Brightness

Starting from an RGB value there are various ways of determining the brightness of that pixel.  The simplest is to compute the average of the R, G and B channels.

        private double GetBrightness(Color clr)
        {
            return (clr.R + clr.G + clr.B) / 3.0; 
        }

Another is to use the HSV hexcone model which takes the maximum of all the colors

        private double GetBrightnessHSV(Color clr)
        {
            return Math.Max(Math.Max(clr.R, clr.G), clr.B);
        } 

Another is to use the HSL method which averages the maximum and minimum of the colors

        private double GetBrightnessHSL(Color clr)
        {
            return 0.5 * Math.Max(Math.Max(clr.R, clr.G), clr.B) + 0.5 * Math.Min(Math.Min(clr.R, clr.G), clr.B);
        }

There is also luma which is based upon the weighted average of gamma corrected RGB values.  Naturally there are different corrections depending upon the source.  Rec.601 refers to NTSC sources.  Rec 709 to sRGB and Rec 2020 to UHDTV.  Noting that in the .net framework each color is represented with 8 bits per color.  Rec 2020 calls for 10 or 12 bits per sample, expanding the range of possible color representation, this requires a different “color” object to represent the pixel’s value.

        private double GetBrightnessLumaRec2020(UHDColor clr)
        {
            return 0.2627 * clr.R + 0.6780 * clr.G + 0.0593 * clr.B; // rec 2020 Luma coefficients
        }

        private double GetBrightnessLumaRec601(Color clr)
        {
            return 0.30 * clr.R + 0.59 * clr.G + 0.11 * clr.B; // rec 601 Luma coefficients
        }

        private double GetBrightnessLumaRec709(Color clr)
        {
            return 0.21 * clr.R + 0.72 * clr.G + 0.07 * clr.B; // rec 709 Luma coefficients
        } 

All of these approximations have flaws, the most accurate representation we have appears to be the latest standard from the International Commission on Illumination (yes it really exists!) called CIECAM02.  This appears to be implemented in Windows from Vista onwards but not yet available in .net.