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RE: Color Matching Functions to model human vision?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg66434] RE: [mg66395] Color Matching Functions to model human vision?
*From*: "Ingolf Dahl" <ingolf.dahl at telia.com>
*Date*: Fri, 12 May 2006 02:03:28 -0400 (EDT)
*Reply-to*: <ingolf.dahl at telia.com>
*Sender*: owner-wri-mathgroup at wolfram.com
I am sometimes using such functions.
The magic words are "CIE 1931", use Google and Wikipedia. You can find
better explanations than I can give here.
Here are some tables for every 5Th wavelength from 360 to 830 nm, taken from
http://cvrl.ioo.ucl.ac.uk/:
CIE (1931) 2-deg color matching functions:
xbar={0.0001299,0.0002321,0.0004149,0.0007416,0.001368,0.002236,0.004243,0.0
0765,0.01431,0.02319,0.04351,0.07763,0.13438,0.21477,0.2839,0.3285,0.34828,0
.34806,0.3362,0.3187,0.2908,0.2511,0.19536,0.1421,0.09564,0.05795001,0.03201
,0.0147,0.0049,0.0024,0.0093,0.0291,0.06327,0.1096,0.1655,0.2257499,0.2904,0
.3597,0.4334499,0.5120501,0.5945,0.6784,0.7621,0.8425,0.9163,0.9786,1.0263,1
.0567,1.0622,1.0456,1.0026,0.9384,0.8544499,0.7514,0.6424,0.5419,0.4479,0.36
08,0.2835,0.2187,0.1649,0.1212,0.0874,0.0636,0.04677,0.0329,0.0227,0.01584,0
.01135916,0.008110916,0.005790346,0.004109457,0.002899327,0.00204919,0.00143
9971,0.0009999493,0.0006900786,0.0004760213,0.0003323011,0.0002348261,0.0001
661505,0.000117413,0.00008307527,0.00005870652,0.00004150994,0.00002935326,0
.00002067383,0.00001455977,0.00001025398,7.221456*^-6,5.085868*^-6,3.581652*
^-6,2.522525*^-6,1.776509*^-6,1.251141*^-6};
ybar={3.917*^-6,6.965*^-6,0.00001239,0.00002202,0.000039,0.000064,0.00012,0.
000217,0.000396,0.00064,0.00121,0.00218,0.004,0.0073,0.0116,0.01684,0.023,0.
0298,0.038,0.048,0.06,0.0739,0.09098,0.1126,0.13902,0.1693,0.20802,0.2586,0.
323,0.4073,0.503,0.6082,0.71,0.7932,0.862,0.9148501,0.954,0.9803,0.9949501,1
.,0.995,0.9786,0.952,0.9154,0.87,0.8163,0.757,0.6949,0.631,0.5668,0.503,0.44
12,0.381,0.321,0.265,0.217,0.175,0.1382,0.107,0.0816,0.061,0.04458,0.032,0.0
232,0.017,0.01192,0.00821,0.005723,0.004102,0.002929,0.002091,0.001484,0.001
047,0.00074,0.00052,0.0003611,0.0002492,0.0001719,0.00012,0.0000848,0.00006,
0.0000424,0.00003,0.0000212,0.00001499,0.0000106,7.4657*^-6,5.2578*^-6,3.702
9*^-6,2.6078*^-6,1.8366*^-6,1.2934*^-6,9.1093*^-7,6.4153*^-7,4.5181*^-7};
zbar={0.0006061,0.001086,0.001946,0.003486,0.006450001,0.01054999,0.02005001
,0.03621,0.06785001,0.1102,0.2074,0.3713,0.6456,1.0390501,1.3856,1.62296,1.7
4706,1.7826,1.77211,1.7441,1.6692,1.5281,1.28764,1.0419,0.8129501,0.6162,0.4
6518,0.3533,0.272,0.2123,0.1582,0.1117,0.07824999,0.05725001,0.04216,0.02984
,0.0203,0.0134,0.008749999,0.005749999,0.0039,0.002749999,0.0021,0.0018,0.00
1650001,0.0014,0.0011,0.001,0.0008,0.0006,0.00034,0.00024,0.00019,0.0001,0.0
0004999999,0.00003,0.00002,0.00001,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.
,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.};
The standard illuminant SD65 is sometimes used (to determine the color of an
object):
sd65={46.8618,49.3637,51.6352,51.0323,50.3827,52.3118,56.0542,68.7015,81.592
4,87.1204,91.0789,92.4589,92.9101,90.057,88.1782,95.7736,104.503,110.936,116
.328,117.41,117.587,116.336,115.102,115.392,115.433,112.367,109.27,109.082,1
09.228,108.578,107.714,106.296,105.145,106.239,107.318,106.047,104.58,104.22
5,103.825,102.023,100.023,98.1671,96.5214,96.0611,95.3946,92.2368,89.191,89.
3459,89.9025,89.8026,89.5095,88.6489,87.5481,85.4936,83.5778,83.4939,83.4542
,81.863,80.2584,80.1207,80.3271,81.2462,81.9144,80.281,78.01,74.0027,70.3484
,70.6652,71.6602,72.979,73.4199,67.9765,62.8656,65.7448,69.7008,72.4863,74.0
853,69.3398,63.2519,55.0054,48.6719,56.6118,65.3768,65.0941,63.6434,63.8434,
63.9576,61.8779,59.2934,55.7054,52.7375,54.6998,57.284,58.8765,60.0253};
Ingolf Dahl
Sweden
_____
From: Steven T. Hatton [mailto:hattons at globalsymmetry.com]
To: mathgroup at smc.vnet.net
Subject: [mg66434] [mg66395] Color Matching Functions to model human vision?
Does anybody know if there are color matching functions that can map a given
frequency (and intensity) of light to a typical response of the human eye?
This is the kind of thing that is obvious until you think about it.
--
The Mathematica Wiki: http://www.mathematica-users.org/
Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html
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