The last formula has an error because is without -1, namely:

yellowness= S*max(( cos(u)-cos(a))/(1-cos(a)) ,0)

References:

1. Vasile Patrascu, New Framework of HSL System Based Color Clustering Algorithm,

The 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013), pp. 416-423.

2. Vasile Patrascu, New Fuzzy Color Clustering Algorithm Based on hsl Similarity, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009,  pp. 48-52

3. V. Patrascu, Fuzzy Image Segmentation Based on Triangular Function and Its n-dimensional Extension, in the volume Soft Computing in Image Processing. Recent Advances, Series: Studies in Fuzziness and Soft Computing , pp 187-208, Vol. 210 , (Eds.) Nachtegael, M.; Van der Weken, D.; Kerre, E.E.; Philips, W. 2007

You can explore different color spaces as YCbCr, Lab, HSV, HSL, RGB, ...

The color space provides a way to represent a color.

But it depends on  the color space you are using.

Which color space are you using?

Using RGB Space. Yellowbeing red + green, is it not prudent to consider yellow intensity = 1 -tristimulus of blue ?

In general there is no just a single value to represent any color. It is a range of values. I assume that you want to make segmentation. In this case the value of the rgb you get in your image depends on the incident light and the property of the surface. If we assume white light then you need to use some color space conversion which can help you to simplify the problem and can make the segmentation easy. I think that hsv colour space is good enough for this task but specific the colour range or you can use a clustering method suc as SOM to do this job for you.

In the RGB space, the color is formed by overlapping Red, Green and Blue channels. You must use three channels to obtain the color that you want.

Considering the decimal representation:

Color= (R value, G value, B value)

Red = (1, 0, 0)

Green = (0, 1, 0)

Blue = (0, 0, 1)

White = (1 , 1, 1)

Black= (0 , 0 , 0)

The pure yellow is formed by overlapping Red=1, Green=1 and Blue=0.

If Yellow = (1 , 1 , 0)

So

Yellow = Red + Green 

Or

If White = (1, 1, 1)

Then

White = Red + Green + Blue [1]

and

Yellow= Red + Green [2]

- Subratracting Blue on both sides of the equation [1], we obtain:

White - Blue = Red + Green + Blue - Blue

White - Blue = Red + Green  [3]

- Reversing both sides of the equation [3], we obtain:

Red + Green = White - Blue [4]

Equating equations [2] and [4], we get [5]:

Yellow = White - Blue [5]

Or

Yelow = (1, 1, 1) - (0, 0, 1) [5]

So Yellow is White - Blue in RGB Space.

Dear All,

I just want to come out with a metric that could signify the intensity of yellow coloration. The context here is , the exudate intensity in fovia. The project work is related to damage quantification in retinal images( diabetic retinopathy).

u=atan2[ (R-G)/sqrt(2)  ,  (R+G-2B)/sqrt(6) ]

V=max(R,G,B)

v=min(R,G,B)

S=2(V-v)/(1+|V-0.5|+|v-0.5|)

yelowness =  S*cos(u)

Good luck!

for VB 6

Function ArcTan2(X As Double, Y As Double) As Double Private Const PI As Double = 3.14159265358979 Private Const PI_2 As Double = 1.5707963267949 Select Case X Case Is > 0 ArcTan2 = Atn(Y / X) Case Is < 0 ArcTan2 = Atn(Y / X) + PI * Sgn(Y) If Y = 0 Then ArcTan2 = ArcTan2 + PI Case Is = 0 ArcTan2 = PI_2 * Sgn(Y) End Select End Function

You can enhance the yellowness formula with the following:

yellowness= S*max( cos(u)/cos(a) - 1,0)

where  0 

In order to have yellowness in the interval [0,1], you can use:

yellowness= S*max(( cos(u)-cos(a))/(1-cos(a)) - 1,0)

where 0 < a < pi/3

Thank you. I just need some quantification for yellow. The formulations you have given seem to augur well for my work. Kindly get me the reference , which I should quote, when I happen to present the research paper.

The last formula has an error because is without -1, namely:

yellowness= S*max(( cos(u)-cos(a))/(1-cos(a)) ,0)

References:

1. Vasile Patrascu, New Framework of HSL System Based Color Clustering Algorithm,

The 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013), pp. 416-423.

2. Vasile Patrascu, New Fuzzy Color Clustering Algorithm Based on hsl Similarity, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009,  pp. 48-52

3. V. Patrascu, Fuzzy Image Segmentation Based on Triangular Function and Its n-dimensional Extension, in the volume Soft Computing in Image Processing. Recent Advances, Series: Studies in Fuzziness and Soft Computing , pp 187-208, Vol. 210 , (Eds.) Nachtegael, M.; Van der Weken, D.; Kerre, E.E.; Philips, W. 2007

Thank you Mr/Dr.  Vasile Patrascu.