A, 9-11 Nov. 1999
jer of points that lie on
spread of the cluster is
nv well the plane fits the
ons are grouped into three
s and solid squares identify
a roof plane. The crosses
lie on a horizontal surface.
s depicted as triangles.
ing planes within the se-
es and solid triangles la-
erent roof planes; circles
likely to be on a horizon-
issified points. The final
ed by a least-squares ad-
the results for the three
ind the DEM points. The
roof planes is very simi-
the building analyzed in
Is again the high ranging
Ye standard deviation for
ly higher simply because
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
Table 1: Results from roof plane analysis.
roof 1 roof 2 | ground
laser
# pts. 21 34 32
a [m] 0.035./. 0.052 | 0.195
photogrammetry
# pts. 25 14 26
o[m] 0.108:| 0.036 | 0.232
Table 2: Results from roof ridge analysis.
laser | DEM | direct |
azimuth [°] 9.3 8.8 6.1
zenith [°] 0.5 0.6 1.3
X 4.12 3.60 3.88
Y 1.13 1.13 1.13
Z -30.86 | -30.99 | -30.95
the physical surface is not exactly a plane and 0 is more
indicating the roughness than the ranging accuracy.
The relatively large standard deviations related to the
surfaces computed with DEM points may surprise at first
sight. Since the DEM was measured dynamically, the ex-
pected point accuracy is higher than Eq. 1 indicates. In
fact, the values in Table 1 are within the range one can
expect from this measuring mode.
The last quality control check performed in this experi-
ment concerns the positional accuracy of the roof ridge,
computed by intersecting the two roof planes. The roof
ridge vector is directly obtained from the plane param-
eters. As shown in Schenk (2000b), the vector compo-
nents can be used to specify the spatial direction of a 3-D
line, for example by the two angles azimuth and zenith.
The azimuth defines the line direction in the x—, y — co-
ordinate plane, while the zenith angle refers to either
one of the other two coordinate planes.
The ridge was computed from the roof points of the laser
data set and from the photogrammetric DEM measure-
ments. The edge was also directly measured on the an-
alytical plotter. Table 2 lists the results. When compar-
ing the angles (azimuth and zenith) one should take the
building size of 15 m into account. The small zenith an-
gle resulting from intersecting the roof ridge indicates
an almost horizontal roof ridge. To compare the posi-
tions of the three roof edges, a reference point on each
edge was chosen with identical Y — coordinates. Consid-
ering the small azimuth, the positional accuracy can be
expressed by the X— differences of the reference point
(see Fig. 9).
The numbers in Table 2 reveal that the roof lines found
by intersecting the corresponding roof planes are in
fairly close agreement with the direct measurements.
Note that a small difference in surface normals may
107
1.6
14H
o bus
s 1.2 F
1 .
9 > 9
o 10 F- D 2 S
> & © SG
& D o
€ c & D
© >
0.8 = 9 ©
Oo ©
= =
0.6 La 1 ı als 1/14
3.4 3.6 3.8 4.0 4.2
X-coordinate
Figure 9: The roof ridge was computed by intersecting the
two roof planes, obtained from laser roof points and from DEM
measurements. The edge was also directly measured. The
figure shows the three roof edges, together with the reference
points whose values are listed in Table 2.
cause a substantial displacement in the roof line. More-
over, the intersection of roof planes does not necessarily
correspond to the physical roof edge.
4 Conclusions
We performed several experiments with airborne laser
ranging data within an urban region of the ISPRS Com-
mission Ill test site ( Ocean City, Md). The analysis of
raw laser points resulted in a point accuracy of approx-
imately =6 cm, confirming the high accuracy potential
of laser ranging. We used two different approaches
for assessing the quality of raw laser points. The first
method entailed a straightforward comparison between
laser points and a DEM, derived from manual measure-
ments on an analytical plotter. Since the point distri-
bution between the two sets of surface points is differ-
ent, no direct point to point comparison is possible—
interpolation to identical x,y positions is inevitable.
That is the pitfall of this method, particularly when re-
gions with surface discontinuities are compared. A bet-
ter approach is to segment the surface and to compare
the segmentation parameters.
The distribution of laser points has no direct relationship
with object boundaries; in this respect, the distribution
is entirely arbitrary. If object boundaries are defined by
intersection of physical surfaces then the boundaries can
be computed if laser points on these surfaces are avail-
able. We have used this approach to compute roof ridges
of buildings in a residential area. The comparison with
independent measurements showed that the accuracy of
derived surface properties depends not only on the laser
point accuracy but also on how well a physical surface
can be mathematically modeled. For example, how close
is a real roof to a plane?
Our experiments also showed that the “problematic”
