Hans-Gerd Maas
deviation in gable direction of buildings, where standard deviations were usually under 10cm and the correlation
between the X- and Y-shift parameters was usually low.
4.1 Matching planar patches
One possible solution to the errors caused by discontinuities is a restriction of matching to planar patches. This can
either be achieved by explicitly extracting planar patches from the laserscanner data, as shown by (Vosselman, 1999), or
by excluding points close to edges after an analysis of height texture measures (Maas, 1999a). The latter option was
implemented by the analysis of a plane-fit through every data point and its neighbours in a Thiessen structure derived
from the TIN. This rejection of points which are not situated on planer patches goes clearly beyond the exclusion of
points falling into irregular triangles (chapter 2.3), as it will generally exclude all points which are less than one point
spacing away from discontinuities.
After the restriction to points on planar patches, the problem of
singularities will be accentuated. Sufficient patch contrast is only
provided by more complex roofs or in a patch containing two
buildings with different gable directions (Figure 4 - right).
Figure 4: Height data with uni-directional and bi-
directional roof gradients
In practice, such configurations are not always present, especially when tie points have to be found in high-resolution
laserscanner strip data with small lateral overlap. In fact, the number of accepted matches of the pointset shown in Figure
3 decreased drastically when the 'planar patches' option was used. Choosing larger patches could only partly compen-
sate for this.
4.2 Refined analysis of gradients
Also after restriction of the matching process to points falling into planar patches the difficulty of estimating realistic
precision measures and detecting singularities remains. This problem originates from the noise of the laserscanner data
points themselves, which is estimated in the order of 3-5cm (van der Wolk, 2000), plus some model noise caused by the
fine-structure of roofs, the laser spot size, and insufficient sampling. This noise propagates into the gradients of the TIN
meshes, which determine the design matrix and covariance matrix used for parameter estimation in LSM.
To solve for this problem, a procedure for a detailed analysis of the design matrix was defined:
* All gradients are analysed on their significance, and the number of triangles with significant gradients is compared
with a pre-set threshold.
e The directional distribution of significant gradients was analysed. This distribution should be uniform or show two
maxima in orthogonal direction. In the case of a directional histogram with a clear single peak, the match was not ac-
cepted.
In addition, the convergence behaviour is analysed, and optionally the results of auto-correlation are examined.
This detailed analysis of the design matrix and the convergence behaviour, combined with the restriction of matching to
points on planar patches, leads to a partial success. The results obtained from the dataset described in chapter 3, using
the planar patches option (chapter 4.1) in combination with the gradient analysis as described above, are visualised in
Figure 5. They show about the same standard deviation as mentioned in chapter 3, but a significantly improved consi-
tency and a clearly recognisable trend of the shift parameters over the region shown in Figure 3. This trend indicates a
the presence of a displacement of about 0.3m between the two crossing strips as well as a tilt. These effects are likely to
result from errors of the position and orientation determination unit of the laserscanner system.
Another outcome of the analysis of the determinability of the shift parameters is a reduction of successful matches from
74% to only 20%. This is unfortunate, but seems realistic considering the structure of the test area, which contains many
buildings with simple gable roofs.
A linear regression analysis of these results yields the following standard deviations of the LSM shift parameters in
X/Y/Z:
* Basic technique (ch. 2, Figure 5 - left): 19.4/19.4/4.0cm
* Planar patches (ch. 4, Figure 5 - right): 13.3/7.1/1.9cm
552 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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