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
−

⇔