nt: The con-
/s e and e^.
wr plane and
fined by the
tion centres.
ext, leading
S geometric
dimensions
bility of the
ld be incor-
e locally a
can be con-
le and rota-
e of. Points
' conjugate
the epipolar
lation coef-
e, however,
il perspecti-
ative stand-
ach can be
ed "8-point-
rmulated as
eters. Solu-
xist (Rinner
92). The 8-
1ggested by
investigated
sai, Huang
89; Hartley
d in photo-
Iahn 1992;
linear algo-
rithm compared to a non-linear one: no initial values are
needed for the unknowns in order to ensure convergence,
and no computationally expensive iterations need to be
performed. In this case, however, initial values are alrea-
dy available (as described, they are necessary for estab-
lishing the correspondence between the primitives), and
the computing time for the parameter estimation is not
critical as compared to that needed in the matching
phase. Moreover, the 8-point-algorithm is geometrically
less stable than the bundle approach, since the relative
orientation only has five degrees of freedom, and thus
non-linear relations exist between the 8 parameters.
After the computation of the orientation parameters and
the three-dimensional coordinates of the conjugate
points, remaining blunders along the epipolar line can be
eliminated if assumptions about the model surface such
as piecewise smoothness are appropriate. This step con-
cludes the computations on one pyramid level.
Subsequently, the results are refined on a lower pyramid
level. It is usually possible to leave out some of the levels
to speed up the computations. Since the position of fea-
tures in scale space is not entirely predictable (see e.g.
Witkin 1983), point extraction should be carried out on
each level independently. Then, matching and parameter
computation are performed again, and the process is
repeated until the original image resolution is reached.
Since in automatic relative orientation arbitrary conjuga-
te features can be used, the power of redundancy can be
readily exploited. Rather than a few conjugate points as
in analytical photogrammetry a few hundred points are
often used. Table 2 shows a typical result for the stereo-
pair Lohja (see also figure 5). The theoretical standard
deviations of the five orientation parameters are given for
manual and automatic relative orientation. Although in
the automatic case the standard deviation for the image
coordinates is worse by a factor of 2, the orientation
parameters are still more accurate by a factor of appro-
ximately 2.6 due to the high redundancy and the better
point distribution. In addition the automatically genera-
ted orientation parameters are more reliable, since blun-
ders can be easily detected due to the high redundancy.
Another consequence is that singular cases of relative
orientation such as the well known dangerous cylinder
have no practical significance, since it is virtually impos-
sible for all conjugate points to lie on one of these surfa-
ces.
black and white, scale 1:15.000,
Hd 60 % overlap
Type of orientation dependent
manual (analy- | automatic (15
Approach ; TES
tical plotter) | Um pixelsize)
Number of points 15 132
co 2.0 Um 4.6 Um
Theoretical Ov 0.47 m 0.18 m
standard devia- Oz 0.16 m 0.06 m
tions of orien- où 11.0 mgon 4.1 mgon
tation parame- ow 7.4 mgon 2.8 mgon
tens OK 3.0 mgon 1.0 mgon
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Table 2: Comparison between the accuracy of the relative
orientation parameters, example Lohja (see also figure5)
Various realisations of automatic relative orientation ha-
ve been reported in the literature. The characteristics of
the individual approaches are depicted in table 3. Most
of them were designed to handle aerial images. Extensive
tests of one algorithm (Hellwich et al. 1994; Batscheider
1996; Tang et al. 1996) have shown that autonomous
relative orientation for aerial imagery is faster than and
at least as accurate as manual measurements. Accuracies
of approximately 0.2 and 0.4 pixels for the standard de-
viation of the image coordinates have been reached, and
the elapsed computing time for an image pair with 15 pm
pixels amounts to about 2 to 3 min on a Silicon Graphics
Indy with R4400 processor (150 MHz). More than 50
different models with black and white and colour images
of different content (urban, agricultural, forest, alpine
environment), scale (1:3.200 up to 1:820.000) and image
quality have been processed successfully. Two examples
of the mentioned tests are shown in figure 5 and 6. This
algorithm has been implemented in a digital photogram-
metric workstation and is commercially available. User
feedback in the near future will demonstrate whether or
not it fulfils the requirements of practice.
Figure 5: Conjugate points, automatic relative orien-
tation, example Lohja
305
