The elimination of outlier points is carried out iteratively, based 
on data snooping, which eventually provides reliable plane fits 
for the match cloud. Now let the corresponding point in the 
reference cloud define a local coordinate system in which the 
plane fit is computed. Then the resulting distance d is the initial 
point-to-plane distance for that location. It is used to identify 
outliers in the reference cloud and, in combination, provide 
reliable point/plane pairs along with their stochastics to the sub- 
sequent point cloud matching. 
2.2.2 Offset Derivation: Point/plane pairs from correspon- 
ding info clouds are used to derive their overall three-dimen- 
sional offset. This is computed in a least squares adjustment by 
introducing the unknown parameters (Xo; fer, Yo ffset» Zof fset) 
into each individual plane's Hessian Normal Form, aiming to 
match the individual point-to-plane distances derived above. 
Based on (1), the observation equations read as follows: 
d= nx Xorfset + NyYoffset + nzZoffset (3) 
The selection of the distance d as observable allows for weight- 
ing the observation equations by the quality of the plane fit in 
such a way that weaker planes with larger standard deviations 
are rewarded less influence for the offset computation than 
more robust plane fits. Practical tests confirm that this weight- 
ing is critical for a meaningful offset computation. 
Even though equation (3) is linear and, accordingly, this very 
adjustment could be solved without iterating, the surface ap- 
proximation by local planes has to be refined. Therefore, the 
overall solution is computed iteratively, applying the resulting 
offset to improve local plane locations as described above. This 
iteration is carried out until the offset increment becomes in- 
significant, i.e. well below the GSD. 
2.3 Combined Geometric/Radiometric Approach 
For point clouds from nadir-looking sensors, geometric mat- 
ching alone does constrain the vertical offset component in 
virtually all cases. However, horizontal correlation becomes 
weak if the data lack significant height gradients in different 
directions, which is obviously the case in flat terrain but also on 
oriented slopes such as building roofs, especially considering 
the small patch size used for the purpose of Shear Analysis. 
This issue has been addressed by several algorithms that utilize 
any available information on intensity to either assist the geo- 
metric matching (Weik, 1997) or extend it towards a combined 
solution (Maas, 2002; Akca, 2007). Intensity gradients tend to 
occur more frequently than height gradients; they can provide or 
complement the required information for the derivation of 
planimetric offsets. Therefore, it suggests itself to use this 
additional information, which is available from the info clouds, 
and integrate it with the geometric point cloud matching into a 
combined adjustment. 
2.3.1 Adjustment Extension to Intensity: In analogy to the 
height Z, the intensity or, respectively, digital number DN is an 
attribute of a point’s planimetric location (X,Y). Accordingly, 
the functional models for the integration of geometry and 
radiometry can be written the same way, the first using height 
gradients (from local X,Y,Z planes), the second intensities (local 
X,Y,DN planes); the underlying idea is the well-known least 
squares (image) matching. The above-described local plane fits, 
applied to both heights and intensities, provide a pair of obser- 
vation equations, (3) and (4), for each reference point for the 
combined geometric/radiometric least squares adjustment. 
104 
2.3.2 Histogram Adaptation: The unavoidable difference in 
viewing geometry as well as potential illumination or even 
temporal differences can result in radiometric differences in the 
overlapping ADS image data and, accordingly, in the corres- 
ponding info clouds. Those differences are compensated as part 
of the combined adjustment by applying brightness and contrast 
correction terms, b and c. Similar to (3), with the heights re- 
placed by corrected intensities, the radiometric observation 
equations read: 
don = nx pnXoffset + Ny,onYoffset + Nzpn(cDN +b) (4) 
This adjustment features a total of five unknown parameters: the 
three-dimensional offset as well as the required contrast and 
brightness adaptation. It is obvious that the additional equations 
(4) can only provide immediate constraints on the Xp rrger and 
Yoffset Components. The Zorrset is determined by equation (3). 
However, the planimetric offset is part of both (3) and (4); the 
latter of which therefore has some (indirect) impact on the re- 
sulting height offset, too. 
2.3.3  Weighting between Geometry and Intensity is based 
upon their group variances: If balanced properly, the relation 
between these variance components before and after the ad- 
justment should be identical for height and intensity observation 
groups. The ratio is used to alter the weights for the intensity 
equations. This adaption is iterative and, theoretically, needs to 
be carried out for each adjustment computation. However, it 
seems feasible to improve weighting along with the overall 
iteration, considering that the main goal is to level largely dif- 
ferent orders of magnitude that occur depending on terrain and 
texture. Test runs have shown weight factors between 1 and 
greater than 10,000, the latter in very flat regions where the 
planimetric offset components are almost exclusively deter- 
mined by intensity. 
2.4 Offset Verification 
In order to provide reliable offsets for Shear Analysis input, the 
results of the combined geometric/radiometric matching are 
verified as part of the computation. First of all, the roles of 
corresponding info clouds are switched between reference and 
match cloud, thus providing two independent offset computa- 
tions that must agree within tight thresholds. The average offset 
becomes the final result, given that further indicators are mea- 
ningful. Those include a minimum number of point/plane pairs 
in a patch, reasonable radiometric corrections as well as the 
maximum number of iterations. Respective limits can depend 
on a variety of parameters, predominantly terrain and imaging 
configuration. Nevertheless, using rather tight general settings — 
a maximum in the order of 5 to 7 iterations, based on at least 
25% point/plane pairs in relation to the number of input image 
points in a patch — might eliminate some correct results; but as 
long as offset are attempted to be computed in a fairly dense 
pattern, there will be sufficient input for the Shear Analysis. 
Most important is the elimination of false positives. 
3. EVALUATION ON DIFFERENT DATA SETS 
The combined geometric/radiometric point cloud matching ap- 
proach was initially verified with synthetic data — heights and 
intensities assigned to predefined locations — and artificially 
introduced offsets. Practical validation and Shear Analysis 
exploration was carried out for a number of ADS blocks with 
different characteristics. Eventually aiming for the replacement 
of the manual QC, a crucial part of it was the verification of 
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