Microscope Image Processing

A ¼

1

2

ð

xdy ydxðÞ (10:7)

where the integration is carried out around the closed curve. We can discretize

Eq. 10.7, yielding [11]

A ¼

1

2

X

N

b

i¼1

x

i

y

iþ1

 y

i

ðÞ

 y

i

x

iþ1

 x

i

ðÞ½

(10:8)

and manipulate this expression into the form of Eq. 10.6. The corresponding

perimeter is the sum of the side lengths of the polygon. Side lengths can easily be

calculated from the boundary chain code (Chapter 9). If all boundary points are

used as vertices, the perimeter will simply be the sum of lateral and diagonal

steps, written as [11]

P ¼ N

e

þ

ffiffiffi

2

p

N

o

(10:9)

where N

e

is the number of even and N

o

the number of odd steps in the boundary

chain code.

10.2.2 Pose Measures

The pose of an