Image Processing Reference
In-Depth Information
The symmetry relation between two points is then defined as
C
(
i
,
j
, σ
) =
D
(
i
,
j
, σ
) ×
P
(
i
,
j
) ×
E
(
i
) ×
E
(
j
)
(6.49)
where
E
is the edge magnitude expressed in logarithmic form as
E
(
i
) = log(1 +
M
(
i
)) (6.50)
where
M
is the edge magnitude derived by application of an edge detection operator. The
symmetry contribution of two points is accumulated at the mid-point of the line joining the
two points. The total symmetry
S
P
at point
P
m
is the sum of the measured symmetry for
all pairs of points which have their mid-point at
P
m
, i.e. those points Γ (
P
m
) given by
PP
P
+
2
i
j
Γ (
P
) =
( , )
ij
=
i
≠
j
(6.51)
m
m
and the accumulated symmetry is then
Σ
Γ
S
() =
σ
C i j
(,
,
σ
)
(6.52)
P
m
ij
,
(
P
)
m
The result of applying the symmetry operator to two images is shown in Figure
6.13
, for
small and large values of σ . Figures
6.13
(a) and (d) show the image of a square and the
edge image of a heart, respectively, to which the symmetry operator was applied; Figures
6.13
(b) and (e) are for the symmetry operator with a
low
value for the deviation parameter,
(a) Original shape
(b) Small
σ
(c) Large
σ
(d) Shape edge magnitude
(e) Small
σ
(f) Large
σ
Figure 6.13
Applying the symmetry operator for feature extraction