• 2023 (Vol.37)
  • 1990 (Vol.4)
  • 1989 (Vol.3)
  • 1988 (Vol.2)
  • 1987 (Vol.1)

Multiplicatively Сlosed Spectral Models in Color Analysis

© 2022 D. P. Nikolaev, I. A. Konovalenko, P. P. Nikolaev

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute) 127051 Moscow, B. Karetny per., 19, Russia

Received 11 Jan 2022

This paper describes methods and tools used in research on color perception. The latter is an integral part of the visual system which should objectively expose the observed scenes. A number of substantial examples regarding the construction of low-parameter spectral representations are provided. Such representations, referred to as spectral models, establish a formal link between luminosity and sensor response spaces. The main types of spectral models including intra-type modifications are explained and illustrated by the examples along with the analysis of advantages and disadvantages. We specify and justify the restrictions on the physical and optical characteristics of a scene registered by a sensor as well as approximation alternatives for spectral models of the scene’s elements. Restrictions and approximations simplify the inverse problem, ensuring its solvability since in the general case, such a problem cannot be solved. In the context of the requirements for spectral models, the issues related to the modeling of color constancy phenomena as well as the camera calibration problem are considered. The advantages of the Gaussian spectral model (as nonlinear and multiplicatively closed), when compared to optimal linear models, are discussed. We also describe three modifications of the Gaussian model which extend the color gamut, since the original model does not reproduce the colors of the magenta segment. In terms of the Gaussian model – with a transition to the optimizing properties of the von Mises model – we describe a method for the chromaticity estimation of the source based on a color picture of internal interreflections within a set of multicolored folded samples. We illustrate the method via numerical experiments employing real spectral data. The manuscript combines an analysis of theoretical premises with a discussion of the results of numerical modeling and physical experiment.

Key words: spectral models, Gaussian spectral model, von Mises spectral model, closure under multiplication, color analysis, color gamut, color constancy, color sensor calibration, fold reflexes

DOI: 10.31857/S0235009222020056

Cite: Nikolaev D. P., Konovalenko I. A., Nikolaev P. P. Multiplikativno zamknutye spektralnye modeli v zadachakh tsvetovogo analiza [Multiplicatively сlosed spectral models in color analysis]. Sensornye sistemy [Sensory systems]. 2022. V. 36(2). P. 153–182 (in Russian). doi: 10.31857/S0235009222020056


