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There are many reasons for color blindness, including pigment loss or inactivation. Thats what this article is all about.

• A normal person is a trichromat

• a person that only needs two numbers to define a color is a dichromat.
  • Protanope
  • Deuteranope
  • Tritanope

if dichromat accepts the color match of the trichromat then the color matching function of the dichromat are linear combinations of the trochromat CMF's

• Its usually due to a genetic loss of pigment.

Eye #1 - A simple trichromatic eye

File:SimpleEye1 CMF.png

Figure 1a: Color matching functions for a very simple eye. The three color matching functions (CMFs) are zero except over a particular wavelength interval. The red and blue CMF are share a common boundary at $\lambda _{2}$ and do not overlap. The green CMF overlaps the red and blue CMFs, extending from $\lambda _{1}$ to $\lambda _{3}$.

File:SimpleEye1 rg.png

Figure 1b: The rg chromaticity diagram for the simple eye. If there were no overlap, the gamut of colors would fill the RGB triangle. Because of the overlap of the green CMF, the portion of the RGB triangle above g=0.5 is unreachable. The spectral locus is in green, the purple line is in purple.

Consider first a very simple model of the human eye. In Figure 1a on the right is shown the color matching functions (CMFs) for this simple example. It consists of three receptors (R, G, and B) which give a constant response over a certain wavelength interval, and zero response otherwise. The green (middle) receptor overlaps the CMFs of the blue and red receptors. The color matching functions are the response of this eye to a monochromatic signal of unit strength at the given wavelength. For any light beam with intensity $I(\lambda )$ the color coordinates (R, G, and B) will be the integral of $I(\lambda )$ over each of the color matching functions:

$R=\int _{\lambda _{2}}^{\lambda _{3}}I(\lambda )\,d\lambda$

$G=\int _{\lambda _{1}}^{\lambda _{2}}I(\lambda )\,d\lambda$

$B=\int _{\lambda _{0}}^{\lambda _{1}}I(\lambda )\,d\lambda$

It can be seen that for monochromatic light of unit intensity there are only four possible colors, and these colors will form the spectral locus for this color space. If we define the rg chromaticity coordinates for this space:

$r=R/(R+G+B)\,$

$g=G/(R+G+B)\,$

then these three colors can be plotted on the chromaticity diagram of Figure 1b where they are denoted R, M, Y, and B. The gamut of colors available to the observer with this eye fills the region in color in Figure 1b. There are many similarities betweeen this diagram and the CIE diagram for the actual human eye. The spectral locus is convex, there is a purple line and together they contain all colors perceivable to this observer.

If color blindness is cause by a complete lack of response of the eye to one of the receptor pigments, then two colors which can be distinguished by a trichromat may appear the same to a dichromat. On the chromaticity diagram, for any color, we can draw an entire set of colors which will appear the same to a dichromat. These "lines of confusion" can be shown to form a family of straight lines which converge to a point, which is called the "point of confusion" or "copunctal point".

The lines of confusion for an observer missing the red receptor pigment can be found by realizing that for fixed values of G and B, any value of R will yield the same color according to this observer. If we let t stand for any value then the parametric equations for the lines of confusion are:

$r={\frac {t}{t+G+B}}$

$g={\frac {G}{t+G+B}}$

Eliminating t and solving for g gives the equation of the line of confusion for the given G and B.

$g={\frac {1-r}{1+G/B}}$

Similarly, by substituting t for G, we get the lines of confusion for an observer missing the green receptor pigment:

$g=1-r(1+B/R)\,$

and for an observer missing the blue receptor pigment:

$g=rB/R\,$

These lines of confusion are shown in the three plots below on the chromaticity diagram for the simple eye. It is seen that the points of confusion are at the corners of the RGB triangle.

