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Close-range imaging, long-range vision

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candidate for that cluster.
e The candidate correspondence becomes a member of the
cluster if all tests of constraints (3) are accepted. These
tests involve three correspondences: the candidate and
two correspondences already in the cluster.
This procedure is repeated as long as new clusters are
created. The result is that overlap between clusters can be
considerable. Many of these clusters contain a set of correct
correspondences with minor differences. The clusters that
contain more than a minimum number of correspondences
are analysed in more detail by applying an integrated
adjustment of all constraints.
3.3.5 Overall adjustment and testing
The clustering procedure results in groups of
correspondences that support the same relative orientation,
while the related object points are expected to recede in the
same object plane. An overall adjustment is set up for all
clusters with more than a minimum number of
correspondences. The functional model contains 7-1
condition equations for coplanarity (equation (8), n is the
number of correspondences), and n-2 condition equations for
intersection of epipolar planes (equation (3)). A set of
independent equations results. The adjusted epipole is
computed from adjusted observations. Two different types of
statistical tests are applied. First an overall test or Fisher test
is applied. The second test examines the alternative
hypothesis of an error in a single correspondence. If such a
test is rejected, the correspondence is removed from the
cluster and the model is built again. This iterative testing
procedure stops if all correspondence tests are accepted. The
cluster with the largest number of correspondences of which
no correspondence tests are rejected is selected. This cluster
is expected to contain corresponding image points of which
the related object points are in (or near to) a plane. More
details on the statistical testing can be found in (van den
Heuvel, 1998).
3.3.6 Towards automatic reconstruction
Apart from the primary cluster detected as described above,
other clusters can also contain correct correspondences of
which the related object points are in a different plane. In
order to detect such clusters, all clusters that meet the
following two requirements are incorporated in the overall
1. The cluster does not have a correspondence (nor an
image point) in common with the primary cluster.
2. The correspondences of the cluster confirm the epipole
of the primary cluster.
For all correspondences — those of the primary as well as
those of the clusters selected by the criteria above — the
epipolar plane intersection constraints are set up. Of course,
the coplanarity constraints are only applied to
correspondences of the same cluster.
With the integrated adjustment of more than only the primary
cluster, there is not only additional evidence gathered for the
epipole, but at the same time different object planes are being
detected. Preliminary faces can be created by a bounding box
around the object points of a cluster. Object planes are then
to be intersected to find the edges of the building. The
detection of object planes is a by-product of the proposed
procedure for automatic relative orientation, but also a first
step towards automatic reconstruction. The experiments
described in the next section aim at the detection of the
primary object plane only.
In this section an experiment is discussed in which the
procedure for automatic relative orientation is applied to
three images of a historic building. The images are taken
from ground level with a handheld calibrated digital camera
(1536x1024 pixels). They were taken from the south-south-
west (SSW), south-east (SE), and east (E) approximately
(Figure 5). The number of extracted straight lines can be
found in Table 1.

Figure 5: The three images (labelled SSW, SE, and E)
The a priori precision of the endpoints of the lines was set to
1 pixel standard deviation in the vanishing point and the
epipole detection. The "vanishing lines" are the lines that
were uniquely grouped to one of the three vanishing points.
These lines are displayed in Figure 6. Especially near the
horizon line of image SE a considerable number of lines is
lost because the vanishing point detection cannot distinguish
between the left and right facade. As a result, for this image
most of the intersection points are created in the upper part of
the facades. Some statistics of the epipole detection are
listed in Table 2.

# lines 339 457 | 202
# vanishing lines 286 276 143
# intersection points 164 78 30

Table 1: Numbers of extracted lines and points

# correspondence hypotheses 1109 144
# coplanarity tests 182899 3308
# accepted tests 15825 1102
# clusters 5638 424
max. # points in a cluster 16 9
# clusters accepted 97 85
max. # points in a cluster 15 7
Fisher-test / critical value 4.4 1.0
Deviation manually measured 1.7 deg 1.6 de

Table 2: Statistics of the epipole detection
The detected correspondences are displayed in Figure 7. Note
that for the first image pair only those corresponding points
are detected that are on the central part of the facade because
this part is in a different plane from the rest of the facade. In
fact, all possible correspondences are detected. However,
looking at the location of the image points in detail, two
corresponding points are often not at exactly the same
location on the building. The reason is that many edges
border occlusions. When there are several points created
close together — which often is the case in the corners of the
windows — the statistical testing cannot distinguish between
different possible correspondences. Indeed, many of the
accepted clusters are very similar in the correspondences
they contain and their Fisher-test. Furthermore, as a result of
a large number of "imperfect" correspondences (the image
points are not projections of exactly the same point on the