Image Processing Reference
In-Depth Information
When we have the means and variances of the different features the box classifier
should be replaced by a statistical classifier since this is a more accurate approach.
In the box classifier we have a binary decision; is a new feature vector (BLOB) in-
side or outside the rectangle? In a statistical classifier we instead measure a distance
between a new feature vector (BLOB) and the prototype. The smaller the distance
the more likely it is that the BLOB is the same type (here a large circle) as the proto-
type. To make this approach operational we need to threshold the distance and hence
end up with a binary decision region like the dashed box in Fig. 7.7 . The difference
is that the region is now a more precise ellipse and not a rectangle, see Fig. 7.7 .One
statistical classifier is the weighted Euclidean distance in our case defined as
(f i ( cir )
mean ( cir )) 2
variance ( cir )
(f i ( area )
mean ( area )) 2
variance ( area )
WED ( f i , prototype ) =
+
(7.7)
where WED (f 1 , prototype ) is the weighted Euclidean distance between feature vec-
tor f i , i.e., the i th BLOB, and the prototype. f i ( cir ) and f i ( area ) are the circularity
and area of the i th BLOB, respectively. The rest of the parameters in the equation
are the means and variances of the two features of the prototype. In the general case
with p different features the weighted Euclidean distance measure is defined as
(f i (m j )
p
mean (m j )) 2
variance (m j )
WED ( f i , prototype )
=
(7.8)
j
=
1
where m j is the j th feature. If the variances of all features are the same, then we
can ignore them and end up with the Euclidean distance measure (ED), where the
decision region is a circle in 2D (see Fig. 7.7 ):
f i (m j )
p
mean (m j ) 2
ED ( f i , prototype )
=
(7.9)
j
=
1
It should be noticed that the three equations above assume that the scale of the
features are the same. In our example the problem is that the area is measured in
1000 s and circularity is a value close to 1. This means that the area will dominate
the distance measure completely. The solution is to normalize the features so they
are scaled similarly and are in the same interval, e.g.
[
0 , 1
]
. This can be obtained,
for example, as
min Area of BLOB
Area of Model , Area of Model
Area feature
=
(7.10)
Area of BLOB
min Circularity ,
1
Circularity
Circularity feature
=
(7.11)
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