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.