G 0 AND THE GAMUT OF REAL OBJECTS

Transcription

1 G 0 AND THE GAMUT OF REAL OBJECTS Rodney L. Heckaman, Mark D. Fairchild Munsell Colour Science Laboratory Rochester Institute of Technology Rochester, New York USA ABSTRACT Perhaps most fundamental to the R. M. Evans notion of brilliance and its percepts of greyness and fluorence in the context of the gamut of real objects is the notion of Evans G 0 as the point where the percept of greyness in a stimulus disappears. Where the viewing mode changes from object mode where colour is said to have grey content to what Nayatani has termed as pseudo-colour and Evans as fluorence where colour takes on an almost surreal character. The point G 0 is uniquely determined by the chromatic strength of colours, and when mapped across a colour order system or appearance space, could be said to form a surface that encloses the entire volume of object colour thus delineating the gamut of real objects. Such a mapping is compared to other representations of the gamut of real objects - the MacAdam Limits and Pointer s gamut of real surface colours where the relative volume of the G 0 gamut in CIELAB is shown to be approximately 50% than Pointer s gamut and approximately 50% less than the volume enclosed by the MacAdam Limits. Keywords: colour gamut, object colour, brilliance INTRODUCTION R. M. Evans notes in the preface of his book, The Perception of Colour 1 that the way in which the eye s sensitivities are used by an observer who is presented with more and more complex situations is a correspondingly complex mixture of the observer s intentions, desires, and interests. In this context, Evans began with the simplest possible stimulus and eventually arrived at a treatment of the perception of colour in everyday situations. In his development of the subject, he introduced the concept of brilliance as a fundamental attribute of colour perception which led him to extend the fundamental perceptions of colour to more complex stimuli and the additional perceptions they invoke. To him, brilliance could not be directly derived from the known physical characteristics of the stimuli and the CIE 1931 Observer as can brightness, lightness, colourfulness, chroma, and hue, nor is it assignable to any known physiological characteristic of visual sensation. Perhaps most fundamental to the notion of brilliance and its percepts of greyness and fluorence in the context of perceptual gamut and the gamut of real objects is the notion of Evans G 0 as the point where the percept of greyness in a stimulus disappears. The notion that as brilliance proceeds from the perception of greyness through G 0, the mode of viewing changes from object mode where colour is said to have grey content in both the Nayatani 2 and Evans sense or veiled in the Herring sense 3. Above G 0 the mode

2 of viewing becomes what Nayatani has termed as pseudo-colour and Evans as fluorence where the perception of colour takes on an almost surreal character. The point G 0 is uniquely determined by the chromatic strength of colour as represented in a colour order system or appearance space. When mapped across all colours in such a system or space, that mapping then could then be said to form a surface that encloses the full volume of object colour thus delineating the gamut of real objects. And such a mapping can be then compared to other representations the gamut of real objects such as those of MacAdam 4,5 in 1935 and Pointer 6 in 1980, and most recently, X. Li, et al, of the University of Leeds 7 who accumulated a large number of reflectance data sets and the newly standardized Reference Colour Gamut 8. THE GAMUT OF REAL OBJECTS (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210o (b) h ab = 300o Figure 1: The MacAdam Limits 4,5 in CIELAB, CIE Illuminant D50 and the º Observer In his paper, Maximum Visual Efficiency of Coloured Materials 4,5, MacAdam stated that One of the most compelling objectives of pigment and dye chemists has been to produce colours of ever greater purity without the sacrifice of brightness. In the interest of insuring that reasonable expectations be set in this regard, MacAdam

3 computed what have come to be called the MacAdam Limits and this representation is referred to the theoretical maximum colour gamut of ideal materials. Figure 1 illustrates the volume in CIELAB, CIE Illuminant D50 and the º Observer, enclosed by these limits at four (4) different viewpoints. In contrast to MacAdam whose limits are specified without realization in the perception of an observer, Nickerson and Newall 9 in the early 1940s constructed a solid representation of the colour space of normal human perception realizable in practice as real conscious responses a psychological colour solid for Munsell chroma from zero to maximum, Munsell value from 1/ to 9/, and the five principle Munsell hues and their complementaries. (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210o (b) h ab = 300o Figure 3: Pointer s gamut of real surface colours mapped to CIELAB, CIE Illuminant D50 and the º Observer, in comparison with the MacAdam Limits, the theoretical maximum colour gamut of ideal materials, shown as a mesh. 6 M. R. Pointer in his 1980 paper 6 considered the gamut of real surface colours in the CIE 1976 L " u " v " and L " a " b " colour spaces for a typical dye set used in photographic paper and typical CRT displays. He compared this gamut to the theoretical maximum gamut as computed from MacAdam and what Pointer calls the real colour gamut composed from the Munsell Limit Cascade for a total of 768 colours. Figure 3 illustrates the resulting Pointer s maximum colour gamut for real colours (inner gamut) derived

