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