Image Processing Reference
In-Depth Information
Fig. D.1
(
a
) The rgb triangle inside the RGB color cube. (
b
) The rgb triangle
Fig. D.2
The location of
different points used to define
saturation
min
{
P
R
,P
G
,P
B
}
P
R
+
S
=
1
−
3
·
(D.4)
P
G
+
P
B
Similar arguments hold for the other two triangles
WG
B
and
WB
R
and Eq.
D.4
is therefore the general expression for saturation in the HSI representation.
Hue is defined as the angle,
θ
, between the two vectors
−−
WR
and
−−
WP
,see
Fig. 3.11. Referring to Eq.
B.16
we can express the angle between the vectors as
cos
−
1
−−
WR
•
−−
WP
−−
WR
·
−−
WP
θ
=
(D.5)
Inserting the actual points yields
⎡
⎤
⎡
⎤
⎡
⎤
1
0
0
1
/
3
1
/
3
1
/
3
2
/
3
−−
WR
=
R
−
W
=
⎣
⎦
−
⎣
⎦
=
⎣
⎦
−
1
/
3
(D.6)
−
1
/
3
(
2
/
3
)
2
6
/
9
2
/
3
−−
WR
=
1
/
3
)
2
1
/
3
)
2
+
(
−
+
(
−
=
=
(D.7)
⎡
⎤
⎡
⎤
⎡
⎤
P
r
P
g
P
b
1
/
3
1
/
3
1
/
3
P
r
−
1
/
3
−−
WP
=
P
−
W
⎣
⎦
−
⎣
⎦
=
⎣
⎦
=
P
g
−
1
/
3
(D.8)
P
b
−
1
/
3
(P
r
−
−−
WP
1
/
3
)
2
1
/
3
)
2
1
/
3
)
2
=
+
(P
g
−
+
(P
b
−
⇔