4 from the Munsell Limit Cascade and the corresponding optimal colour gamut from MacAdam mapped to CIELAB, CIE Illuminant D50 and the º Observer. (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210o (b) h ab = 300o Figure 4: ISO Reference Color Gamut 8 in CIELAB in their respective colour in comparison with the MacAdam Limits, the theoretical maximum colour gamut of ideal materials, shown as a mesh. In 2002, Steingrimsson et al 10 considered that... new colouring and imaging techniques have allowed to generate surface colours with higher chroma values than Pointer has found. To this end, the gamut obtainable with surface colours by over 3,000 paper samples of Pantone colours used to specify, identify, and display specific colours or inks in the graphic arts industry was constructed and mapped to CIELAB, CIE Illuminant D50 and the º Observer, compared to the optimal colour solid using MacAdam s approach of calculating colour responses from spectral curves with the values of unity or zero showing only either one single transmission band or one single absorption band 10. In 2004, the ISO Reference Color Gamut 8 was published from three different colour gamut that developed under ISO TC 130 consisting principally of the Pointer gamut data, a Hewlett-Packard derived printer gamut, and a gamut PhotoGamutRGB based in photographic printing. Figure 3 illustrates this gamut in the whose data was obtained from Holm, Tasti, and Johnson s CIC 14 paper. 11

5 Finally and most recently, X. Li, et al, of the University of Leeds presented a paper 7 in 2007 that accumulated a large number of reflectance data sets (85,900 samples in total) for comparison to Pointer s gamut and the newly standardized Reference Colour Gamut 7. Their results are claimed to be more reliable principally due to the shear number of samples. A COMPUTATIONAL BASIS FOR GREYNESS By way of acknowledgment of Evans work in the paper, On Attributes of Achromatic and Chromatic Object Colour Perceptions 12, Nayatani notes that the chroma perception in the chromatic colour series is always assessed only by considering its chromatic component, but neglecting its greyness although the perception of greyness always exists. Furthermore, in opponent colour theory, greyness is also important for whiteness-blackness perception. Without greyness, object colour perceptions in opponent colour responses are represented in a triangular or oblique representation like the Natural Colour System (NCS). With greyness, an orthogonal representation is possible. Figure 5: Nayatani Theoretical (NT) Colour Perception Space in the Modified Opponent Colour System 13,14,15 To this end, Nayatani proposed a modification to Hering s opponent colour theory 13,14,15 which came to be known as the Nayatani Theoretical (NT) opponent colour space (Figure 5) having some basis in Hering s veiling glare concept 3 that Nayatani notes by citing a quote from the Hering book: If a chromatic colour appears definitely whitish, greyish, or blackish, I call it, as I already said, a veiled colour. And further on, It can be said that in each clearly veiled chromatic colour both a chromatic and a black-white can be distinguished. In Nayatani s paper, A Modified Opponent Colour Theory Considering Chromatic Strengths of Varies Hues 14, he brings together the concepts of chromatic strength and the perception of greyness developed since the early 1990 s into almost a unified theory of colour appearance. And contrary to the NCS representation of

6 chromaticness as being constant independent of hue, Nayatani proposed that maximum chroma c rel,max for each hue is determined by its chromatic strength: c rel,max =100CS rel (1) where CS rel is the chromatic strength Es (") at hue" relative to yellow. Furthermore, the chromatic strength function is necessary to transform a uniform colour space for estimating colour differences to a colour appearance space 14. In Nayatani s NT system, greyness gr is given by: gr = 0 for c gen "100 (2) and gr =100 " c gen for c gen < 100 (3) ( ) + ( r g) + ( y b) = ( w bk) + c rel. In the Natural Colour System where c gen = w bk (NCS), Nayatani s relationships 13 between greyness gr and NCS chromaticness C, whiteness W, and blackness S can be expressed simply as: gr = 2min( W,S) (4) where W is computed from W = 100 "C " S, the normalization relationship for the NCS notation. THE MAPPING OF THE SURFACE OF THE LOCI OF G 0 FROM THE NATURAL COLOUR SYSTEM TO THE APPEARANCE SPACE CIELAB The primary attributes of the Natural Colour System (NCS) for the set of twentyfour (24) NCS aim colour patches and their corresponding measured CIE XYZ values in illuminant A, the CIE 1931 observer, are available in Swedish Standard SS and Bencuya 17. Figure 6 illustrates, for example, the set of NCS aim colour patches for the NCS hue R10B. As the NCS is an octahedral representation, lines of constant whiteness ranging from 0 to 100 are shown slanted downward, and lines of chromaticness also ranging from 0 to 100 as vertical lines. Table 1 tabulates the corresponding primary NCS attributes of blackness and chromaticness and their CIE tristimulus values from the NCS hue R10B. The NCS attribute of whiteness is computed from the normalizing relationship for the NCS system, W = 100 "C " S, and grey value gr from Equation 4 in the above. Zero values of grey ( gr = 0) represent G 0. The set of all zero grey values in this, the R10B plane, then represents the loci of G 0 in this plane along with their corresponding CIE tristimulus values.

