"ut
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Figure 11. The tilted, correct plane and the horizontal,
false plane from Fig. 10, including the found 2D lines
that fit to the corresponding plane and intersect the
horizontal lines in right angles. Two structures are
clearly visible for the correct plane, whereas the
perpendicular lines for the false plane are fewer and
more randomly distributed.
All the 2D lines inside a window are tested if they can (i)
fit into the 3D plane and (i) intersect the parallel,
horizontal lines perpendicularly. If so, the intersection
point (due to the constraints only a one-parameter
position on one of the 3D lines) is computed.
Fig. 11 shows all the perpendicular lines, from all
images, that were found for the correct and the false plane
hypothesis, respectively, in Fig. 10. It is noted that less
lines were found for the false, horizontal plane, than for
the correct, tilted plane. This is because the only real
structure that can fit the plane and intersect the horizontal
lines perpendicularly are the base lines of the shorter
facades, but they are only visible in a few images. For the
correct plane more lines were found and, more
importantly, many lines intersect at approximately the
same position. There are two clear maxima, which
correspond to the outlines of the plane. In general, the
more perpendicular lines that intersect the two horizontal
lines of a plane at approximately the same point, the
larger is the probability that there is an actual
perpendicular feature causing the lines. One may assume
that if the perpendicular lines intersect the horizontal lines
randomly the plane is false, whereas if there is at least one
pronounced intersection point, the plane may be correct.
The same reflections can be made for the other true and
false planes.
Radiometry provides further evidence of an actual
perpendicular line. The two radiometric criteria used here
are (7) that the area at one side of the perpendicular line,
the one inside the 3D plane, should be radiometrically
homogeneous over all images and (ii) that the contrast of
each contributing 2D line should be high. The first
statement assumes that the difference in grey tones
between the images is small for the same imaged object.
The second statement favours large differences in grey
tone between the two sides of a line in one image, and
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
consequently suppresses weak lines, which may occur e.g.
inside a roof.
The geometric and radiometric criteria are
summarised in one measure. This measure is used first to
determine the two largest clusters of intersection points
for each plane, secondly to select the best non-
overlapping planes. Currently, the best non-overlapping
plane hypothesis will always be accepted regardless of
how small the measure is. Another restriction is, that there
need to be two clear intersections, indicating a 3D
rectangle, so that U-shapes can not yet be found. For the
best non-conflicting planes the intersection points are
determined by averaging the intersection points in that
cluster, weighted by the 2D lengths of the lines. The best
non-overlapping plane hypothesis and their extensions are
shown in Fig. 12.
4. DISCUSSION
A system for finding 3D structures using multiple images
has been presented. The system is intended to describe
three dimensional buildings using aerial images. Rather
than attempting to find the building volumes, the task has
been limited to describe only the roofs. Vertical walls and
their boundaries are generally only visible in a few
images, where the building is far from the nadir point.
The ability to find these vertical structures is, we believe,
significantly increased by first finding the roof, which in
general is visible in all images.
Characteristic for the system is its intense use of
object space relations, starting from simple (s.a. there are
two main directions) and going to more complex (s.a. two
parallel horizontal lines intersected by perpendicular lines
at two separate points may form 3D rectangles). There is
no image-to-image processing involved; image features
are accumulated in a common frame in object space, and
analysed in this frame.
The system has been illustrated by a simple
example, for which the system works excellently. In spite
of rather poor accuracy of the feature extraction, the 3D
lines are quite accurate, at least partly explained by the
use of multiple images. The chimney and its shadow are
bridged over by the use of global search for horizontal
lines. The roof of the small addition to the main building
structure is in reality not connected to the horizontal
boundary of the main structure, but intersects the vertical
wall somewhat under the main roof. It is however
unrealistic to hope for such small deviations to be
detected by the system; it is even difficult to interpret for
a human. More complex buildings would require
additional relations to be defined. For example, it is
required that there are at least two salient perpendicular
intersection of two horizontal, parallel lines for a plane to
be accepted. This omits U-shaped planes, characteristics
for houses with additions. Also, the best non-conflicting
plane hypothesis is always accepted, regardless of how
weak the geometric and radiometric evidence is. This may
be overcome by thresholding the measure, that is used for
comparing plane hypothesis. Radiometric evidence is
used moderately, and should perhaps be used earlier in
the process, e.g. by weighting 2D lines contributing to 3D
