Table 1: Comparison between ALR and photogrammetry.
photogrammetry laser ranging |
data acquisition
flying height H « 6000 m « 1000 m
swath « 108^ < 40°
coverage continuous irregular
footprint size i5um x Hjf 1 mrad x H
flying time ] hour 3 to 5 hrs
weather cond. very restrictive flexible
surface reconstruction
redundancy 2 x photo — 3 0
accuracy
planimetry «1i5umxH/f 1dm«5"x H
elevation = H/10,000 m = | dm
surface charact. explicit implicit
automation
degree medium high
complexity medium low
2.1 Data Acquisition
Essentially, both methods sample the surface. The fly-
ing height of existing ALR systems—typically less than
1000 m—is quite limited, compared to photogramme-
try. The sampling size (ground pixel size in case of pho-
togrammetry, footprint size in case of ALS) is consider-
ably smaller in photogrammetry when the same flying
height is assumed. For H = 1000 m and f = 0.15 m we
have a pixel size on the ground of 15 cm, but a footprint
size of 1 m, for example. In ALR systems the average dis-
tance between samples is several times larger than the
footprint size, resulting in an irregular sampling pattern
with gaps. On the other hand, photogrammetry provides
continuous ground coverage.
The smaller swath angle of laser scanning systems and
the limited flying height cause much longer flying times
for covering the same area. Baltsavias (1999) mentions
a factor of three to five. Since the initial equipment cost
and the shorter life time result in substantially higher
amortization cost, the data acquisition with ALR is quite
a bit more expensive. Now, this is partially compensated
by the much less stringent weather conditions for ALR
missions; the waiting time for crew and equipment is
certainly much longer in photogrammetry.
Another interesting aspect in this comparison is the sur-
face characteristic. It is clear that photogrammetric sur-
face reconstruction methods require a reasonable image
function, that is, good contrast or texture. Sand, snow,
ice, or water bodies defy photogrammetric methods. In-
terestingly enough, ALR works very well in these condi-
tions.
2.2 Surface Reconstruction
In this section we briefly compare ALR and photogram-
metry in terms of surface reconstruction. Fig. 1 illus-
trates the principle of determining a surface point by
ALR. Although grossly simplified, it captures the basic
notion of establishing relationships between different
coordinate systems. Let us begin with what we may call
the laser beam coordinate system (x', y', z') whose ori-
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
gin is at the center of the laser's firing point and whose
Z'—axis is oriented opposite to the direction of the laser
beam. In this system, point P on the surface is expressed
by the range vector r = [0,0,7]" with r the measured
distance (range).
Figure 1: Relationship of local laser coordinate sys-
tems and object space reference system for transform-
ing range data to surface points.
Obviously, the laser beam system changes with every
new range measured. Let us transform it into the laser
reference system, denoted by x, y, z. Its origin is also
at the laser's firing point. The orientation depends on
the particular system; for example, in nutating mirror
systems, the z — axis would be collinear with the rotation
axis and the x — axis points to the starting position of
the rotating mirror; in the case of a scanning system, the
X — z plane would be identical to the scan plane with z
indicating scan angle zero.
The transformation from the beam system to the refer-
ence system is accomplished by the rotation matrix R;
since there is only a rotation involved. R; is determined
by the laser system. In the case of a profiler, R; is the
identity matrix; for a scanning system, the rotation ma-
trix is determined by the scan angle; two angles are nec-
essary to determine R; for a nutating mirror system. Let
us call the relationship of an individual laser beam with
respect to the reference system the interior orientation
of the laser system.
To establish a relationship of the laser system to the ob-
ject space, the exterior orientation is required. Thus, we
obtain for the position of the center of the laser footprint
p=c+ReRjir (1)
In this equation, c expresses the positional and R, the
angular component (attitude) of the exterior orientation
(see also Fig. 1). These two components are usually ob-
tained from GPS and inertial measurements. We omit
here the details of establishing the relationship between
the platform orientation system and the laser system
for it does
laser/photo
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Figure 2: Re
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