated conditions. • For all 13 pairs, Y ≈ 30. • To be described with the same function, Grey stimuli data provided by other experimentalists was narrowed down to the pairs with Y ≈ 30. • Within stated restrictions, there are 31 pairs in the examined data pool: • 8 pairs from DONG-HO KIM. • 13 pairs from KLAUS WITT. • 10 pairs from M. R. LUO.
Analysis of Grey stimuli • According to our assumptions all these experimental data should be approximated by a straight line passing through zero. • Next slides demonstrate you that these data correlate with our assumption except following: • For every experimentalist there are some points outstand a line. • All lines do not pass through zero.
Analysis of Grey stimuli. DONG-HO KIM data Outstanding pair (#243) The line does not pass through zero
Analysis of Grey stimuli. DONG-HO KIM data But Visual Differences differ ~ 30% There are 3 pairs with almost identical stimuli Visual Differences differ ~ 20%
Analysis of Grey stimuli. KLAUS WITT The line does not pass through zero Outstanding pairs (#363, #673)
Analysis of Grey stimuli. KLAUS WITT But Visual Differences differ about two times There are 3 pairs with almost identical stimuli Visual Differences differ about two times
Analysis of Grey stimuli. M. R. LUO Outstanding pair (#2125) The line does not pass through zero Pay attention to this pair (#3248)
Analysis of Grey stimuli. M. R. LUO According to Wyscezki & Fielder grey stimuli are indiscriminateif their luminance differ < 2%. For this pair luminance change is ~ 0.5%but Visual Difference was measuredwith 6 significant digits!
Analysis of Grey stimuli • All experimental data should be approximated by the same line. However, they are not • dV = 0.64·|dY| + 0.18 DONG-HO KIM. • dV = 2.47·|dY| + 0.97 KLAUS WITT. • dV = 0.63·|dY| + 0.20 M.R. LUO. • DONG-HO KIM and M. R. LUO linear functions are almost the same. • KLAUS WITT linear function differs a lot. • Multiplication by 3.9 of DONG-HO KIM andM.R. LUO Visual Differences allows tobring them to the same scale as KLAUS WITT: • dV = 2.50·|dY| + 0.70DONG-HO KIM. • dV= 2.46·|dY| + 0.78M.R. LUO.
Analysis of Coloredstimuli • For the analysis of colored stimuli we chose sets of Red, Yellow, Green, and Blue stimuli from KLAUS WITT andM. R. LUO experimental data. • DONG-HO KIM and ROY S. BERNS experimental data does not provide a representative set of samples and therefore is excluded from further discussion. • M. R. LUO data was scaled similar to what has been done with grey stimuli.
Scale factor • Scale factor depends on color: • 3.89for Grey stimuli • 3.40 for Red stimuli • 3.91 for Yellow stimuli • 3.50 for Green stimuli • 3.50 for Blue stimuli • We suggest to use 3.7 as a universal scale factor. • A difference between KLAUS WITT interpolation function and M. R. LUO data taken with the universal scale factor is about to spread in M. R. LUO data.
Conclusion • In this presentation, we… • Showed that experimental data received by DONG-HO KIM, KLAUS WITT, M. R. LUO andROY S. BERNS should be additionally processed prior to its use for evaluation of Color Difference Formula quality. • Discussed experiment’s potential errors that were found as a result of testing experimental data for reproducibility. • Showed that experimentalists used different scales for Visual Difference measuring. • Showed that a methodical error of the experiment exists: dV ≠ 0for concurrentstandard and batch. • Showed that data spread might be scientifically reduced if Visual difference recorded by DONG-HO KIM and M. R. LUO is multiplied by 3.7.
