relief) or orthorectified images with the direct use of
RPC
coef-
ficients (without bias-compensation).
In the case of a multitemporal image sequence, the user is
required to generate classification polygons for the different
images, which can be independently segmented and classified
with different solutions available on the commercial market
(Figure 3, top). The aim of this work is not the implementation
of a new solution for object-based classification. The main aim
is the development of a general procedure able to handle the
spatial inconsistency in the comparison of classification maps
(Figure 3, bottom). The proposed solution offers a large flex-
ibility for the choice of the software and the procedure for clas-
sification, which is strictly dependent on project requirements.
Detection of Corresponding Points from Images with Weak Geo-localization
Given two images,
I
1
and
I
2
, from which classifications
c
1
and
c
2
are derived using object-based image analysis, rigorous
comparison for change detection needs an exact overlap of
object edges extracted at different epochs.
The proposed solution is based on a registration approach
by means of piecewise affine transformation functions auto-
matically estimated from a set of homologous points. Because
input images could be affected by different geometric issues,
an approach based on image tiling was developed. The sub-
division of images into smaller tiles allows one to reduce the
lack of rigorous image orientation and terrain correction (raw
images), since geometric deformation should be less within
small image subsets. The method uses a default tile size of
1,280 × 1,280 pixels, which can be adjusted after checking the
final point distribution. The tiles of both images are inde-
pendently matched by using initial georeferencing param-
eters as approximate values. The implementation is derived
from a solution for close-range image orientation described
in Barazzetti
et al.
(2013), which was adapted to handle
medium-resolution satellite images (Barazzetti
et al.
, 2014).
The matching of images
I
1
and
I
2
is carried out with an
additional, robust check based on an affine transformation
limited to tile extension. Given a set of corresponding image
points
x
1
= (
x
1
,
y
1
, 1)
T
x
2
= (
x
2
,
y
2
, 1)
T
(written in homoge-
neous coordinates) between two generic tiles, the condition
x
x
1
1
1
2
2
2
1 0 0 1 1
=
=
=
x
y
a b c
d e f
x
y
H
(1)
must be checked. The estimation of transformation param-
eters (encapsulated in matrix
H
) needs to be coupled with
robust techniques, as robust methods allow the detection of
possible outliers in the observations. The proposed method
is based on the analysis of several sets of image coordinates
randomly extracted from the whole dataset. A solution for
H
can be identified and removed with an iterative process
where several
H
matrices are estimated. A minimum number
of trials
m
is given by:
m
log P
e
s
=
−
− −
(
)
(
)
(
)
log
1
1 1
(2)
where
P
is the probability from a given size of sample
s
,
with a percentage of outliers
e
. The goal is the extraction of a
good subset of
m
corresponding points [
x
1
x
2
] where outli-
ers are rejected and the transfer error
d
2
r
=
d
(
x
2
,
H
–1
x
1
)
2
+
d
(
x
1
,
H
x
2
)
2
(3)
Figure 2. The same objects (grey polygons and black, thick lines) extracted from two satellite images do not match precisely match : ac-
curate object-to-object comparison is not feasible.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
February 2016
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