Image Processing Reference
In-Depth Information
0.5
0.5
Di(j, 0.6)
Di (j, 5)
0
5
0
5
10
10
j
j
(b) Large
(a) Small
σ
σ
Figure 6.11
Effect of σ
on distance weighting
P
(
i
,
j
) = (1 - cos(θ
i
+ θ
j
- 2α
ij
)) ×
(1 - cos(θ
i
- θ
j
))
(6.47)
where θ is the edge direction at the two points and where α
ij
measures the direction of a
line joining the two points:
y
() - ()
() -
P
y
P
j
i
= tan
-1
(6.48)
ij
x
P
x
()
P
j
i
where
x
(
P
i
) and
y
(
P
i
) are the
x
and
y
co-ordinates of the point
P
i
, respectively. This function
is minimum when the edge direction at two points is in the same direction (
θ
j
=
θ
i
), and is
a maximum when the edge direction is away from each other (
θ
i
=
θ
j
+
), along the line
joining the two points, (
α
ij
).
The effect of relative edge direction on phase weighting is illustrated in Figure
6.12
where Figure
6.12
(a) concerns two edge points that point towards each other and describes
the effect on the phase weighting function by varying
θ
j
=
α
ij
. This shows how the phase weight
is maximum when the edge direction at the two points is along the line joining them, in this
case when
θ
i
= 0. Figure
6.12
(b) concerns one point with edge direction along
the line joining two points, where the edge direction at the second point is varied. The
phase weighting function is maximum when the edge direction at each point is towards
each other, in this case when |
ij
= 0 and
θ
j
| =
.
4
4
(
1 -
cos(
θ
)) · (1 - cos(-
θ
))
(1 -
cos(
π
-
θ
))· 2
2
2
-2
0
2
-2
0
2
θ
θ
(a)
θ
j
=
and
θ
i
= 0, varying
(b)
θ
i
=
ij
= 0, varying
θ
j
ij
Figure 6.12
Effect of relative edge direction on phase weighting