  • Nikolaev P.P. Gaussovskaja model' i procedury cvetovoj konstantnosti dlja scen dvojnogo osveshhenija. I. Cvetnost’ i svetlota [Gaussian Spectral Model and Colour Constancy Procedures in Scenes under Double Illumination. I. Chromaticity and Lightness]. Sensornye sistemy [Sensory systems]. 2007. V. 21 (3). P. 195–214 (in Russian).
  • Nikolaev P.P. Model’ konstantnosti cvetovosprijatija dlja sluchaja nepreryvnyh spektral’nyh funkcij [Color Perception Constancy Model for the Case of Continuous Spectral Functions]. Biofizika [Biophysics]. 1985. V. 30 (1). P. 112–117 (in Russian).
  • Nikolaev P.P. O novyh metodah ocenki cvetnosti osveshhenija v algoritmah cvetovoj konstantnosti [About New Estimation Methods for Primary Illuminant Chromaticity in Colour Constancy Algorithms]. Sensornye sistemy [Sensory systems]. 2007. V. 21 (1). P. 29–44 (in Russian).
  • Nikolaev P.P. Trihromaticheskaja model' konstantnosti vosprijatija okraski ob''ektov [Trichromatic model of object color perception constancy]. Biofizika [Biophysics]. 1989. V. 34 (2). P. 287–294 (in Russian).
  • Nikolaev P.P., Karpenko S.M., Nikolaev D.P. Spektral’nye modeli cvetovoj konstantnosti: pravila otbora [Spectral models of color constancy: selection rules]. Trudy Instituta sistemnogo analiza Rossijskoj akademii nauk (ISA RAN) [Proceedings of the Institute for System Analysis of the Russian Academy of Sciences (ISA RAS)]. 2008. V. 38. P. 322–335 (in Russian).
  • Nikolaev P.P., Nikolaev D.P. Modeli konstantnogo zritel’nogo vosprijatija. III. Spektral’nye i perceptivnye invarianty v procedurah zritel’noj obrabotki [The models of constant visual perception. III. Spectral and perceptive invariants in image processing]. Sensornye sistemy [Sensory systems]. 1997. V. 11 (2). P. 181–204 (in Russian).
  • Njuberg N.D., Bongard M.M., Nikolaev P.P. O konstantnosti vosprijatija okraski.I [On the constancy of color perception.I] Biofizika [Biophysics]. 1971. V 16 (2). P. 285–293 (in Russian).
  • Njuberg N.D., Nikolaev P.P., Bongard M.M. O konstantnosti vosprijatija okraski.II [On the constancy of color perception.II] Biofizika [Biophysics]. 1971. V. 16 (6). P. 1052–1063 (in Russian).
  • Bianco S., Bruna A.R., Naccari F., Schettini R. Color correction pipeline optimization for digital cameras. Journal of Electronic Imaging. 2013. V. 22 (2). P. 1–11. https://doi.org/10.1117/1.JEI.22.2.023014
  • Brill M.H. A device performing illuminant-invariant assessment of chromatic relations. Journal of Theoretical Biology. 1978. V. 71 (3). P. 473–478. https://doi.org/10.1016/0022-5193(78)90175-3
  • Brill M.H. Further features of the illuminant-invariant trichromatic photosensor. Journal of Theoretical Biology. 1979. V. 78 (2). P. 305–308. https://doi.org/10.1016/0022-5193(79)90271-6
  • Brill M.H. The relation between the color of the illuminant and the color of the illuminated object. Color Research & Application. 1995. V. 20 (1). P. 70–76. https://doi.org/10.1002/col.5080200112
  • Brill M.H., West G. Chromatic adaptation and color constancy: A possible dichotomy. Color Research & Application. 1986. V. 11 (3). P. 196–204. https://doi.org/10.1002/col.5080110306
  • Buchsbaum G. A spatial processor model for object colour perception. Journal of the Franklin Institute. 1980. V. 310 (1). P. 1–26. https://doi.org/10.1016/0016-0032(80)90058-7
  • Can Karaimer H., Brown M.S. Improving color reproduction accuracy on cameras. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2018. P. 6440–6449. https://doi.org/10.1109/CVPR.2018.00674
  • Cohen J. Dependency of the spectral reflectance curves of the munsell color chips. Psychonomic Science. 1964. V. 1 (1). P. 369–370. https://doi.org/10.3758/BF03342963
  • Finlayson G.D., Mackiewicz M., Hurlbert A. Color correction using root-polynomial regression. IEEE Transactions on Image Processing. 2015. V. 24 (5). P. 1460–1470. https://doi.org/10.1109/TIP.2015.2405336
  • Gijsenij A., Gevers T., Van De Weijer J. Computational color constancy: Survey and experiments. IEEE Transactions on Image Processing. 2011. V. 20 (9). P. 2475–2489. https://doi.org/10.1109/TIP.2011.2118224
  • Gusamutdinova N., Ershov E., Gladilin S., Nikolaev D. Verification of applicability two multiplicative closed spectral models for multiple reflection effect description. Proc. SPIE 10253, 2016 International Conference on Robotics and Machine Vision. 2017. V. 10253. P. 16–20. https://doi.org/10.1117/12.2266404
  • Ives H.E. The relation between the color of the illuminant and the color of the illuminated object. Transactions of the Illuminating Engineering Society. 1912. V. 7. P. 62–72.
  • Konovalenko I.A., Smagina A.A., Nikolaev D.P., Nikolaev P.P. Prolab: perceptually uniform projective colour coordinates system. IEEE Access. 2021. V. 9. P. 133023–133042. https://doi.org/10.1109/ACCESS.2021.3115425
