Image Processing Reference

In-Depth Information

steps of one: 1
,
2
,
3
,
4
,
5
,...,
1040
,
1041
,
1042. What comes after the summation is

a function, which is controlled by
i
and it is the values of this function (for each
i
)

that are added together. Below, some examples of different summations are given:

12

i

=

1

+

2

+

3

+

4

+

5

+

6

+

7

+

8

+

9

+

10

+

11

+

12

=

78

(B.4)

i

=

1

4

2

ยท

i

=

0

+

2

+

4

+

6

+

8

=

20

(B.5)

i

=

0

1

i
2

=

4

+

1

+

0

+

1

=

6

(B.6)

i

=โ

2

Say that you want to sum the pixel values of the first row in an image with width

=

200. This is then written as

199

f(i,
0
)

(B.7)

i

=

0

In general the summation is written as

m

h(i)

(B.8)

i

=

n

In terms of C-programming the summation is implemented as a
for-loop
:

Result =0;

for

(i = n;

i < (m+1);

i = i+1)

{

Result

=

Result

+ h( i );

}

We can also do a summation using more indices than
i
. For example, if we want to

add all pixel values in an image, then we need two indices representing rows and

columns. Concretely we would write

M

โ

1

N

โ

1

f(i,j)

(B.9)

j

=

0

i

=

0

where
N
is the number of columns and
M
is the number of rows. In terms of C-

programming the double summation is implemented as two
for-loops
: