Information Technology Reference
In-Depth Information
In case of digital image, the integral are replaced by summation, given as follows
m
+
1
Z
=
I x y V
(, )
(, ),
r
ʸ
x
2
+
y
2
≤
1
(4)
mn
mn
ˀ
xy
Dual tree complex wavelet transform and Zernike moments both have its own
properties such as: shift-invariant [27], translation invariant [22], rotation invariant
[23] etc. So if we use combination of these two features in one methodology then we
can expect for more accurate object classification results in comparison to use of only
Dual tree complex wavelet transform or Zernike moment.
3
Support Vector Machine Classifier
Support vector machine (SVM) is very popular classifier, which classifies objects into
two categories: object and non-object data [28]. An n-dimensional object
x
has n-
coordinates.
(
)
, where, each
for
i
=
1, 2, 3,
…
. ,
n
.
i
xR
∈
x
=
x
,,
x
,
x
,
……
,
n
x
1
2
3
Each object
x
j
belongs to a class
. Consider a training set
T
of
m
patterns
{
}
y
∈− +
1,
1
j
together with their classes,
{
(
) (
)
(
)
}
and a dot product space
S
,
Tx
=
,
y
,
x
,
y
,...,
x
,
nn
y
11
2 2
xx
,
,.....,
m
x
∈
S
in which the objects are embedded,
. Any hyperplane in the space
12
S can be written as
{
}
xSwxb
∈
|
.
+
=
0,
wSbR
∈
,
∈
(5)
The dot product w.x is defined by:
n
(6)
wx
.
=
wx
ii
i
=
1
A training set of objects is linearly separable if there exists at least one linear clas-
sifier defined by the pair
(w, b)
which correctly classifies all objects. The linear classi-
fier is represented by the hyperplane
H (w.x+b=0)
and defines a region for class
+1
and another region for class
-1
objects. After training, the classifier is ready to predict
the class membership for new objects, different from those used in training. The class
of object
x
k
is determined with the equation:
+
1
if
wx
.
+>
b
0
()
k
class
x
=
(7)
k
−
1
if
wx
.
+<
b
0
k
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