7 Figure 6: NCS aim colour patches for NCS hue R10B 17 Table 1: NCS blackness S, chromaticness C, whiteness W, grey value gr, and CIE XYZ for Illuminant A, 1931 Observer, for the NCS aim colour patches for hue R10B 17 s c w gr CIE X CIE Y CIE Z s c w gr CIE X CIE Y CIE Z The collection of G 0 loci for each of the twenty-four (24) NCS hues then form the surface of zero grey or G 0 and is said to contain the totality of object colour. The mapping illustrated in Figure 6 plots this collection in the appearance space CIE L*a*b* as converted from the! respective CIE tristimulus values for each G 0 point then chromatically adapted to illuminant! D50. The points are plotted as disks coded by their respective CIELAB colour.!

8 Figure 7: The points G 0 for each of the twenty-four (24) NTS aim hues mapped to CIELAB and shown as circles of their respective colour (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210o (b) h ab = 300o Figure 8: The loci of G 0 mapped to CIELAB in their respective colour in comparison with the MacAdam Limits, the theoretical maximum colour gamut of ideal materials, shown as a mesh.

9 In Figure 8, the surface of G 0 or zero grey is mapped to the appearance space CIELAB for four separate viewpoints. The corresponding surface formed from the MacAdam Limits, the theoretical maximum colour gamut of ideal materials, is shown for comparison. In spite of the slight concavity of the mapping shown in Figure 7, the surface was never-the-less generated using Matlab s function convhull which finds the outer boundaries of the volume of data formed from the scalar RGB grid and, as such, assumes the surface is convex. In Figure 7, the G 0 loci in CIELAB is generally convex except in its lower extremities of lightness. Hence, the mapping in Figure 8 may slightly exaggerate the fullness in these lower extremities but does not exaggerate its extent at maximum chroma and above. The maximum extent of G 0 in this plane of maximum chroma approaches that of the MacAdam Limits in the blues and greens (cyan) and between red and yellow (orange) and falls short in the greens, reds, and yellows. And as has been noted 18, the surface of G 0 possibly is a representation of our estimate of the perception of pure colour. (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210 o (b) h ab = 300 o Figure 9: The Pointer gamut of object colours 6 mapped to CIELAB as a surface in comparison with the loci of G 0 or zero grey shown as a mesh.

10 COMPARISON WITH THE POINTER AND THE ISO REFERENCE COLOR GAMUT ESTIMATES OF OBJECT COLOUR GAMUT Figure 9 illustrates Pointer s maximum colour gamut for real colours (inner gamut) as derived from the Munsell Limit Cascade compared to the loci of G 0 or zero grey (the mesh). As shown, Pointer s estimate of object colour gamut is less in both its extent and fullness than the G 0 mapping particularly in the greens. Yet, in the reds, both mappings are virtually coincident. And while the G 0 mapping is slightly less in extent and fullness than that formed by the MacAdam Limits, the mapping of the Pointer set is correspondingly less in extent and fullness than the G 0 mapping. (a) h ab = 30 o (b) h ab = 120 o (a) h ab = 210 o (b) h ab = 300 o Figure 10: The ISO Reference Colour Gamut in CIELAB in comparison with the loci of G 0 or zero grey shown as a mesh. Figure 10 illustrates the ISO Reference Colour Gamut as compared to the loci of G 0 (the mesh).as shown, both estimates are, at first, surprisingly equivalent considering one has a theoretical basis in Evans brilliance and the other purely empirical. The mappings are virtually coincident in all but the greens where the G 0 estimate is significantly extended.

