3.2 Direct Comparison of Laser Points and Pho-
togrammetry
The first experiment is simple but very effective. Fig. 4
shows the laser points, projected back to the imagery. It
is the same principle discussed in the previous section
where a synthetic laser point stereogram was generated
(Fig. 2).
Figure 4: Illustration of projecting the laser points to a stere-
opair (backprojection). The stereopair can be viewed on an an-
alytical plotter or on a softcopy workstation. If the laser points
are not on the visible surface, defined by the stereo image, dif-
ferences can be measured and analyzed. This technique is also
very useful to examine "problematic" laser points, for example
around buildings. It is also possible to perform the compari-
son automatically by image matching techniques (see text for
details).
The 3-D laser points are projected to the stereopair with
the exterior orientation established during the process
of aerial triangulation. This basically mimics the image
formation process— instead of recording light intensities
from a point in the scene by a camera, the process is
performed analytically. We have used this method ex-
tensively to check if photogrammetry and laser data are
in the same reference system. Analytical plotters and
softcopy workstations are particularly suited for this task
because they position the measuring mark automatically
on points entered as a file.
How valid is an analysis of recorded differences? Are dif-
ferences due to laser errors or due to measuring errors?
As a rule over the thumb we can expect the following
elevation accuracy 0- from photogrammetry
g; = (0.06 = 0.08) - H (1)
If the flying height H is entered in meters then oz will
be in millimeters. In our case, with H « 370m, the ex-
pected accuracy of a well defined point is better than
3 cm. Points on roofs, parking lots, streets, etc. are
well defined and thus very suitable to check the accu-
racy of laser points. Examples of less well defined points
include vegetated areas, ranging in uncertainty from
grassy areas to crops, shrubs, and trees. Such points
should be left out in an accuracy study.
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
Backprojection is also very useful for examining laser
points in critical areas, for example around buildings.
Having the possibility to analyze the surface within the
footprint may offer new insight into the interaction of
the laser beam with surfaces. Waveform analysis as a
function of surface properties, such as material, rough-
ness, topography surely would benefit greatly from this
approach. We are currently analyzing surfaces around
footprints of weak laser returns. This information is
available for ATM laser data, processed by NASA Wal-
lops, for example.
We should like to point out to an interesting modification
of backprojection. Instead of letting a human measure
the differences between laser points and surface, we use
automatic image matching techniques. If the laser point
is really on the visible surface then its backprojected po-
sition in the images is conjugate. We can check by com-
paring a small image patch around the conjugate points
by area-based matching (Schenk (1999b)). The match-
ing vectors of all the points checked in this fashion are a
direct indication of how well laser points agree with the
visible surface.
3.3 Detailed Study of a Tall Building
We have analyzed the laser data set over the building
area shown in Fig. 3 in various aspects. First we briefly
describe the comparison of the laser points with the data
set obtained from photogrammetry. We then analyze
extracted surface properties and present results.
Although the laser and photogrammetry data sets de-
scribe the same surface there are no identical points and
the comparison is usually performed with interpolated
points. Fig. 5 shows a perspective view of the model
created from the two data sets. Since the building was
manually measured, including breaklines, it is no sur-
prise that its model, shown in Fig. 5(a) looks more re-
alistic than the TIN model created from the irregularly
distributed laser points (Fig. 5(b)).
Figure 5: Perspective view of the building model. The left im-
age shows the model created from photogrammetrically mea-
sured points. The right image is a TIN model of the laser points.
The photogrammetric model is superior because twice as many
points were measured. The building outline (breakline) was
also measured.
The comparison between the two data sets was per-
formed by computing the vertical differences between
points in the photogrammetric model to the correspond-
ing laser point surface. This includes interpolation and
the result is influenced by interpolation errors. These
errors are quite large, especially near breaklines. Not
surprisingly, the resulting standard deviation of «1.08
m is an order of magnitude larger than what one would
expect. The test clearly demonstrates the inability of
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