Digital Signal Processing Reference
In-Depth Information
1
0.5
0
0
5
10
15
20
25
30
35
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45
40
35
30
25
45
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15
10
5
0
(a) source image
(b) confidence map
Figure 13.8
The plot shows the confidence map (b) generated with grid value
γ
=5fromthe
source image (a).
containing a possible bias). The inherent decision rule
ζ
(
I
1
)
>
0then
translates to the inner product of
I
1
and
W
being greater than
σ
−1
(0).
By definition, the confidence map
κ
h×w
of an image
I
of size
∈ R
h
×
w
is given by
κ
(
u, v
)=
ζ
(
I
(
u...u
+
n,v...v
+
n
))
(13.16)
σ
x,y
I
(
u
+
x, v
+
y
)
W
(
x, y
)
=
(13.17)
σ
x,y
y
)
I
(
x, y
)
W
(
u
=
−
x, v
−
(13.18)
W
(
u, v
))
=
σ
(
I
∗
(13.19)
after sucient zero-padding of
W
and again with
W
denoting the
reflected image. Application of the filter
W
can now be easily speeded
up by using multiplication in the Fourier space (see section 13.3):
κ
=
σ
F
−1
(
(
W
))
.
F
(
I
)
F
(13.20)
(
W
)canbe
calculated beforehand, so that only two 2-D FFTs have to be calcu-
lated. Similar to the case of image-stitching, this results in a consid-
Here
σ
is implicitly applied for each pixel; in addition
F
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