11 DISCUSSION AND CONCLUSIONS The boundary separating the two mutually exclusive perceptual components of Evans brilliance, 1 greyness or object colour and fluorence or Nayatani s pseudo-colour, was constructed in the appearance space CIELAB from Nayatani s relationships for greyness 13,14,15 and the primary attributes of the Natural Colour System. From such a representation, the gamut of real object colours is estimated and compared with Pointer s estimate, the ISO Reference Colour Gamut, and the MacAdam Limits. Table 2 tabulates the respective volumes and projected areas onto the plane of chroma for each of these estimates. As such, the G 0 estimate contains almost 50% more colour than the Pointer estimate, yet does not begin to approach the volume of pure colour as estimated by MacAdam. Hence, while it would be difficult to attribute the G 0 estimate as simply a representation of our estimate of the perception of pure colour as proposed in the above, such an estimate could be said to bound perceptually the entirety of object or surface colour gamut. Table 2: Estimates of the volume and projected areas onto the plane of colour Estimate of the gamut of object colour Volume (L* x a* x b* x 10-5 ) MacAdam ISO G Pointer Projected Area (a* x b* x 10-4 ) The gamut volumes for both the ISO Reference Colour Gamut and the G 0 estimate are virtually identically in volume, and this result, while noted as perhaps surprising in the above, is really not so surprising as the G 0 estimate was computed from the NCS aim colour patches. Hence, while grounded in Evans and Nayatani s theories of brilliance, the estimates are also empirically derived and serve to both add legitimacy to the theory and credence to the NCS system. In essence, an object colour gamut derived from the NCS aim colour patches and Evans and Nayatani s theories of brilliance seem as close an estimate of object colour gamut as the ISO Reference Colour Gamut consisting of literally thousands of samples collected over a period of twenty (2) to thirty (30) years. The notion that the perception of greyness is indigenous to all of object or surface colour and the assertion by Nayatani based in the NCS colour order system that greyness is the lesser of NCS whiteness and blackness are almost purely theoretical. Little empirical data short of Evans experiments in the 1950s are available in support. Yet, as the visual media becomes fully capable of rendering colours beyond those of objects or surfaces, such a notion becomes very compelling as a basis for understanding perception in such an extended gamut beyond even object colour. Furthermore, efforts to estimate the bounds of real object colour for the purpose of somehow bounding the requirements for both display [and print media technologies as was MacAdam s original motive] seems an effort whose time has past. Today, it is clear that the technology will soon be available to reproduce colour beyond that possible in objects - colour that we experience everyday.

12 REFERENCES 1. R.M. Evans, The Perception of Colour, John Wiley and Sons, New York, Y. Nayatani, et al, Relation on Helmholtz-Kohlrausch Effect, Purity Discrimination, and G 0 Function, Proc. Of the 7 th Congress of International Colour Association, Vol. B Budapest, Hungary, (1993) 3. E. Hering, Outline of the Theory of Light Sense, L. M. Hurvich amd D. Jameson, translation, Harvard University Press (1964) 4. D.L. MacAdam, The Theory of Maximum Visual Efficiency of Coloured Materials, J. Opt. Soc. Am. 25, 249 (1935) 5. D.L. MacAdam, Maximum Visual Efficiency of Coloured Materials, J. Opt. Soc. Am. 25, 361 (1935) 6. M. R. Pointer, The Gamut of Real Surface Colours,, Colour Res. Appl. 5, (1980) 7. C. Li, C.J Li, M.R. Luo, and M. Pointer, A Colour Gamut Based on Reflectance Functions, Proceeding of the 15 th Colour Imaging Conference (CIC16), Albuquerque, NM (2007) 8. ISO/WD , Annex B, Definition of the reference gamut, ISO (2004) 9. Nickerson and S.M. Newell, A Psychological Colour Solid, Wavelength, J. Opt. Soc. Am. 33, (1943) 10. U. Steingrimsson, et al, The Gamut Obtainable with Surface Colours, Proc. Of the First Conference on Colour Graphics, Imaging, and Vision, CGIV (2002) 11. J. Holm, I. Tasti, and T. Johnson, Definition and Use of the ISO Reference Color Gamut, Proceeding of the 14 th Colour Imaging Conference (CIC14), Scottsdale, Arizona (2006) 12. Y. Nayatani, On Attributes of Achromatic and Chromatic Object-Colour Perceptions, Colour Res. Appl. 25, (1999) 13. Y. Nayatani, Some Modifications to Hering s Opponent Colours Theory, Colour Res. Appl. 26, (2001) 14. Y. Nayatani, A Modified Opponent Colours Theory Considering Chromatic Strengths of Various Hues, Colour Res. Appl. 28, (2003) 15. Y. Nayatani, Proposal of an Opponent Colours System Based on Colour Appearance and Colour Vision Studies, Colour Res. Appl. 29, (2004) 16. Swedish Standard SS , Tristimulus Values and Chromaticity Coordinates for the Colour Samples in SS , Swedish Standards Institute, Stockholm (1979) 17. H. K. Bencuya, Relations between the Natural Colour System and th Munsell Colour Order System, Masters thesis, Fred W. Billmeyer, advisor, Rensselaer Polytechnic Institute (1984)

13 18. R. W. G. Hunt, A model for colour vision for predicting colour appearance, Colour Res. Appl. 7, (1982)