B3. Istanbul 2004
he form provides
(0o,o2P^!X (5)
or; A, the coef-
£, the vector of
or; P, the weight
e number of laser
meters are solved
in^ yw (6)
ion
ent errors are re-
| that register the
the ground. The
tural control enti-
ny, if any, control
ol information will
These entities are
rface constraints.
given point posi-
) +s1 =0 (7)
, and ex,ey,ez
noted that linear
el.
f control informa-
it procedure, ob-
lementation con-
ace elements that
1e laser strips are
ties. In a similar
ent surfaces that
0 a priori surface
faces). Their ap-
the data and re-
nent. The identi-
t of the strip ad-
strip adjustment
able tie regions in
ation. The iden-
ducted under the
ntation here con-
gions and points
strip adjustment,
ere not too many
h the partition of
ce of a segmenta-
|) is based on the
d regions for per-
The dependency
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
v
Figure 1: Segmentation of the overlapping part of two parallel
strips
on surface parameters implies that noisy data can result in
noisy parameters. Therefore, attenuation of the noise com-
ponent in the laser data, or in other words regularization of
the laser surfaces becomes mandatory.
The segmentation algorithm that was developed for this pur-
pose is based on clustering the laser points was (see Filin,
2002). The implementation is based on computing a feature
vector for each laser point followed by an unsupervised clas-
sification of the attributes in a feature space. In the feature
space each point is represented by its feature vector, where
the values of the feature vector determine the laser point co-
ordinates in this space. Clusters are then identified according
to proximity of points in feature space. Validation and refine-
ment phases follow the extraction of clusters from the feature
space. The validation phase concerns verification that indeed
all of the cluster points are part of one surface, and the refine-
ment phase tests the extension of the cluster to neighboring
points or neighboring clusters. The validation and refinement
phases are controlled by the fitting accuracy of an analytical
surface to the point clusters, where upper and lower bounds
for the fitting accuracy are set to avoid under and over seg-
mentation. The choice of fitting accuracy as a control fits
well to the strip adjustment application. In general, segmen-
tation algorithms tend to aggregate points that are part of
the same physical surface, sometimes on the expense of the
overall accuracy of the fitted surface. In the current case
where the reconstruction of the actual physical surface is of
somewhat less importance the accuracy criterion allows to
generate surface with a given level of accuracy and include
points within it that indeed belong to it. The results of the
point clustering algorithm are presented in Figure 1 and show
that the accuracy criterion allows still to reconstruct well the
physical surfaces. As one can notice the segmentation results
segment both the ground and detached objects, which is dif-
ferent than filtering algorithms that usually extract the bare
earth only.
4 Discussion and Results
The surface based model allows the application of the strip
adjustment procedure over general surfaces and with the seg-
mentation algorithm natural as well as man-made surface can
be incorporated into the adjustment. Estimation of the bi-
ases does not require the existence of any distinct landmarks
or flat horizontal surfaces either as control or tie entities in
the overflown area. As a result there are only little restric-
tions on initial condition in which the model can be applied.
The algorithm does not require knowledge of the correspon-
dence between the laser points and their actual location on
the ground, mostly because of the association of points to
surfaces from the outset. As surface elements are defined
here explicitly via the point clustering algorithm, problems
due to occlusion or height jumps that occur when comparing
points to TIN based surfaces are avoided with this represen-
tation. Equation 4 allows the derivation of criteria for the
estimation of the different parameters. As can be noticed,
over horizontal or near horizontal areas the positional biases
cannot be estimated well or estimated very weakly. The esti-
mation of these biases require sloped surfaces. The inability
to recover some errors over horizontal surfaces indicates the
simple fact that the effect of these errors is unnoticeable. Fol-
lowing similar analysis to the one performed in Filin (2003a),
one can see that the estimation of the positional offsets re-
quires surfaces with slopes in different directions. Steeper
slopes contribute to smaller variances and the variation in
normal directions reduces the correlation between the esti-
mates. Experience shows that even modest slopes of about
10 percent are sufficient for obtaining estimates with small
variances.
Considering the approximation of the system observations. In
general the geolocation of a laser point requires 14 observa-
tions — eight system measurements (GPS, INS, and the laser
scanner measurements), and six more for the offset vector
and the mounting bias. The user is usually provided only with
the three coordinates of the laser point. Therefore the error
recovery model requires these observations to be recovered.
Equation 4 shows however that for the offsets the influence of
the observations does not appear on the left-hand-side of the
equation but only in the right-hand-side which refers to the
differences between the laser point position and the control
or tie surface, these differences can be computed by the given
laser point coordinates. As a result for the computation of
the offsets, there is no need for approximation of the system
observations. The data that is usually provided in the form
of the z, y, z coordinates of the laser point can be regarded
as sufficient.
The application of the model with the computation of the
offsets per strip is demonstrated over the Eelde area in the
Netherlands. The dataset consists of twenty strips that are
composed of two sub-blocks of ten parallel strips each where
one sub-block crosses the other. The flight configuration is
illustrated in Figure 2. No control information was available
for the adjustment thus forcing an adjustment with tie sur-
faces only. To avoid rank deficiency an adjustment with a :
fixed datum constraint was applied by fixing the offset of the
first strip to zero.
Tie surfaces were extracted in the overlapping regions of the
parallel strips of one of the two sub-blocks (see Figure 2),
and in the overlapping region between the two sub-blocks.
As Figure 2 shows the same region could have appeared in
four individual strips, and thus be segmented four times. To
avoid multiple segmentations of the same area, each area was
segmented only in one strip and corresponding laser points
from other strips were later referred to that segment. The
choice of which strip to segment and then what region in
the strip to segment was performed by ordering the strip and