  • Kordecki A. Practical testing of irradiance-independent camera color calibration. Proc. SPIE 11041, Eleventh International Conference on Machine Vision (ICMV 2018). 2019. V. 11041. P. 340–345. https://doi.org/10.1117/12.2522907
  • Krinov E.L. Spectral reflectance properties of natural formations. Technical report. National Research Council of Canada. 1953. 268 p.
  • Land E.H., McCann J.J. Lightness and retinex theory. J. Opt. Soc. Am. 1971. V. 61 (1). P. 1–11. https://doi.org/10.1364/JOSA.61.000001
  • Lee S.D., Kim C.Y., Seo Y.S. Linear model of surface and scanner characterization method. Proc. SPIE 2414, Device-Independent Color Imaging II. 1995. V. 2414. P. 84–93. https://doi.org/10.1117/12.206536
  • Logvinenko A.D. Object-colour manifold. International Journal of Computer Vision. 2013. V. 101 (1). P. 143–160. https://doi.org/10.1007/s11263-012-0555-2
  • Macleod D.I., Golz J.A. Computational Analysis of Colour Constancy. In Rainer Mausfeld & Dieter Heyer (eds.), Colour Perception: Mind and the Physical World. Oxford University Press, 2003. P. 205–246. https://doi.org/10.1093/acprof:oso/9780198505006.001.0001
  • Maloney L.T. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A. 1986a. V. 3 (10). P. 1673–1683. https://doi.org/10.1364/JOSAA.3.001673
  • Maloney L.T., Wandell B.A. Color constancy: a method for recovering surface spectral reflectance. J. Opt. Soc. Am. A. 1986б. V. 3 (1). P. 29–33. https://doi.org/10.1364/JOSAA.3.000029
  • Maloney L.T. Physics-based approaches to modeling surface color perception. In K. R. Gegenfurtner, & L. T. Sharpe (Eds.), Color vision: From genes to perception. Cambridge University Press, 1999. P. 387–422.
  • Marimont D.H., Wandell B.A. Linear models of surface and illuminant spectra. J. Opt. Soc. Am. A. 1992. V. 9 (11). P. 1905–1913. https://doi.org/10.1364/JOSAA.9.001905
  • Mirzaei H., Funt B. Object-color-signal prediction using wraparound gaussian metamers. J. Opt. Soc. Am. A. 2014. V. 31 (7). P. 1680–1687. https://doi.org/10.1364/JOSAA.31.001680
  • Mizokami Y., Webster M.A. Are gaussian spectra a viable perceptual assumption in color appearance? J. Opt. Soc. Am. A. 2012. V. 29 (2). P. A10–A18. https://doi.org/10.1364/JOSAA.29.000A10
  • Nelder J.A., Mead R.A simplex method for function minimization. The Computer Journal. 1965. V. 7 (4). P. 308–313. https://doi.org/10.1093/comjnl/7.4.308
  • Nikolaev D.P., Nikolayev P.P. Comparative analysis of gaussian and linear spectral models for colour constancy. Proceedings of 19th European Conference on Modelling and Simulation. 2005. P. 300–305.
  • Nikolaev D.P., Nikolaev P.P. On spectral models and colour constancy clues. Proceedings of 21st European Conference on Modelling and Simulation. 2007. P. 318–323.
  • Nikolaev D.P., Nikolayev P.P. Linear color segmentation and its implementation. Computer Vision and Image Understanding. Special Issue: Colour for Image Indexing and Retrieval. 2004. V. 94 (1). P. 115–139. https://doi.org/10.1016/j.cviu.2003.10.012
  • Nikolaev D.P., Nikolayev P.P., Bozhkova V.P. Efficiency comparison of analytical gaussian and linear spectral models in the same colour constancy framework. Int. J. Simul. Syst. Sci. Technol. 2006. V. 7 (3). P. 21–36.
  • Parkkinen J.P.S., Hallikainen J., Jaaskelainen T. Characteristic spectra of munsell colors. J. Opt. Soc. Am. A. 1989. V. 6 (2). P. 318–322. https://doi.org/10.1364/JOSAA.6.000318
  • Sällström P. Color and physics: Some remarks concerning the physical aspects of human colour vision. Technical Report 9. Un. Stockholm Inst. of Phys. 1973.
  • Smagina A., Ershov E., Grigoryev A. Multiple light source dataset for colour research. Proc. SPIE 11433, Twelfth International Conference on Machine Vision (ICMV 2019). 2020. V. 11433. P. 635–642. https://doi.org/10.1117/12.2559491
  • Stiles W.S., Wyszecki G.W. Counting metameric object colors. J. Opt. Soc. Am. 1962. V. 52 (3). P. 313–328. https://doi.org/10.1364/JOSA.52.000313
  • Stokes M., Anderson M., Chandrasekar S., Motta R. A standard default color space for the internet – srgb, version 1.10. Technical report. International Color Consortium. 1996.
  • Vazquez-Corral J., Connah D., Bertalmío M. Perceptual color characterization of cameras. Sensors. 2014. V. 14 (12). P. 23205–23229. https://doi.org/10.3390/s141223205
  • Vrhel M.J., Gershon R., Iwan L.S. Measurement and analysis of object reflectance spectra. Color Research & Application. 1994. V. 19 (1). P. 4–9. https://doi.org/10.1111/j.1520-6378.1994.tb00053.x
  • Weinberg J.W. The geometry of colors. General Relativity and Gravitation. 1976. V. 7 (1). P. 135–169. https://doi.org/10.1007/BF00762021
  • Yilmaz H. Color Vision and a New Approach to General Perception. In Bernard E.E., Kare M.R. (eds)Biological Prototypes and Synthetic Systems. Springer, Boston, MA., 1962. P. 126–141. https://doi.org/10.1007/978-1-4684-1716-6_22