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
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