ENT
‘ircular image block
hods, but simply to
traditional approach
mera stations cannot
cal model had to be
s of rays unlike the
racy and robustness.
int set with varying
(d tests with similar
method in an object
'n projection centres
be drawn which goes
| orientation of cam-
this circle. The final
iave overlap between
the first and last im-
but in practice, it is
litions by using a rod
he camera is fixed in
will be fixed to some
rod is only around
ne. This yields to an
° full 360° deg from
vill be the correspon-
ges. The weakness
mera positions have
overcome this prob-
recommended to be
locks should be done
of angular difference
ixed perpendicularly
n of +90° and in the
an find camera posi-
ons at most two times
other, see Figure 1.
wltiple images, bun-
and substitute their
ock parameters. As
| block we might in-
adjustment process.
image parameters in
requirements for the
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
Block II.
x d Block I
Block TV
EZXZESOXSNUNZZZIZUEESG S :
Block I
Figure 1: Circular image block imaging constellation. Be-
tween first and second block creation the camera will be
turned into opposite direction.
block. We have here a free net type estimation problem.
As we have no exterior co-ordinate information, we cre-
ate a co-ordinate system of our own. In order to solve in-
sufficient datum problem we might minimize the sum of
variance-covariances of the parameters, which is a com-
mon approach. Another approach, which we have used, is
to fix sufficient number of parameters. The rotation of the
camera in supposed to be done on xz-plane. So all cam-
era poses have their y-coordinate fixed to zero. The x-axis
is fixed into direction of the first camera pose of the first
image block and origin of the co-ordinate system is in the
centre of rotation. All other camera pose co-ordinates are
expressed in polar-co-ordinates.
À; = 1 - COS
face ya
Y; constant (1)
Zi =r Sino;
The rotation of the camera in each camera pose respect
to this local co-ordinate system is also dependent of this
one parameter o; unique for each camera pose. Also, it is
dependent of the orientation of first camera pose in image
block.
Re: imi = Bon tn 50 3 Ra; (2)
Here rotation matrices R are assumed to be 3 x 3 orthonor-
mal rotation matrices, where rotations are supposed to be
done subsequently. For each image block we have four
common parameters wg, @q, ko and r and for each camera
pose we only have one unique parameter cv;. Only for first
camera pose of the first image block we have fixed ag = 0.
This way we can express the block with fewer parame-
ters in more compact form and benefit from overdetermi-
nation in our measurements. By adding at least one dis-
tance measurement we can also have our image block in
a right scale. More thorough representation of the method
can be found in (Heikkinen, 1998; Heikkinen, 2000; Heikki-
nen, 2002).
31
2 SIMULATION
The method has been tested previously with simulation.
The purpose of simulation was to verify the correctness of
the mathematical model of the system. Finding the power
of the method was also one purpose of the simulations.
Measuring system of the circular image block resembles
a geometry of stereo imaging, so it is natural to test the
same parameters which are most important in a stereo pair
imaging system. Namely, the length of the baseline; here
the length of the radius; and the precision of the image
measurements. However, this imaging system cannot be
regarded as a group of stereo pairs. Each photo in an im-
age block is considered as an individual image ray bundle,
whose pose and orientation are bounded by common block
parameters. In this sense the number of photos included in
a image block also has significance on the measuring ac-
curacy. Therefore finding the effect of different number of
photos in image block was one of the goals of simulation
tests.
In all simulations the arrangements were similar; the same
object point group; the same camera orientation for the first
camera pose in a block Ro,0,0 and Ry 150.0 ; the same cam-
era model (1024x1280pix; c=1400pix). The object point
group was generated by random point generation. Only
some restrictions were given how far from the center points
were allowed to align. Image observations were generated
by back-projecting the object points onto image plane ac-
cording to camera orientation information. In order to sim-
ulate the accuracy of image observations random noise was
generated and added to the image points. So the varying
test parameters were; the level of random noise added on
image observations, the length of the radius and the num-
ber of photos included in image block. Only one of the
test parameters was alternated in one simulation. In each
simulation 100 test runs were accomplished and random
noise was added to image observations individually be-
tween each test run to achieve reliable test results. The
results of a simulation of varying length of radius in the
imaging constellation are represented in Figure 2 . The
number of photos in one block was 30 and noise level
added into the image observation was 0.2 pixels. More
information of simulation results can be found in previous
publications (Heikkinen, 2001; Heikkinen, 2002).
The simulation environment was also used on testing the
limits of the goodness of initial values. The parameter val-
ues were slightly changed from their correct values and
only one parameter was alternated at a time. The test was
first accomplished without noise and then with only a small
amount of noise added to the image observation. The orien-
tation angles of the first camera were more sensitive to in-
correctness of initial values than a-angle of each photo or
length of radius r. For v, $, &-angles the initial values were
required to be better than 3— 5 deg in order to meet conver-
gence. For a-angles 5 deg was generally good enough and
for length of radius r initial value +5¢m was acceptable.
