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This is a repository copy of Rendering the CIE 1931 Chromaticity Diagram.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/86672/Version: Accepted VersionProceedings Paper:Rhodes, PA (2013) Rendering the CIE 1931 Chromaticity Diagram. In: MacDonald, L, Westland, S and Wuerger, S, (eds.) AIC Colour 2013: Proceedings. 12th Congress of the International Colour Association, 08-12 Jul 2013, Newcastle upon Tyne, UK. The Colour Group , pp. 1469-1472. ISBN 978-0901623027 © 2013 The Colour Group (Great Britain). This is an author produced version of a paper published in the Proceedings of AIC Colour 2013. eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.   Rendering the CIE 1931 Chromaticity Diagram Peter A. RHODES School of Design, University of Leeds, UK ABSTRACT Widely used in scientific and educational applications, this iconic colour chart consists of a two-dimensional projection of colour coordinates specified by CIE tristimulus values.  It is frequently to be found in text books and on posters promoting colour-measuring instruments and related products.  Despite its ubiquity, little attention seems to have been paid to correctness of reproduction.  On the contrary, most versions simply strive to create a “pleasing” representation which both precludes the diagram being employed for colour identification tasks and also gives a misleading impression of colour relationships. In this paper, an approach is described through which an improved rendering of the chromaticity diagram may be created in print or other media.  The goal is to create a colorimetrically accurate reproduction (given the colour gamut constraints of the medium) whilst preserving hue and chroma smoothness and continuity.  In addition, the chart needs to include both white point and also the technically correct depiction of colours close to the spectrum locus. 1. INTRODUCTION In 1931, the CIE published their system of colorimetry (CIE 1986) which enabled a colour stimulus to be defined by just three numbers, XYZ, for a given set of viewing conditions.  The system is still in widespread use today for industrial and scientific colour-matching tasks.  It had long been recognised that three dimensions were cumbersome, and so a two-dimensional projection was created which ignored the brightness (Y) dimension thereby enabling colours to be plotted on an xy chromaticity diagram (Wright 2007).  On this diagram, additive mixing can be predicted via straight lines connecting the points representing the lights’ chromaticities.  Chromaticity coordinates are used in numerous applications such as international standards for signal lighting.  The diagram is also helpful for examining the dominant wavelength and excitation purity of stimuli. While many attempts have been made to reproduce the CIE chromaticity diagram, this is typically done of the basis of aesthetic appeal rather than accuracy.  As a result, users are presented with a distorted view of CIE colour space which precludes its use for visual matching of a specimen’s chromaticity.  To produce a “better” diagram, the two most significant obstacles are colour fidelity and colour gamut.  Approaches such was the industry-standard ICC system for colour management (Green 2010) can help address the former, however dealing with gamut is rather less straightforward.   2. COLOUR GAMUT The CIE system of colorimetry was designed to encompass the entire range of visible colour, whereas any practical printing or display system is only capable of reproducing a subset.  Furthermore, colour gamut is a device-d pendent property, meaning that it varies according to the specific technology and its components.   2.1 Medium Gamut The range of colours that are reproducible on an imaging medium (e.g. printer and paper) can be described in terms of a gamut boundary through colour measurement.  Only colours within this boundary are reproducible.  An example of this for the printer used in thisstudy is shown in Figure 1.  Similarly, image-acquisition devices (cameras and scanners) have their own colour gamuts which limit how bright or colourful stimuli may be.  In addition, images themselves contain a certain range of colours.  Gamut mismatch is typically addressed by colour management.  With the ICC system, for example, users need to select one of four separate rendering intents according to their application (Green 2010).   Figure 1: colour gamut of the  printer used in this study. Figure 2: chromatic limits of real  colours (MacAdam 1935). 2.2 CIE Gamut The CIE chromaticity diagram is somewhat misleading in that the chromatic domain does not extend to the spectrum locus at every luminance.  Calculations by MacAdam (1935) have shown that lighter colours have a much more restricted range of chromaticities.  Only when the luminance factor is zero do colours reach the extremities.  This meansthat a chromaticity diagram becomes darker as distance from the white point increases. 2.3 Gamut Mapping There have been numerous algorithms proposed for mapping colours from one medium’s gamut to another – for a survey of some of these, see Morovič (2008).  