înmeyer, Geneva
Experiences with the Digital Photogrammetric Program Package Orpheus ...
643
djustment can be
'the object can be
, it is necessary to
has to be covered
non edge, and (4),
vertices have been
intation (B-rep) is
: reported, and the
ig B-rep model is
iESTALTs can be
by a final overall
is projected to the
tion closest to the
1 inspection of the
n model created in
PHEUS. From the
aside. The camera
ie determination of
ited in (Streilein et
)lympus data set, a
mb lines and from
With respect to the
: the facades of the
, four GESTALTs
e points per image
ne is considered to
lent (its object co-
tional GESTALTs
sides of the “block
these categories of
g different a priori
id for modelling in
GENT. For each of
ariance component
detection had to be
part of the data set.
lifferent facades. It
fted with respect to
ts remaining in the
>01-212, and (-0.82
in the data set. The
it sketch in the data
set description, but the average size of the residuals strongly indicates a systematic shift. The new co-ordinates of control points 201 -
323 are given in table 1.
With respect to one variant of the Olympus data set, only distances were used instead of control points to define the geodetic datum
of the block. The distances between points 101 and 111, 111 and 121, 101 and 121, and between 301 and 321 were computed from
the co-ordinates of these points (these are the distances which could be easily measured using a tape). They were used to define the
scale of the block. The four vertical lines at the building edges corresponding to four GESTALTS (cf. section 3.1.1) were used to
define the vertical axis and, thus, also to define two rotations of the block (co and (p). In order to determine the shift of the block,
point 101 was introduced as a control point. In order to determine the third rotation (k) of the block, the y co-ordinate of point 121
was introduced as a “control co-ordinate”. Note that the four (3+1) co-ordinates of these two points are just used to avoid
singularities of the block.
Point
201
202
211
212
301
302
303
311
312
321
322
323
X
114.93
114.99
116.31
116.30
150.08
150.06
150.00
132.24
132.26
116.33
116.31
116.42
Y
249.06
248.99
237.22
237.25
255.11
255.12
255.12
252.96
252.99
251.15
251.16
251.17
14.68
3.65
14.67
3.64
14.72
10.42
3.72
14.68
8.30
14.68
10.38
3.69
Table 1: New co-ordinates of points 201-323 as derived from photogrammetric triangulation (Olympus data set). The r.m.s. errors of
these co-ordinates are ±4.5 cm (X, Y) and ±3 cm (height), which is in accordance with measurements from a reflectorless theodolite.
Self-calibration: In order to perform self-calibration, the parameters of inner orientation as given in the data set description were
used as approximate values. The co-ordinates of the principal point were introduced as observations with an a priori r.m.s. error of
±10 pixels. Several variants were computed using different parameterisations of the distortion polynomial. Initially, all images were
given identical, but unknown parameters of inner orientation and distortion. There were no contradictions to this assumption in the
Fuji data set. However, performing robust estimation in the Olympus data set, it was obvious that the tie points not being situated in
the facades were eliminated as gross errors even though they were obviously correct. This observation and the fact that the
distribution of residuals appeared to be systematic initiated the suspicion that some of the photos might have been taken using
another focal length. Adjustment was repeated using individual parameters of inner orientation and distortion for all images. Of
course, these parameters were determined rather badly (typically, the r.m.s. error of the focal length was ±50 pixels), but the results
could be used to find hypotheses about groups of images having identical parameters. In an iterative procedure, groups of images
were declared to have identical parameters of inner orientation and distortion if the results of self-calibration did not differ
significantly. Two groups of images with different inner orientation parameters remained: Images 1-5 and 12-16 have been taken
with a focal length of 1334 pixels, and images 6-11 (those showing the east facade) with a focal length of 1572 pixels. The distortion
polygon for modifying the components (u 0 ,v 0 ) of p 0 in equation 1 depending on the co-ordinates of the principal point (u pp ,v pp ), the
reduced image co-ordinates u and v and the polynomial coefficients (the distortion parameters) a, is given by equation 3:
'«o'
Ы
ci 3 -u-\r 2 -1) + a A -u - (r 4 - l) + <7 5 -(/- 2 + 2-м 2 )+a 6 -(2-wv) + a 37 • и - (r 6 -l)+ a 3s ■?/ -j/- 8 - l)
A
a 2 - v + a 3 ■ v-(/- 2 -1) + «4 -v-(r 4 -l)+ a 5 -(2-/7-v) + r/ 6 - (л 2 + 2-v 2 )+r/ 37 ■ v ■(/• 6 -l)+« 38 ■ v-(/- 8 -l)
with П = — , v = ——— , and r J = u 2 + v 2 . p 0 is the normalisation radius; it is the radius of a cucle of zero distortion.
Po Pa
In equation 3, a 2 corresponds to a scale of the v-axis, a 3 , a 4 , a 37 and a 38 describe a radial component of distortion, and a 5 and a 6
describe an asymmetric distortion component. Table 2 shows the values for the distortion parameters, the principal point (u pp , v pp )
and the focal length/for all variants as well as the theoretical r.m.s. errors о of these parameters from self calibration.
Camera
Upp [pixel]
v pp [pixel]
/[pixel]
a 2
a 4
«5
a 6
a 37
a 38
Po [pixel]
Oc
610.4
-495.5
1334.3
-
15.135
-22.628
-
-
14.564
-3.398
621.0
Of I
624.2
-481.3
1334.0
-2.012
-27.386
0.196
0.503
-0.713
-
-
621.0
G
±4.5
±4.5
±3.0
±0.45
±2.1
±1.6
±0.36
±0.36
-
-
Ofll
608.6
-480.7
1572.3
1.082
-18.784
4.557
-0.497
-0.016
-
-
621.0
G
Fc
±4.7
±4.8
±3.1
±0.42
±1.8
±1.1
±0.32
±0.32
-
-
-
651.9
-511.1
1260.0
-
0.00075
0.00006
-
-
-
-
605.8
Ff
637.1
-482.2
1254.5
0.887
-28.504
6.558
0.533
0.230
-
-
605.8
о
±4. 6
±4.5
±1.8
±1.9
±0.95
±0.65
±0.38
±0.35
-
-
-
Table 2: The parameters of inner orientation. Oc, Fc: Olympus / Fuji, calibration from the data set description. Of I, Of II: the
parameter sets for the Olympus data set derived by self-calibration. Ff: the results of self calibration for the Fuji data set.
Comparison of variants: The results of adjustment for the five variants are compared in table 3. Note that in each variant, variance
component analysis has been used to achieve a realistic stochastic model. Thus, the a priori r.m.s. errors of the image co-ordinates
indicate how well the mathematical model of adjustment fits to the data. It can be seen that with the Olympus data set, the r.m.s. error
of an observed image co-ordinate was ±2.0 pixels and, thus, worse by a factor of two than with the variants using self calibration,
which results in worse r.m.s. errors of the computed object points. In addition, more observations had to be eliminated in that version.