ecades, Wilfried
ong influence on
mely the plumb-
proposed single
compares their
Brown was only
ished.
tive application.
results obtained
Simultaneous
S Distortion of a
0 had laid the
nent method (see
mbered for his
it was the good
th him during a
3 in 1985, that
le station self-
1is concepts had
vere published
1s other projects
ge cameras (see,
\ SELF-
libration usually
S of convergent
ur to eight well-
nera orientations
1iques proposed
Brown (1985)
be taken from a
camera is tilted
d Y axes by
nage is obtained
' camera around
sure aids the
ipal point. The
mera and lens
y large numbers
(1982, 544) he
OJ
showed that after approximately 50 well-distributed
targets were imaged, further improvements arising from
additional numbers of targets were only marginal.
Wester-Ebbinghaus acknowledged that it would be
unrealistic to assume that the projection centre would
remain fixed in space while the camera was inclined. He
noted that the projection centre and the centre of rotation
will not coincide during an actual calibration procedure
and made allowance for this difference (he termed it
"eccentricity") in his formulation of the bundle
adjustment.
The single station self-calibration procedure proposed by
Brown has not been documented. In fact the author is
unaware of his concepts being discussed with anyone else,
so the finer details of actual implementation of his
calibration procedure were not developed. The main
difference in Brown's approach was to use only an
approximately linear row of targets (he suggested street
lights along a road on the horizon) rather than an array of
close range targets as in Wester-Ebbinghaus' technique.
Brown was always interested in terrestrial techniques for
the calibration of large format aerial cameras, so his
thoughts were accordingly attuned to focus at infinity,
hence his concept of a row of distant street lights.
Brown suggested that several images, say 8 to 10, be
collected as the camera was tilted through its angular field
of view. He further implied that after these rotations
about the X axis, the camera would be rolled through 90*
and the image capture be repeated about the Y axis. Since
the camera to object distance would be relatively large,
say 1 km or more, the slight eccentricity problem
highlighted by Wester-Ebbinghaus would be insignificant
to the solution of the camera's position. As the pioneer
of the bundle adjustment, Brown was aware that as long
as he had some approximate positions for his distant
targets, and there was "reasonable" number of them (say
10 to 20), then he could produce parameters for camera
and lens combinations without ever determining final
values for his opportunistic targets. Wester-Ebbinghaus
also noted that an accurate determination of the
coordinates of the targets was not necessary. Of course,
results for the principal distance will be reliant on
knowing the relativity of the camera station and the target
range.
EXPERIMENTAL COMPARISONS
To obtain some practical experience with these concepts
of single station camera self-calibration, both procedures
were used to calibrate a Fotoman camera. The Fotoman
digital still camera has an array of 768 by 512 pixels,
with a pixel size of 9 by 9 um. The principal distance is
approximately 9 mm and the cost of a Fotoman digital
still camera in 1996 is close to US$1,000.
The three-dimensional test range of retro-reflective targets
attached to an air-conditioning plant, associated piping
and background wall in the laboratory building of the
Department of Civil Engineering and Surveying at the
University of Newcastle was used. The target array
covers an area of approximately 4 m by 3 m by 1
m(depth).
With a camera to target distance of approximately 8
metres, the camera was effectively focused at infinity.
Care was taken with the camera/tripod mounting so that
‘eccentricity’ effects of any offset between the projective
centre and the centre of rotation were minimised. From
the array of targets imaged for each exposure, a row of 19
targets were selected to simulate Brown's target criterion
while the entire array of 80 targets were used in Wester-
Ebbinghaus’ procedure.
Nine sets of images taken about each of the X and Y axes
(a total of 18 images) were used for the bundle adjustment
based on Brown's hypothesis. A total of 9 images were
used for the Wester-Ebbinghaus technique. These
consisted of one central image and eight tilted images
with the camera in both the normal and rolled positions
in each of the + and - X and Y directions. The results are
shown in Table 1.
Also shown in Table 1 is a more conventional bundle
adjustment using 8 well spaced and convergent images.
This 'mormal’ self-calibration bundle adjustment was
computed to provide a comparison for the camera and lens
parameters. In addition a plumbline calibration was
performed to provide independent comparisons for the
parameters of radial and decentering distortion. The best
way to appreciate the results for the radial and decentering
lens distortions is to examine Figures 1 and 2. The small
spread of results even at the extreme edge of the sensor
area is a testament to the effectiveness of all techniques.
Camera Principal | x,y, Offsets of
: No. Targets RMS x,y 0» 70
Method Stations | No. Images per image (um) D Princ. Pt. (mm)
Plumbline 1 2 8 lines 1.0 x 1.0 - Not determined
Conventional 8 8 80 1.4 x 1.3 8.415 - 0.059. - 0.018
Bundle
Brown 1 18 19 1.4 x 1.4 8.513 - 0.068, + 0.017
Wester-Ebbinghaus 1 9 80 1.4 x 1.4 8.520 - 0.079, - 0.007
Table 1. Comparison of Techniques
179
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