These are generally aimed at producing pleasing images and are thus unsuitable to the task of faithfully reproducing the CIE diagram.  3. PROPOSED SOLUTION Although it is evidently not possible to render colours beyond the target device’s gamut, the out-of-gamut regions should at least be expected to preserve the correct hue if not the chroma.  In order to include the white point without further reducing available colour gamut, it is necessary to reduce lightness as chroma is increased.  A function was therefore defined which accomplished this as follows:   L´ = Lmax + Į•C2 + ȕ•C if C < Cmax L´ = L0  otherwise where Į = (Lmax – L0) / Cmax2 and ȕ = -2•Į• Cmax  In the above, L´ represents the new CIELAB lightness value to be rendered based on the hue-dependent maximum CIELAB chroma, Cmax at a CIELAB lightness of L0.  Lmax is the lightness of the white point (i.e. when a* = b* = 0).  In this case, constant values for L0, Į and ȕ of 50, 0.5 and -10 respectively were chosen in order to make lightness flatten out once the gamut threshold at L* = L0 and C* = Cmax has been crossed.  Beyond this boundary, lightness could either be preserved or alternatively – at the risk of changing hue – diminished to better reflect the MacAdam limits. 3.1 Gamut Smoothing A further complication arises at the interface between in- a d out-of-gamut regions.  Gamut boundaries differ significantly between devices not only in volume but also shape.  The irregularities and practical uncertainties of this boundary can lead to unacceptable discontinuities and so a smoothness constraint needs to be applied.  Th s was accomplished using a combination of averaging of the maximum chroma values at each hue together with a slight relative reduction.  The specific parameters used were determined empirically in order to produce visually acceptable results. 3.2 Creating the Diagram For this study, an HP Designjet Z3200 pigmented inkjet printer was used since it offered a relatively wide colour gamut and also included built-in spectrophotometer that could be used to both calibrate (ensuring repeatability) and characterise (profile) the device.  The printer is capable of printing on a wide variety of substrates, however a s mi-gloss instant-dry paper was chosen since this was found to deliver superior colour gamut compared to matt paper and also had good lightfastness and stabilisation properties. The basis for computation was an ICC profile for the printer.  Given this, gamut checking calculations were performed to determine the gamut boundary befo e creating a composite image of the final chart.  This image was stored as a 16-bit CIELAB TIFF file to ensure colorimetric fidelity.  Other elements of the diagram such as the spectrum locus, axes, grid lines, labels and black body curve were created as vector images using the Postscript language and these were subsequently rasterised as layers within the final TIFF image.  These components are illustrated in Figure 3.  (It should be pointed out that the colours shown are only approximate: hey are meant to be rendered onto a specific printer and so are device dependent.) 4. CONCLUSIONS Clearly any attempt to render the CIE chromaticity diagram has to involve a compromise due to real-world gamut limitations, however this work has succeeded in creating a much more faithful representation of the chart.  The same technique could be applied to the reduction of other – more perceptually uniform – chromaticity diagrams such as the CIE 1976 UCS or L*a*b* which are more approprate for tasks such as comparing colour gamuts. 50607080901000 2 4 6 8 10  The entire method has been implemented using a 12-channel wide-format printer which, in conjunction with an enhanced colour-management algorithm, is capable of reproducing individual colours to an accuracy of around 1 〉E.  The resultant charts are now being considered for adoption by the CIE as their official version of the chromaticity d agram. background axes and grid final diagram    colour space labels   Figure 3: constructing the CIE 1931 chromaticity diagram. ACKNOWLEDGEMENTS The author would like to express appreciation toMike Pointer, Phil Green and Ronnie Luo for their valuable suggestions.  Thanks are also due to the CIE for their encouragement. REFERENCES CIE, 1986. Colorimetry.  Publication 15.2 (second edition). Green, P., (ed.) 2010.  Color Management: Understanding and Using ICC Profiles, Wiley. MacAdam, D.L., 1935. Maximum Visual Efficiency of Colored Materials.  Journal of the Optical Society of America 27, 294-299. Morovič, J., 2008.  Color Gamut Mapping, Wiley. Wright, W.D., 2007.  Professor Wright’s Paper from the Golden Jubilee Book: the Historical and Experimental Background to the 1931 CIE System of Colorimetry in Colorimetry: Understanding the CIE System, ed. J. Schanda, 9-23. Address: Dr Peter A. Rhodes, School of Design,  University of Leeds, Leeds LS2 9JT, UK E-mail: P.A.Rhodes@leeds.ac.uk 

Rendering the CIE 1931 Chromaticity Diagram

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Rendering the CIE 1931 Chromaticity Diagram

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