orners and
r prelimi-
atch step
the right
ares).
about two pixels apart, remaining after the final step.
It is important to remember that hypothesis evaluation based
on image or scene geometry is strictly limited by the avail-
able geometry. In this case, the oblique image was taken ina
direction perpendicular to the baseline of the two vertical im-
ages, giving nearly optimal intersection geometry and there-
fore eliminating many ambiguous matches. A corresponding
test case, run with a vertical image (fhn713) from the same
flight line as fhn715 and fhn717, resulted in a large number of
hypotheses remaining after the geometric verification proce-
dure. Since the epipolar lines between the three images from
the same strip were nearly parallel, many matches appear to
be geometrically consistent. This problem can be alleviated
somewhat by using strips with 60% sidelap.
The experimental results given above were run with the image
parameter covariances set to very small values and therefore
not allowed to adjust, with the intent being to prevent the
image parameters from absorbing any of the matching er-
rors. The same set of experiments was run with the image
parameter covariances as determined from the original block
adjustment to see what effect it might have. This made no
significant difference in the results for the example described
above. The runs with realistic image covariances produced
one additional point match which passed the individual right
angle evaluation, but the final point match selections were the
same for both cases. This is significant in terms of computa-
tional expense since it implies that instead of a full simultane-
ous solution incorporating weighted image parameters, only
the points and constraints would need to be included. This
possibility should be verified for more test cases.
4 EVALUATION OF GEOMETRIC HYPOTHESES
The previous section has shown how the use of geometric
information improves the detection of bad feature matches.
However, we must also be able to evaluate these geometric
assumptions. It is entirely possible that, although we have
matched a feature correctly across several images, the corre-
sponding object-space point may not be the building corner
that we have assumed it is.
By using the statistics derived in Section 2, we can evaluate
the constraint equation residuals and determine whether the
geometric conditions are being met. A problem is separat-
ing the effects of bad feature matches from bad geometric
conditions; a bad constraint typically results in high image
residuals for all of the features involved.
Our approach of starting from minimal subsets and building
up to final complete solution provides an answer for this. As
described above, point or feature matches are first evaluated
using only the image information, without added geometry.
As individual features are combined into small geometric units
and constraints added to the solution, a bad geometric as-
sumption will affect only some of the solutions.
For instance, suppose that in the point matching example
discussed above, point 2 had been incorrectly identified at
the roof vent nearest the actual building corner and that cor-
responding points had been matched on the other images
(Figure 8). While we would have a perfectly valid 3D point it
is not a roof corner, it is not coplanar with the other corners,
nor will it form right angles with them.
The evaluation of the point match shows that this is indeed a
valid match. However, during the next stage, forming right-
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Figure 8: Image fhn715 with bad point 2.
corner points 0-1-2 | 1-2-3 | 2-3-0 | 3-0-1
pt 0 6.2 = 2.0 0.5
pt 1 1.4.1 114 = 0.7
pt 2 (bad) 88 {135 1 16 -
pt 3 = 7 Sp. 25 1.0
right angle constraint || 21.6 | 252 4.3 0:3
Table 9: Standardized residuals from individual corner solu-
tions with bad point.
angle corners with subsets of three points, the three subsets
involving point 2 show up as bad. The statistics are sum-
marized in Table 9, where the image residuals given are the
root-mean-square of each point's vector standardized residu-
als on each image. Subsets 0-1-2 and 1-2-3 both have bad
point standardized image residuals and bad constraint resid-
uals; subset 2-3-1 has good image residuals but a bad con-
straint residual on the angle constraint. This can be explained
by noticing that, for this solution, the bad point is on the long
side of the building so that its angular offset from the correct
location is less than for the other cases, where it was on the
short side of the angle or was the central point.
Systematic detection of bad geometry requires searching the
bad subsets for the common elements; in this case, point
2 is the common element among the three bad subsets. A
bad subset must be identified by examining the constraint
residuals also; the table shows that the image residuals for
angle 2-3-0 were satisfactory, with only the constraint residual
bad, due to the location of the bad point.
5 CONCLUSIONS
Using geometric constraints in a bundle adjustment to verify
feature matches or geometric hypotheses can be part of an
effective hypothesis testing strategy, when supported by the
image geometry and when knowledge or inferences of the
scene geometry are available. The combinatoric problems
inherent in the method can be avoided by early editing of the
hypotheses and by utilizing sequential evaluations of minimal
redundant geometric subsets.
Use of these methods in full-sized systems will require that
the computations be optimized as much as possible. While
the tests in this paper were done using a general-purpose si-
multaneous orientation solution, a real application should use
special purpose routines, each optimized to verify a particular
geometric configuration such as right angles, coplanarity, etc.
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