
White balance 161
which is the formulation of the in-camera white balance process by which a
color corrected triplet (R
1
, G
1
, B
1
) is obtained from (R
2
, G
2
, B
2
), as we saw
in Chapter 3, Equation 3.7.
Secondly, from Equations 7.18 and 7.3,
R
1
=
780
X
i=380
s
r
(λ
i
)ρ(λ
i
) = ρ
R
G
1
=
780
X
i=380
s
g
(λ
i
)ρ(λ
i
) = ρ
G
B
1
=
780
X
i=380
s
b
(λ
i
)ρ(λ
i
) = ρ
B
, (7.20)
and this shows that with Equation 7.19 we are estimating the surface re-
flectances ρ
R
, ρ
G
, ρ
B
. In other words, we have shown that under all the above
assumptions we can achieve perfect color constancy. Let us remark once more
that the main assumption here is that there’s no overlap in the response
functions, but this does not ...