Digital Signal Processing Reference
In-Depth Information
According to the measure of similarity, we can gain the most similar matching virtual
triangles pair to achieve virtual triangles matching. Their corresponding vertexes are
used as control points.
4
Estimation of Similarity Transformation
Similarity transformation is used in this paper
. Suppose
XY
,
xy
,
XY
,
(,
)
(, )
(,
)
11
11
22
xy
are coordinates of three corresponding vertexes of the
most similar matching virtual triangles pair gained in section 3. The lengthes of three
corresponding sides of them are denoted as
(, )
xy
and
(,
XY
,
)
(, )
22
33
33
θθθ θ θ θ
are the
angles between
three corresponding sides and horizontal orientation respectively.
The scale s can be estimated as following:
llllll
.
'
'
'
' ' '
11 2 2 3 3
,
,
,
,
,
,,,,,
12
12
13
13
23
23
l
l
l
(11)
s
=
(
12
+
13
+
23
)
3
'
'
'
l
l
l
12
13
23
Computing the rotation angle
θ
by formulation (12):
'
'
'
(12)
θθθθθθθ
=−+−+−
(
) 3
1
1
2
2
3
3
Via
XY
,
xy
,
XY
,
xy
,
XY
,
xy
and formulation (10), we can get
(,
)
(, )
(,
)
(, )
(,
)
(, )
11
11
22
22
33
33
three horizontal and vertical translation:
.
And
ΔΔ
can be
ΔΔΔ Δ Δ Δ
xyxyxy
,
,
,
,
,
,
xy
1
1
2
2
3
3
computed:
Δ=Δ +Δ +Δ
x
(
x
x
x
) 3
1
2
3
(13)
Δ=Δ +Δ +Δ
y
(
y
y
y
) 3
1
2
3
5
Experimental Results
The reference image and the sensed image are shown as fig.4. Corners extracted by an
improved technique based on Harris are denoted as red “+” dots in fig.5. The registra-
tion result of the proposed method is shown as fig.6.
Fig. 4.
Reference and sensed image taken under different conditions
