Pentachromatic colour spaces

We generalise previous results to dimension 5. We exploit the geometric properties of the 5-hypercube [0, 1]5 in order to give a mathematical model for colour vision in the case of 5 photoreceptor types and for the corresponding additive colour combination with five primary lights. Five photoreceptors or five types of camera pixel filters with responses normalised to the interval [0, 1] give rise to a 5 dimensional hypercube [0, 1]5 of combined responses (colours). As previously done, for the trichromatic and tetrachromatic cases, we identify an equatorial PL 3- sphere in the PL 4-sphere boundary ∂[0, 1]5 of the hypercube. This equatorial sphere is the set of hues of the chromatic colour points in the hypercube. The remaining attributes of luminance and chromatic saturation are given by the midrange and range of the colour coordinates. From the 5-cube we go to a polytopal hexcone type space, to a double-cone type space and to a round Runge space.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  Alfredo Restrepo.  Tetrachromatic Metamerism - A Discrete, Mathematical Characterization , 2014, VISAPP.

[3]  Almut Kelber,et al.  Invertebrate colour vision , 2006 .

[4]  Alfredo Restrepo,et al.  Hue processing in tetrachromatic spaces , 2013, Electronic Imaging.

[5]  Livia S. Carvalho,et al.  Evolution and spectral tuning of visual pigments in birds and mammals , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[6]  S. Zeki.  A vision of the brain , 1993 .

[7]  Alfredo Restrepo,et al.  HSV-domain Enhancement of High-contrast Images - Power Laws and Unsharp Masking for Bounded and Circular Signals , 2009, VISAPP.

[8]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[9]  Alfredo Restrepo.  Tetrachromatic colour space , 2012, Electronic Imaging.

[10]  Alfredo Restrepo.  Tri and tetrachromatic metamerism , 2014, Electronic Imaging.

[12]  Alfredo Restrepo.  Colour processing in Runge space , 2011, Electronic Imaging.

[13]  David S. Witte,et al.  On Hamiltonian circuits in Cayley diagrams , 1982 .

[14]  Nimrod Megiddo,et al.  Partial and complete cyclic orders , 1976 .

[15]  Selmer M. Johnson.  Generation of permutations by adjacent transposition , 1963 .

[16]  E. Artin.  Zur Isotopie zweidimensionaler Flächen imR4 , 1925 .

[17]  Alfredo Restrepo Palacios.  Colour Processing in Tetrachromatic Spaces - Uses of Tetrachromatic Colour Spaces , 2013, VISAPP 2013.