Question

The “hue” is the color, independent of brightness and how much pure white has been added to it. We can make a simple definition of hue as the set of ratios R:G:B. (a) Suppose a color (i.e., an RGB) is divided by 2.0, so that the RGB triple now has values 0.5 times its former values. Explain using numerical values: i. If gamma correction is applied after the division by 2.0 and before the color is stored, does the darker RGB have the same hue as the original in the sense of having the same ratios R:G:B of light emanating from the display device? (we are not discussing any psychophysical effects that change our perception—here we are just worried about the machine itself). ii. If gamma correction is not applied, does the second RGB above, = RGB/2, have the same hue as the first RGB, when displayed? And are these the same hues as for the original color as stored, not the light as displayed?

problem #12 (a)(i.) and (a)(ii.) only

Answer #1

a) 2 with gamma correction RGB is stored as(RGB)^(1/gamma)and (RGB/2) is stored as(RGB/2)^(1/gamma). after the CRT gamma takes effects color^gamma the gamma-correction power law is reserved and we're back to RGB and RGB/2 so the hue does not change

b) 2 but if there is no gamma-correction then RGB result in light(RGB)^gamma and RGB/2 is viewed as (RGB/2)^gamma so we see the different hue. as an example suppose RGB=1,1/2,1/4 suppose gamma is 2.0 then the color viewed is 1,1/4,1/16 which is different hue

c) 1 suppose RGB=1,1,1 then the color viewed is also1,1,1 and RGB/2=1/2*(1,1,1) is viewed as 1/4*(1,1,1) so the hue is unchanged just darker.

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