File:SimpleEye1 XXX.png Figure 1c: Lines of confusion for a dichromat missing the red receptor for the simple eye

File:SimpleEye1 XXX.png Figure 1d: Lines of confusion for a dichromat missing the green receptor for the simple eye

File:SimpleEye1 XXX.png Figure 1e: Lines of confusion for a dichromat missing the blue receptor for the simple eye

The above simple example illustrates certain characteristics which are true for any set of CMFs:

• The locus of confusion when one of the pigments is missing will always be a family of straight lines converging on the primary associated with the missing pigment. We can see that this is true because the derivation of the lines of confusion made no reference to the particular CMFs used in the color space.

Experimental results on the human eye

File:HumanConeResponse.png

Human cone response

The images below are the results of experiments done by Pitt in 1935 and by ??? in ??? showing the lines of confusion for three types of color blindness: protanopic, deuteranopic, and tritanopic. Note from the discussion above that:

• The protanope shows all the symptoms of red pigment loss with a primary located at the red corner of the chromaticity diagram. (point of confusion x=.7635, y=0.2365 on Judd-Vos revised???

(Smith & Pokorny 2003) Smith and Pokorny 1975 give .7465 .2535 which is closer to the red corner.

• The tritanope shows all the symptoms of blue pigment loss, with a primary located near the blue corner of the chromaticity diagram. x=0.1748,y=0 (Smith & Pokorny 2003)

• The deuteranope does not appear to be the result of green pigment loss. If it were, we would expect a point of confusion above the gamut, but instead the point of confusion is on the RG line and below the gamut. Experimental results from a number of sources give repeatable results for the locations of the red and blue points of confusion, but the results for the green point of confusion are variable. The only thing they have in common is that thay lie on a straight line pointing to the red point of confusion. It has been postulated that Pitt's deuteranope is a case where the red and green receptors have merged in some proportion. To investigate this, we return to the above model of the simple eye.

x=1.4, y=-0.4(Smith & Pokorny 2003)

File:CIELuv Protanope.png Figure 3a: Lines of confusion for a protanope (From Pitt 1935)

File:CIELuv Tritanope.png Figure 3b: Lines of confusion for a tritanope (From ???)

File:CIELuv Deuteranope.png Figure 3c: Lines of confusion for a deuteranope (From Pitt 1935)

Eye #2 - The simple eye revisited

File:SimpleEye3 CMF.png

Figure 3d: Color matching functions for a simple eye (#1) with the red and green functions merged in a ratio of x to x.

$r=$

$g=$

These lines of confusion are shown in Figure ??? on the right. Notice the point of confusion lies on the RG line below the gamut. These results are consistent with the idea that the deruteranope response is the result of a merging of the red and green receptor responses in proportions which are variable from person to person, while the protanope and deuteranope are the result of red and blue pigment loss entirely.

File:SimpleEye3 XXX.png

Figure 3e: Lines of confusion for Eye #2

External Links

• The good one

References

• Pitt, F. (1935). Characteristics of dichromatic vision. Report of the Committee on the Physiology of Vision: XIV Special Report Series, London: Medical Research Council of Britain, No. 200. London: His Majesty's Stationery Office.

• Tritanope reference = Benjamin

• http://webvision.med.utah.edu/KallColor.html - KallColor - excellent web page

• Sharpe, L. T. (1999). "Opsin genes, cone photopigments, color vision and colorblindness" (PDF). In K. Gegenfurtner & L. T. Sharpe (ed.). Color vision: from genes to perception. Cambridge: Cambridge University Press. pp. 3–50. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

• http://home.uchicago.edu/~eye1/PDF%20files/Smith%20Pokorny%2075.pdf Smith & Pokorny (1975) (COPUNCT)
• http://home.uchicago.edu/~eye1/PDF%20files/03Chapter1097.pdf Smith & Pokorny (2003) Color Matching (COPUNCT)
• http://www.cvrl.org/database/text/cones/sp.htm Smith & Pokorny - cone fundamentals

• Wyszecki, Günter (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae (2nd ed.). New York: Wiley-Interscience. ISBN 0-471-39918-3. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)