Image Processing Reference
In-Depth Information
V
−
min
{
R,G,B
}
V
S
=
(E.5)
where
S
. Similar reasoning for the other five sextants in the hexagon shows
that Eq.
E.5
is indeed a general equation that holds for the entire hexagon.
∈[
0
,
1
]
E.1.2 HSV: Hue
In Fig.
E.1
(b) hue is illustrated as the angle between
−−
WR
and
−−
WP
. Hue is, however,
not
calculated as an angle but rather as the following ratio:
=
−
AP
−
AD
H
(E.6)
where
A
,
P
, and
D
are defined in Fig.
E.1
(b). This definition is only valid when
P
is located in the sextant shown in Fig.
E.1
(b), i.e., then
R
=
V
and
G
≥
B
.Inthis
sextant hue will be a value in the interval
[
0
,
1
]
where hue
=
0 corresponds to red
and hue
1 corresponds to yellow. The calculated hue value is normally multiplied
with 60° in order to obtain a hue value in the range of
=
when considering
all sextants.
2
Below we show how hue is calculated in the sextant
RWY
.
Looking at Fig.
E.1
(b) we can see that
[
0°
,
360°
[
−
AP
=
−
EP
−
−
EA
−
EA
=
−
AF
,
−
AD
=
−−
WD
and that
. From this follows that
=
−
AP
=
−
EP
−
−
AF
H
(E.7)
−
AD
−−
WD
−−
WD
Above we saw that
and stated that the “position” of
P
in this sextant is given as
(G, B)
. Combining this with Eq.
E.7
and converting the
ratio into degrees we have
=
V
−
min
{
R,G,B
}
G
−
B
H
deg
=
{
R,G,B
}
·
60°
(E.8)
V
−
min
A similar geometric reasoning can be carried out for the sextant
MWR
where
R
=
V
and
B>G
resulting in:
5
R
−
B
H
deg
=
}
+
·
60°
(E.9)
V
−
min
{
R,G,B
=
Moving on to the sextant
YWG
where
G
V
and
R>B
we can derive that
2
Note that the range is defined as
[
0°
,
360°
[
as opposed to
[
0°
,
360°
]
. The reason for this is that
360°
=
0°, hence 360° is not included in the interval, but 359
.
99999° etc. is.
