Image Processing Reference
In-Depth Information
collectively called the object whereas those outside are called the background. For
convenience, we also assume that
f
=1for object points and
f
=0for the back-
ground.
Area
Formally, this is given by
A
=
f
(
x, y
)
dxdy
(17.15)
D
which in practice, translates to the count of points with
f
=1.
Perimeter
The formal definition of the perimeter is
P
=
f
(
x
(
s
)
,y
(
s
))
ds
(17.16)
∂D
where
∂
and (
x
(
s
)
,y
(
s
)) is a parametrization of
the boundary curve. In practice, one decides on a neighborhood connectivity type,
e.g., 8- or 4- connectivity in 2D, then counts neighborhoods containing
both
points
with
f
=1and
f
=0.
D
is the boundary of the region
D
Bounding Box
This is the tightest “cuboid” that contains an image volume. For a 2D region, this is
given by the rectangle represented by a four-tuple:
(min
r
k
X
(
r
k
)
,
min
r
k
Y
(
r
k
)
,
max
r
k
X
(
r
k
)
,
max
r
k
Y
(
r
k
))
(17.17)
where
X
(
r
k
) and
Y
(
r
k
) represent the coordinates of image points
r
k
in the region.
Bounding boxes can be used for having a simple idea on the shape of a region, i.e.,
elongated versus compact shape. It is also used for avoiding collisions, i.e. if two
regions that move have nonoverlapping bounding boxes then they are not in collision.
Circularity/Compactness
The dimensionless ratio defined via the perimeter and the area is called circularity or
compactness,
C
:
C
=
P
2
A
(17.18)
It has a lower bound. In 2D it satisfies 4
π
≤
C
and reaches its minimum when the
region is a circle.
