Image Processing Reference
In-Depth Information
=
0 we are in the sextant
RWY
and find
R
,
G
, and
B
in the following
way. First we realize that
R
When
K
=
V
in this sextant. Next we use the fact that
B
=
min
{
R,G,B
}
in this sextant. Inserting this into Eq.
E.5
we get
B
=
V
·
(
1
−
S)
.
G
is found using the following equation derived above:
G
−
B
H
=
(E.14)
V
−
min
{
R,G,B
}
Substituting we have
G
−
V
·
(
1
−
S)
H
=
⇔
V
−
V
·
(
1
−
S)
G
=
H
·
V
−
H
·
V
·
(
1
−
S)
+
V
·
(
1
−
S)
⇔
G
=
V
·
(H
−
H
+
H
·
S
+
1
−
S)
⇔
·
1
H)
G
=
V
−
S
·
(
1
−
(E.15)
When
K
1 the point is located in the sextant
YWG
. In this sextant we know from
above that
G
=
=
V
and
B
=
min
{
R,G,B
}
.
R
is found using the following equation,
derived above:
V
−
R
H
=
(E.16)
V
−
min
{
R,G,B
}
Substituting we have
V
−
R
V
−
V
·
(
1
H
=
⇔
(E.17)
−
S)
R
=
V
−
H
·
V
+
H
·
V
·
(
1
−
S)
⇔
(E.18)
R
=
V
·
(
1
−
S
·
H)
(E.19)
For the remaining four sextants we end up with similar results. The last thing re-
maining before we can put it all together and derive a general conversion from HSV
to RGB is a method to map from
H
deg
to
H
. This is done as follows:
H
deg
60°
H
=
(E.20)
=
H
K
(E.21)
H
−
H
=
K
(E.22)
where
x
means the floor of
x
, see Appendix
B
. The final conversion is now given
as