Image Processing Reference
In-Depth Information
Fig. B.1
(
a
) Point
representation. (
b
) Vector
representation
Result =0;
for
(j = 0;
j < M;
j = j+1)
{
for
(i = 0;
i < N;
i=i+1)
{
Result
=
Result
+
GetPixel ( input ,
i ,
j );
}
}
B.5
Vector
In the 2D coordinate system in Fig.
B.1
a point is defined as
P(x
1
,y
1
)
.Thesame
point can be represented as a
vector
:
x
1
y
1
p
=
(B.10)
A vector is often written as a lowercase letter with an arrow above. It can be
interpreted a
s a line w
ith a slope
y
1
x
1
and a length. The
length of the vector
is defined
x
1
+
p
y
1
.
We can arrange the vector as a row (as opposed to a column) by taking the
trans-
pose
of the vector,
p
T
. That is,
as
=
p
T
=[
x
1
y
1
]
(B.11)
or in other words:
x
1
y
1
T
x
1
y
1
T
=[
x
1
y
1
]
,
[
x
1
y
1
]
=
(B.12)
Say we have two vectors:
p
1
T
and
p
2
T
=[
55
]
=[
20
]
. We can then calcu-
late the sum of
p
1
and
p
2
as
