Histograms of Images Valued in the Manifold of Colours Endowed with Perceptual Metrics

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

We address here the problem of perceptual colour histograms. The Riemannian structure of perceptual distances is measured through standards sets of ellipses, such as Macadam ellipses. We propose an approach based on local Euclidean approximations that enables to take into account the Riemannian structure of perceptual distances, without introducing computational complexity during the construction of the histogram.

Keywords

Colour images Image histograms Riemannian metrics 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Sapiro, G., Caselles, V.: Histogram modification via differential equations. J. Differ. Equ. 135(2), 238–268 (1997)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Portilla, J., Simoncelli, E.P.: A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Comput. Vis. 40, 47–71 (2000)CrossRefMATHGoogle Scholar
  3. 3.
    Gong, Y., Chuan, C.H., Xiaoyi, G.: Image indexing and retrieval using color histograms. Multimedia Tools Appl. 2, 133–156 (1996)Google Scholar
  4. 4.
    MacAdam, D.L.: Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. 32(5), 247–274 (1942)CrossRefGoogle Scholar
  5. 5.
    Luo, M.R., Rigg, B.: Chromaticity-discrimination ellipses for surface colours. Color Res. Appl. 11(1), 25–42 (1986)CrossRefGoogle Scholar
  6. 6.
    Berns, R.S., Alman, D.H., Reniff, L., Snyder, G.D., Balonon-Rosen, M.R.: Visual determination of suprathreshold color-difference tolerances using probit analysis. Color Res. Appl. 16(5), 297–316 (1991)CrossRefGoogle Scholar
  7. 7.
    Pelletier, B.: Kernel density estimation on Riemannian manifolds. Stat. Probab. Lett. 73(3), 297–304 (2005)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Riemann, B.: Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. Abh. Ge. Wiss. Gött 13(1), 133–152 (1868)Google Scholar
  9. 9.
    von Helmholtz, H.: Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem. Z. Psychol. Physiol. Sinnesorg. 2, 1–30 (1891)Google Scholar
  10. 10.
    Schrödinger, E.: Grundlinien einer Theorie der Farbenmetrik im Tagessehen (III. Mitteilung). Ann. Phys. 368(22), 481–520 (1920)CrossRefGoogle Scholar
  11. 11.
    Stiles, W.S.: A modified Helmholtz line-element in brightness-colour space. P. Phys. Soc. 58, 41–65 (1946)CrossRefGoogle Scholar
  12. 12.
    Farup, I.: Hyperbolic geometry for colour metrics. Opt. Express 22(10), 12369–12378 (2014)CrossRefGoogle Scholar
  13. 13.
    Robertson, A.R.: The cie 1976 color-difference formulae. Color Res. Appl. 2(1), 7–11 (1977)CrossRefGoogle Scholar
  14. 14.
    Ebner, F., Fairchild, M.D.: Development and testing of a color space (IPT) with improved hue uniformity. In: The Sixth Color Imaging Conference: Color Science, Systems and Applications, IS&T, pp. 8–13 (1998)Google Scholar
  15. 15.
    Luo, M.R., Cui, G., Rigg, B.: The development of the CIE 2000 colour-difference formula: CIEDE2000. Color Res. Appl. 26(5), 340–350 (2001)CrossRefGoogle Scholar
  16. 16.
    Chevallier, E., Barbaresco, F., Angulo, J.: Probability density estimation on the hyperbolic space applied to radar processing. HAL, \(<\)hal-01121090\(>\) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Emmanuel Chevallier
    • 1
  • Ivar Farup
    • 2
  • Jesús Angulo
    • 1
  1. 1.CMM-Centre de Morphologie MathématiqueMINES ParisTech, PSL-Research UniversityFontainebleauFrance
  2. 2.Gjøvik University CollegeGjøvikNorway

Personalised recommendations