The epipolar line constraints derived from this first approxi-
mate orientation are then employed to find further matches
for centroids of features previously not matched successfully.
A second, updated relative orientation is executed with these
additional points. The newly obtained epipolar constraint
is now utilised to match the corner points of all conjugate
features by area based matching. A third and final relative
orientation incorporating the sub-pixel matched corner points
then provides final orientation parameters. The procedure de-
scribed here is fully automated and does not require any user
support.
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Figure 5: Relative orientation from matching feature cen-
troids and corner points
In the test case of the PCB images thirteen matching fea-
ture centroids, indicated as squaresin figure 5, were entered
into the first relative orientation. Two further features (the
rectangular shapes in the top left corner of the images) were
detected in the next stage and a second orientation with these
fifteen centroids was successfully executed. For the final rela-
tive orientation calculation only the forty five sub-pixel coor-
dinates of the matching corner points, indicated by crosses,
were used. During the first two orientations the assumption
was made that the centroids of matching features in each
image match, which is not entirely accurate. Due to large
disparities and the different viewing perspectives for different
images, these centroids can only be treated as crude approx-
imations to the matching points, and are thus discarded for
the final relative orientation calculation.
The relative orientation and subsequent epipolar line equa-
tions are solved for using the coplanarity condition, as de-
scribed by Haralick and Shapiro [10]. During the corner-
matching step, image correlation as described by Rosenfeld
and Kak [15] is employed to solve any ambiguities resolving
from more than one corner matching candidate appearing on
an epipolar line. The sub-pixel corner matches are calculated
using Least-Squares Matching (LSM) as described by Gruen
et al [7] [8] [9].
6 FEATURE-GEOMETRY CONSTRAINED AREA
BASED MATCHING
During the final step in the matching procedure intermediate
points on the matched feature outlines are matched to sub-
pixel level.
The initial estimates to the matching points for points situ-
ated on a matched line feature, as opposed to corner points,
are obtained by searching for the intersection between the
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
corresponding line feature and the epipolar line.
Figure 6: Initial Maching Point Approximations Using Match-
ing Features and Epipolar Geometry
If in figure 6 the feature matching stage has matched feature
F, in the left image to feature FJ in the right image and the
subsequent corner matching stage using the epipolar condi-
tion and Least Squares Matching has correctly matched the
four corner points, then the search space for points on the
feature boundary can dramatically be reduced. In this exam-
ple corners 2 and 3 in the left image match corners 1 and 2 in
the right image. The search space for matching points along
line 2-3 in the left image is now reduced to line 1-2 in the
right image. If any ambiguities occur they are resolved using
area correlation, as done with corner matching.
It should be noted that the intersections between feature
boundaries and epipolar lines are subject to the well known
geometric conditions of the intersection, with best solutions
for rectangular intersects and no solutions for paralell lines.
Only by using more than two images and therefore more than
one epipolar line can this problem be solved.
Figure 7: Example of Finding Initial Maching Point Approxi-
mations
Figure 7 shows an example of finding the initial matching
point approximations for points on matched line features. In
this example the initial approximations to every tenth edge
element (edgel) of each line segment between feature corners
are shown. The edgels are indicated by crosses in the left im-
age and the corresponding point approximations with the rel-
evant epipolar line segments are indicated in the right image.
Note that, as expected, the line intersections for line seg-
ments parallel to the epipolar lines, which are near-horizontal
in this case, are poorly defined as shown in figure 8.
From these initial estimates the high accuracy, sub-pixel
matching is performed using LSM or Geometrically Con-
strained Least Squares Matching (GCLSM), as described by
Gruen [7] and Baltsavias [1].
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