wo homologous
The formulas to
are given in the
| Figure 2.
, let u and v be
image points in
scalars 7 and /;
point À in object
d in orientation
ctor, given by:
(7)
r. Parameters n
inimum:
-(v-b)
y
(8)
1 problem. The
int of p:
(9)
e assumed as an
(10)
lt and does not
ersection.
AL BLOCKS
r has involved
| terrestrial and
metric analogue
metry of camera
0 on simulated
ed example and
different block
At first, the space resection algorithm alone has been tested, in
order to empirically investigate whether critical geometric
configurations for the solution may exist. Given 4 non-coplanar
points, a set of images has been simulated that should represent
a series of convergent images taken about an object. Taking the
gravity center of the points as the center of an ideal sphere, the
camera stations have been placed over its surface, on the nodes
of a grid regularly spaced in latitude and longitude, with camera
axis pointing towards the centre of the sphere. Simulated image
coordinates were corrupted by random errors. All EO
parameters have been correctly solved by RESECT. The same
test has been executed by introducing a fifth point, to check
whether the maximum perimeter criterium was always leading
to the best solution. While as expected all cases have been
solved. Though this does not constitute (in a mathematical
sense) any proof, these results suggest that there should not be
critical sets of values for attitudes angles which cannot be
recovered (with the obvious exception of the case ¢=100 gon
for the computation of the cardanic angles o, ©, K).
The second group of tests has concerned the check of the whole
procedure to compute the bundle adjustment of close range
blocks. For each test input data has been as follows:
1. image coordinates of GCPs and tie points (already
corrected for distorsions in case of non-metric
cameras);
object coordinates of GCPs;
alist of the block images;
principal distance of the camera;
accuracy of image and object coordinates.
hide lo 12
Blocks have been selected to cover two different cases: in the
first the block surrounds the objects with convergent images; in
the second, basically a courtyard, network geometry is weaker
and less regular. The main features of each block described in
the following are summarized in Table 3.
The first block (referred to as fountain”) is made up by 12
images acquired by a Rollei 6006 metric camera around a
sculpture. Images have been taken at two levels, almost
regularly spaced, so that every area of the object is covered by
at least 3 photos with convergent angles. Orientation of this
block has been performed by TRIACR in 6 stages, starting from
a small set of 5 GCPs. Images 3 and 4, that include 4 GCPs,
have been used to start the procedure. Nine tie points are shared
by this pair of images: after the space intersection and the
computation of a block adjustment of the two images they play
the role of GCPs for the other images not yet oriented by
RESECT. At following stages, other photos are then included
into the block (see Table 4). Not only each stage is expected to
increase the number of known object points, but also improve
their accuracy and reliability of the observations. Indeed, in
every bundle block adjustment, only true GCPs are effectively
constrained, while all tie points object coordinates are
recomputed; the higher the number of images that are included
into the block, the better may be the accuracy of object point
determination and the capability to discriminate blunders. For
instance, at stages 5 and 6 no new object points were computed
but images 8 and 7 could be added to the block improving its
strenght.
The second test has been performed on a block measured in the
Cloister of S. Giovanni Monastery of Parma (Italy). The topic
feature of this block is that the object is depicted by means of
photos acquired from inside its perimeter. Images have been
taken by a DCS 420 digital camera with a 24 mm lens, that
unfortunately results in a rather small field angle, requiring the
acquisition of many images (57) to cover the building (one of
the images is shown in Fig. 6).
Here the initial kernel of images is larger, because the 5 images
form a connected set through the 8 GCPs, even if not every
image sees all GCPs. As mentioned in 2.1, there may be more
than one kernel in this block (actually this is the case) but the
current implementation does not handle more than one block at
each step of the iteration (the bundle adjustment program
accepts only connected blocks!): so the “building up” of the
block proceeds leftwards and rightwards along the main walls
from this only kernel, until the two “growing” ends meet.
project Fountain Cloister
Camera Rollei 6006 | Kodak DCS 420
Principal distance (mm) 51.10 24.39
Format (mm) 60 x 60 13.716 x 9.108
Acc. of image coord.(um) 20 9
# of images 12 47
# of GCPs 5 23
# of TPs 37 261
Average # of rays per point 4.4 4.8
Average # of TPs per image 15 26
# of oriented images 12 47
Theoretical accuracy | X 1.6 19.8
in object space (mm) |y 1.6 14.6
Z 1.2 6.0
RMS of residualson |X 2.8 27.3
check points (mm) Y 1.2 12.8
Z 0.8 16.1
# of check points 3 7
Table 3 — Main features of test blocks and outcomes of bundle
adjustment
Stage | Known New Total # Oriented images
points | points | of images
1 4 8 2 3-4
2 9 12/5 1-2-5
3 21 20 18 6—11- 12
4 4] ] 10 9-10
5 42 0 11 8
6 42 0 12 7
Table 4 — Orientation stages of block "fountain"
Stage | Known | New | Total # of Oriented images
points | points images
8 35 |5 1-7-12-19-22
37 80. | 13 2-4-6-8-9-17-23-39
80 102 |18 3-11-13-18-60
104 129 | 21 5-48-59
130 148 |25 14-15-42-51
152 168 | 30 20-44-45-50-52
173 204 | 37 21-37-43-46-49-53-57
24-25-26-27-28-33-39-47-
54-55-56-58-61
RNIN NAW N | =
204 257 [50
9 257 280 |55 29-30-34-35-36
10 280 283 |57 31-32
Table 5 — Orientation stages of block "cloister"
—457-
