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