Differential geometry and color perception

SummaryCombined with well known facts about the affine structure of color space P, a local homogeneity hypothesis implies that P=G/K is equivalent to either R+xR+xR+ or R+SL(2, R)/SO(2). The G-invariant metrics yield in the first case Stiles' generalization of Helmholtz' color metric, in the second a new color metric with respect to which P is not isometric to a Euclidean space. The paper contains an extensive historical introduction.

[1]  J. V. Goethe.  Theory of Colours , 1810 .

[2]  H. Helmholtz.  Ueber die Theorie der zusammengesetzten Farben , 1852 .

[3]  Hermann Grassmann,et al.  Zur Theorie der Farbenmischung , 1853 .

[4]  J. Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: Experiments on Colour as perceived by the Eye, with remarks on Colour-Blindness , 2011 .

[5]  James Clerk Maxwell,et al.  On the theory of compound colours, and the relations of the colours of the spectrum , 1993, Proceedings of the Royal Society of London.

[6]  B. Riemann.  Über die Hypothesen, welche der Geometrie zu Grunde liegen , 1868 .

[7]  H. Helmholtz,et al.  On the relation of optics to painting. , 1881 .

[8]  W. Abney,et al.  I. The Bakerian lecture.—Colour photometry , 1886, Proceedings of the Royal Society of London.

[9]  F. edridge-green.  RESEARCHES IN COLOUR VISION. , 1913 .

[10]  History of the Theories of Aether and Electricity , 1913 .

[11]  E. Schrödinger.  Grundlinien einer Theorie der Farbenmetrik im Tagessehen , 1920 .

[12]  J. Lense.  Über die Hypothesen, welche der Geometrie zu Grunde liegen , 1922 .

[13]  The principles of physical optics , 1926 .

[14]  S. Hecht.  A THEORY OF VISUAL INTENSITY DISCRIMINATION , 1935, The Journal of general physiology.

[15]  Louis-Bertrand Castel, Anti-Newtonian Scientist , 1941 .

[16]  W. Stiles.  A modified Helmholtz line-element in brightness-colour space , 1946 .

[17]  Color discrimination and the influence of color contrast on visual acuity. , 1949, Archives d'ophtalmologie et revue generale d'ophtalmologie.

[18]  MacADAM Dl.  Color discrimination and the influence of color contrast on visual acuity. , 1949 .

[19]  D. L. Macadam.  Loci of Constant Hue and Brightness Determined with Various Surrounding Colors , 1950 .

[20]  L. Riggs,et al.  The disappearance of steadily fixated visual test objects. , 1953, Journal of the Optical Society of America.

[21]  Edmund Taylor Whittaker.  Reviews of Books and Recordings: A History of the Theories of Aether and Electricity , 1954 .

[22]  S. S. Stevens.  On the psychophysical law. , 1957, Psychological review.

[23]  G. Ekman.  Weber's Law and Related Functions , 1959 .

[24]  Huseyin Yilmaz.  On color perception , 1962 .

[25]  M. Koecher.  On real Jordan algebras , 1962 .

[26]  M. Koecher.  Jordan algebras and their applications , 1962 .

[27]  S. Helgason.  Differential Geometry and Symmetric Spaces , 1964 .

[28]  T. Cornsweet,et al.  Luminance discrimination of brief flashes under various conditions of adaptation , 1965, The Journal of physiology.

[29]  C. H. Graham,et al.  Vision and visual perception , 1965 .

[30]  S. S. Stevens.  Neural events and the psychophysical law. , 1970, Science.

[31]  T. Young,et al.  A Course of Lectures on Natural Philosophy and the Mechanical Arts , 2010 .

[32]  E. Land,et al.  Lightness and retinex theory. , 1971, Journal of the Optical Society of America.

[33]  David L. MacAdam,et al.  Sources of Color Science , 1972 .

[34]  J. J. Vos,et al.  An analytical description of the line element in the zone-fluctuation model of colour vision. I. Basic concepts. , 1972, Vision research.