Information Technology Reference
In-Depth Information
3 Proposed Approach
The goal is to compute the parameters of the polyhedral model given
N
aerial
images. One of these images contains the external boundary of the building. We
call this image the master image since it will be used as a reference image. The
building boundary in the master image is provided either manually or automat-
ically. The basic idea relies on the following fact: if the shape and the geometric
parameters of the building (encoded by the vector
w
) correspond to the real
building shape and geometry, then the pixel-to-pixel mapping between the mas-
ter image
I
m
and any other aerial image (in which the building is visible) will be
correct for the entire building footprint. In other words, the dissimilarity asso-
ciated with the two sets of pixels should correspond to a minimum. Recall that
w
is defining all support planes of all the building's facets and thus the corre-
sponding pixel
p
of any pixel
p
is estimated by a simple image transfer through
homographies (3
3 matrices) based on these planes. Therefore, the associated
global dissimilarity measure reaches a minimum. The global dissimilarity is given
by the following score:
×
N−
1
I
j
(
p
)
e
=
ρ
(
|
I
m
(
p
)
−
|
)
(3)
p
∈S
j
=1
where
N
is the number of aerial images in which the whole building roof is
visible (in practice,
N
is between 2 and 5),
S
is the footprint of the building in
the master image
I
m
,
p
is the pixel in the image
I
j
=
I
m
that corresponds to
the pixel
p
∈
I
m
,and
ρ
(
x
) is a robust error function.
The choice of the error function
ρ
(
x
) will determine the nature of the global
error (3) which can be the Sum of Squared Differences (SSD) (
ρ
(
x
)=
2
x
2
),
the Sum of Absolute Differences (SAD) (
ρ
(
x
)=
x
), or the saturated Sum of
Absolute Differences. In general, the function
ρ
(
x
) could be any M-estimator [9].
In our experiments, we used the SAD score since it is somewhat robust and its
computation is fast.
We seek the polyhedral model
w
=(
λ
M
,λ
N
,Z
A
,Z
M
,Z
N
,Z
C
)
T
that mini-
mizes the above dissimilarity measure over the building footprint:
=
arg
min
w
w
e
(4)
We can also measure the fitness of the 3D model by measuring the gradient
norms along the projected 3D segments of the generated 3D models. In general,
at facets discontinuities the image gradient is high. Thus, for a good fit, the
projection of the 3D segments will coincide with pixels having a high gradient
norm in all images. Therefore, we want to maximize the sum of gradient norms
along these segments over all images. Recall that we have at most nine segments
for our simple 3D polyhedral model. Thus, the gradient score is given by:
N
1
N
g
=
g
j
(5)
j
Search WWH ::
Custom Search