Image Processing Reference

In-Depth Information

Fig. 7.5
(
a
) Bounding box. (
b
) Bounding circle. (
c
) Convex hull

center is the radius in this direction. We do this for all possible directions (for

example with an angular resolution of 10°) and the biggest radius defines the radius

for the minimum circle.

Convex hull
of a BLOB is the minimum convex polygon which contains the

BLOB, see Fig.
7.5
. It corresponds to placing a rubber band around the BLOB.

It can be found in the following manner. From the topmost pixel on the BLOB

search to the right along a horizontal line. If no BLOB pixel is found increase

(clockwise) the angle of the search line and repeat the search. When a BLOB pixel

is found the first line of the polygon is defined and a new search is started based

on the angle of the previous search line. When the search reappears at the topmost

pixel, the convex hull is completed. Note that morphology also can be applied to

find the convex hull of a BLOB.

B
ounding box ratio
of a BLOB is defined as the height of the bounding box di-

vided by the width. This feature indicates the elongation of the BLOB, i.e., is the

BLOB long, high or neither.

Compactness
of a BLOB is defined as the ratio of the BLOB's area to the area

of the bounding box. This can be used to distinguish compact BLOBs from non-

compact ones. For example, fist vs. a hand with outstretched fingers.

Area of BLOB

width

Compactness

=

(7.1)

·

height

Center of mass
(or center of gravity or centroid) of a physical object is the location

on the object where you should place your finger in order to balance the object. The

center of mass for a binary image is similar. It is the average x- and y-positions of

the binary object. It is defined as a point, whose x-value is calculated by summing

the x-coordinates of all pixels in the BLOB and then dividing by the total number of

pixels. Similarly for the y-value. In mathematical terms the center of mass,
(x
c
,y
c
)

is calculated as

N

N

1

N

1

N

x
c
=

y
c
=

x
i
,

y
i

(7.2)

i

=

1

i

=

1