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-dimensional offsets
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il der ADS sind die
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1 ADS-Bildstreifen
bestimmt. Der vor-
(Intensitäten); die
Kleinste-Quadrate-
je Erweiterung der
lienten häufiger als
standskomponenten
rifiziert die Ergeb-
itilizing info clouds
ica ADS line-scan-
is two-fold: Abso-
control points and
flight lines (strips)
well-defined check
joints are manually
offsets in-between
ters, e.g. root mean
he number of strip-
tly process in both
012).
The automation of the relative geometric QC is based on a very
large number of patches of SGM-derived info clouds rather than
comparatively few individual point measurements per overlap.
It makes use of the SGM implementation by Gehrke et al.
(2010, 2011, 2012), which provides info clouds based on all
panchromatic stereo views of the ADS. Panchromatic intensity
as well as full, calibrated color information from ADS RGB and
near infrared bands is assigned to each individual point. That
information is used in a combined geometric/radiometric point
cloud matching that provides three-dimensional offsets for a
pattern of patches along overlapping ADS strips. This method
has been coined “Shear Analysis” and is now becoming a tool
for North West to automatically evaluate and verify the geo-
metric quality of ADS data and products. Shear Analysis is
being applied to flight recordings or image blocks before and/or
after aerial triangulation.
The basic idea behind the geometric/radiometric point cloud
matching is least squares (image) matching. It is, in that regard,
similar to the approaches of Maas (2002) or Akca (2007), who
base their matching on triangulated irregular networks (TIN) or,
respectively, gridded surface representations. Here the surface is
locally approximated by planes, generally based on more than
the minimum of three points (as in a TIN). Point-to-plane dis-
tances are used in the matching algorithm, which is described
and evaluated in the remainder of this paper. Results from both
the geometric and the combined geometric/radiometric ap-
proach are compared with manual measurements, based on
different ADS data sets from North West’s production. The use
of the derived offsets in QC and interactive Shear Analysis is
only indicated in this paper; for the detailed investigation of an
ADS block see Gehrke et al. (2012).
2. POINT CLOUD MATCHING APPROACH
The computation of ADS strip offsets for Shear Analysis is
based on the automatic definition, derivation, matching, and
evaluation of info cloud pairs. Below the point cloud matching
is initially explained using solely the geometry information —
which is a valid method by itself — and then extended to include
the radiometry that is provided in the info clouds.
2.1 Info Cloud Derivation and Properties
The collection of info clouds is based on SGM, carried out on
two panchromatic stereo views available from the ADS sensor:
nadir/backward and nadir/forward. It generates info clouds of
very high density in the order of the ground sample distance
(GSD), which allows for the application in small patches of a
few hundred pixels square (Figure 1).
Figure 1. Corresponding info clouds from overlapping ADS
strips, based on image patches of 512 x 512 pixels.
103
The ADS sensor has a high quality GPS/IMU and a well-known
interior orientation. This is of advantage for the point cloud
matching in two ways: First, the expected offset between corres-
ponding info clouds typically lies within a few image pixels or
GSD units and, second, the relative scale and rotations are
negligible. The fact that corresponding patches for Shear Analy-
sis are derived near the edges of ADS image at very different
view angles leads to different surface representations and es-
pecially to reverse gaps in case of occlusions as illustrated in
Figure 1.
2.2 Geometric Point Cloud Matching
The main challenge to point cloud matching is that points are
discrete samples of a continuous surface. The correspondence
between individual points does generally not exist, and a means
of a surface representation is required. There is a broad variety
of solutions for point cloud matching or, respectively, iterative
closest point algorithms for various purposes and based on
different assumptions and preconditions; see overviews in Ru-
sinkiewicz & Levoy (2001) or Akca (2007).
A simple yet robust method to match inherently close point
clouds is based on point-to-plane distances, i.e. the local appro-
ximation of the surface by planes (cp., e.g., Chen & Medioni,
1991). For all points in the reference cloud, a plane is fit to
those points of the corresponding match cloud that are located
in a small radius around each reference point. All valid point/
plane pairs are then combined in a least squares adjustment, in
which the average three-dimensional offset is estimated.
2.2.1 Local Plane Fit: Any point location (X,Y,Z) on a plane
can be described by the Hessian Normal Form, in equation (1)
based on the unit normal vector 11 (ny,ny,nz) and the distance d
to the origin of the coordinate system:
nyX nyY - ngZ-d 20 (1)
With the unit normal vector's length condition, it can be seen
that a minimum of three points is needed to define a plane — as,
e.g., in a TIN surface representation as proposed by Maas
(2002) or Akca (2007) for matching LiDAR point clouds. Com-
pared to LiDAR, the SGM-derived info clouds typically feature
much higher point density, however, along with slightly lower
accuracy in height (Gehrke et al., 2010). The resulting relative
noise level — especially in vegetation — as well as the afore-
mentioned gaps due to occlusions (Figure 1) are addressed by
fitting a plane to all points that are located in a GSD-dependent
neighborhood in the match point cloud. This allows for the
elimination of outliers and noise reduction; larger gaps are in-
herently omitted if there are no points to compute a plane.
The plane fit to a local sub-set of an info cloud is carried out in
a least squares adjustment. The observation equations are de-
rived from equation (1) by division by nz and making Z the
dependent variable. This modeling corresponds to the info cloud
collection by dense image matching, in which disparities and,
based on that, (stochastic) heights are derived for all (fixed)
image pixel locations:
Z 2-n,X —njY 4 d Q)
Such observation equations for each point (X,Y,Z) in the defi-
ned neighborhood lead to a linear least squares adjustment with
the unknown parameters ny, ny, and d'. The unit normal vector
7 (ny,ny,nz) and the Euclidian distance d can be derived after-
wards by division by the length of 7’ (ny,ny, ny), with nz = 1.
