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a. convert to linear, Y = 0.3*R+0.59*G+0.11*B, convert back
b. square, Y = 0.3*R+0.59*G+0.11*B, square root
c. Y = 0.3*R+0.59*G+0.11*B
d. Y = (R+G+G+B)>>2
e. Y = G

FYI, most interesting image operations are only valid on
linear data. This includes scaling and alpha blending.
Lots of programmers degrade images by screwing this up.
We should all try to do better, especially when the image
is something that might be important to the user.