Journal of Comparative Physiology A

, Volume 170, Issue 5, pp 533–543 | Cite as

The colour hexagon: a chromaticity diagram based on photoreceptor excitations as a generalized representation of colour opponency

  • Lars Chittka


A chromaticity diagram which plots the 3 photoreceptor excitations of trichromatic colour vision systems at an angle of 120° is presented. It takes into acount the nonlinear transduction process in the receptors. The resulting diagram has the outline of an equilateral hexagon. It is demonstrated by geometrical means that excitation values for any type of spectrally opponent mechanism can be read from this diagram if the weighting factors of this mechanism add up to zero. Thus, it may also be regarded as a general representation of colour opponent relations, linking graphically the Young-Helmholtz theory of trichromacy and Hering's concept of opponent colours. It is shown on a geometrical. basis that chromaticity can be coded unequivocally by any two combined spectrally opponent mechanisms, the main difference between particular mechanisms being the extension and compression of certain spectral areas. This type of graphical representation can qualitatively explain the Bezold-Brücke phenomenon. Furthermore, colour hexagon distances may be taken as standardized perceptual colour distance values for trichromatic insects, as is demonstrated by comparison with behavioural colour discrimination data of 3 hymenopteran species.

Key words

Colour vision Chromaticity diagrams Opponent processes Colour computation Bezold Brücke phenomenon 


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  1. Backhaus W (1991a) Color opponent coding in the visual system of the honeybee. Vision Res 31:1381–1397Google Scholar
  2. Backhaus W (1991b) Bezold Brücke colour shifts exist in the bee as predicted. In: Elsner N, Penzlin H (eds) Synapse — transmission — modulation. Proceedings of the 19th Göttingen Neu-robiology Conference. Georg Thieme, Stuttgart, p 558Google Scholar
  3. Backhaus W, Menzel R (1987) Color distance derived from a receptor model of color vision in the honey bee. Biol Cybern 55:321–331Google Scholar
  4. Backhaus W, Menzel R, Kreißl S (1987) Multidimensional scaling of color similarity in bees. Biol Cybern 56:293–304Google Scholar
  5. Buchsbaum G, Gottschalk A (1983) Trichromacy, opponent colour coding and optimum colour information transmission in the retina. Proc R Soc Lond B 220:89–113Google Scholar
  6. Chittka L, Beier W, Hertel H, Steinmann E, Menzel R (1992) Opponent colour coding is a universl strategy to evaluate the photoreceptor inputs in Hymenoptera. J Comp Physiol A 170:545–563Google Scholar
  7. Daumer K (1956) Reizmetrische Untersuchungen des Farbensehens der Bienen. Z Vergl Physiol 38:413–478Google Scholar
  8. Guth LS, Massof RW, Benzschawel T (1980) A vector model for normal and dichromatic color vision. J Opt Soc Am 70:197–212Google Scholar
  9. Helversen O von (1972) Zur spektralen Unterschiedlichkeitsempfindlichkeit der Honigbiene. J Comp Physiol 80:439–472Google Scholar
  10. Hurvich LM, Jameson D (1955) Some quantitative aspects of an opponent colour theory. II. Brightness, saturation and hue in normal and dichromatic vision. J Opt Soc Am 45:602–616Google Scholar
  11. Küppers H (1976) Die Logik der Farbe. Callway. MünchenGoogle Scholar
  12. Küppers H (1977) Farbe, Ursprung, Systematik, Anwendung. Callway, MünchenGoogle Scholar
  13. Laughlin SB (1981) Neural principles in the peripheral visual system of invertebrates. In: Autrum HJ (ed) Invertebrate visual centers and behaviour (Handbook of sensory physiology, vol. VII/6b). Springer, Berlin Heidelberg New York, pp 133–280Google Scholar
  14. Lipetz LE (1971) The relation of physiological and psychological aspects of sensory intensity. In: Loewenstein WR (ed) Principles of receptor physiology. (Handbook of sensory physiology, vol I). Springer, Berlin Heidelberg New York, pp 191–225Google Scholar
  15. MacLeod DIA, Boynton RM (1979) Chromaticity diagram showing cone excitation by stimuli of equal luminance. J Opt Soc Am 69:1183–1186Google Scholar
  16. Menzel R, Steinmann E, De Souza JM, Backhaus W (1988) Spectral sensitivity of photoreceptors and colour vision in the solitary bee, Osmia rufa. J Exp Biol 136:35–52Google Scholar
  17. Menzel R, Ventura DF, Hertel H, de Souza JM, Greggers U (1986) Spectral sensitivity of photoreceptors in insect compound eyes: comparison of species and methods. J Comp Physiol A 158:165–177Google Scholar
  18. Menzel R, Ventura DF, Werner A, Joaquim LCM, Backhaus W (1989) Spectral sensitivity of single photoreceptors and color vision in the stingless bee, Melipona quadrifasciata. J Comp Physiol A 166:151–164Google Scholar
  19. Menzel R, Backhaus W (1991) Colour vision in insects. In: Gouras P (ed) Vision and visual dysfunction, vol VI. The perception of colour. MacMillan Press, Houndsmills, pp 262–293Google Scholar
  20. Naka KI, Rushton WAH (1966) S-potentials from color units in the retina of the fish (Cyprinidae). J Physiol 185:536–555Google Scholar
  21. Peitsch D, Backhaus W, Menzel R (1989) Color vision systems in hymenopterans; a comparative study. In: Erber J, Menzel R, Pflüger HJ, Todt D (eds) Neural mechanisms of behavior. Thieme, Stuttgart New York, p 163Google Scholar
  22. Rodieck RW (1973) The vertebrate retina — principles of structure and function. Freeman and Company, San FranciscoGoogle Scholar
  23. Schroedinger E (1920a) Grundlinien einer Theorie der Farbenmetrik im Tagessehen. Ann Phys 63:397–426, 427–456Google Scholar
  24. Schroedinger E (1920b) Grundlinien einer Theorie der Farbenmetrik im Tagessehen. Die Farbenmetrik II. Teil: Höhere Farbenmetrik (eigentliche Metrik der Farbe). Ann Phys 63:481–520Google Scholar
  25. Valberg A, Seim T, Lee BB, Tryti J (1986) Reconstruction of equidistant color space from responses of visual neurones of macaques. J Opt Soc Am A 3:1726–1734Google Scholar
  26. Werner JS, Wooten BR (1979) Opponent chromatic mechanisms: Relation to photopigments and hue naming. J Opt Soc Am 69:422–434Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Lars Chittka
    • 1
  1. 1.Freie Universität BerlinInstitut für NeurobiologieBerlinGermany

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