primaries, horseshoes and v(lambda)

I am trying to work out why the coefficient for converting r,g,b into a grey value are what they are:

L = 0.265R + 0.670G + 0.065B

I started off with the 1931 horseshoe diagram onto which I drew the Radiance colour gamut. The primitives are defined in src/common/color.h:

0.640 0.330 (red)
0.290 0.600 (green)
0.150 0.060 (blue)
0.333 0.333 (white)

I then determined the dominant wavelength for r,g,b by projecting the x,y coordinates from the white point onto the perimeter of the horseshoe. This was rounded to the nearest 5 nm, because the data I had for the v(lambda) curve only had a 5 nm resolution:

http://luminance.londonmet.ac.uk/pickup/primaries_vlambda.png

The dominant wavelengths of the r,g,b primaries are drawn as arrows. The little coloured rings are the weighting coefficient as used by Radiance.

Since 1 = r + g + b, I normalised the values I got (where the little arrows hit the v(lambda) curve).

L = 0.326R + 0.635G + 0.039B

The derived coefficients are qualitatively similar to the Radiance ones in the sense that b < r < g, but I would have liked them to be closer in their absolute values, too. Although the methodology and drawings are a bit crude, I was hoping to get a better match.

Can anybody suggest a better solution?

Thanks

Axel

Hi Axel,

The calculation of the coefficients for red green and blue conversion to luminance (Y) is spelled out in src/common/color.h. The math is a little bit complicated, and I admit that I do not fully understand its relationship to the geometry of the CIE horseshoe diagram, so I'm not sure I can resolve your conundrum. I know you have to account for the white point, which in the case of the Radiance color space is set to neutral gray (x,y)=(1/3,1/3). It looks like the CIE formulas, which I copied out of a text somewhere, apply ratios of cross products, but I really have no idea why.

I'm sorry I can't be of more help. If I knew of a text that explained this intuitively, I would refer you (and myself) to it....

Best,
-Greg

ยทยทยท

From: Axel Jacobs <[email protected]>
Date: January 16, 2011 1:42:29 PM PST

I am trying to work out why the coefficient for converting r,g,b into a grey value are what they are:

L = 0.265R + 0.670G + 0.065B

I started off with the 1931 horseshoe diagram onto which I drew the Radiance colour gamut. The primitives are defined in src/common/color.h:

0.640 0.330 (red)
0.290 0.600 (green)
0.150 0.060 (blue)
0.333 0.333 (white)

I then determined the dominant wavelength for r,g,b by projecting the x,y coordinates from the white point onto the perimeter of the horseshoe. This was rounded to the nearest 5 nm, because the data I had for the v(lambda) curve only had a 5 nm resolution:

http://luminance.londonmet.ac.uk/pickup/primaries_vlambda.png

The dominant wavelengths of the r,g,b primaries are drawn as arrows. The little coloured rings are the weighting coefficient as used by Radiance.

Since 1 = r + g + b, I normalised the values I got (where the little arrows hit the v(lambda) curve).

L = 0.326R + 0.635G + 0.039B

The derived coefficients are qualitatively similar to the Radiance ones in the sense that b < r < g, but I would have liked them to be closer in their absolute values, too. Although the methodology and drawings are a bit crude, I was hoping to get a better match.

Can anybody suggest a better solution?

Thanks

Axel