Image Processing Reference

In-Depth Information

where
N
is the number of pixels in the BLOB and
x
i
and
y
i
are the
x
and
y

coordinates of the
N
pixels, respectively. In situations where the BLOB contains

“appended parts” the median can replace Eq.
7.2
. An example could be if you

want to find the center of a person's torso. The configurations of the arms will

effect the result of Eq.
7.2
, but the median is less effected. The median is more

computational demanding than the center of mass. An alternative to the median is

to erode the BLOB with a large structuring element and then calculate the center

of mass.

Center of the bounding box
is a fast approximation of the center of mass. In math-

ematical terms the center of the bounding box,
(x
bb
,y
bb
)
is calculated as

x
max
−

x
min

x
max

2

x
min

2

x
min
+

x
max

x
bb
=

x
min
+

=

x
min
+

−

=

(7.3)

2

2

y
max
−

y
min

y
max

2

y
min

2

y
min
+

y
max

y
bb
=

y
min
+

=

y
min
+

−

=

(7.4)

2

2

Perimeter
of a BLOB is the length of the contour of the BLOB. This can be found

by scanning along the rim (contour) of an object and summing the number of pixels

encountered. A simple approximation of the perimeter is to first find the outer

boundary using the method from Sect. 6.3.4 (or another edge detection algorithm).

Following this we simply count the number of white pixels in the image.

Circularity
of a BLOB defines how circular a BLOB is. Different definitions exist

based on the perimeter and area of the BLOB. Heywood's circularity factor is, for

example, defined as the ratio of the BLOB's perimeter to the perimeter of the circle

with the same area:

Pe
rimeter of BLOB

2
√
π

Circularity

=

(7.5)

·

Area of BLOB

A different way of calculating the circularity is to find the different radii as de-

scribed for the bounding circle. The variance (see Appendix C) of the radii gives

an estimate of the circularity. The smaller the variance the more circular the BLOB

is.

In Fig.
7.6
two of the feature values are illustrated for the BLOBs in Fig.
7.4
(left).

So after extraction of features a binary image has been converted into a number of

feature values for each BLOB. The feature values can be collected in a so-called

feature vector
. For the BLOBs in Fig.
7.6
, the feature vector for BLOB number one

is

0
.
31

6561

f
1
=

(7.6)

Since we have seven BLOBs, we will also have seven feature vectors:
f
1
,...,f
7
.