The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008
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feature measurements which offer higher flexibility for
measurements. The hybrid model is the most flexible method
for measuring the geometric features in image space by offering
both point and line features measurement selection.
The CSR approach is detailed in the following sections.
3.1 Construct
3.1.1 Determination of Junction Points: The core idea
behind the Construct procedure is the characteristic of
intersection of the 3D line features when projected onto XY-
plane (Jaw and Cheng, 2007): When extended, a 3D line feature
will be suspended when running into other 3D line features and
thus candidate junction points are determined, as seen in Figure
5.
In order to obtain the correct intersection of 3D line features
that correspond to building comers, two thresholds of geometric
inference are imposed: (1) Distance threshold: The distance
threshold is set taking account the random error of measurement
and then used to filter out the improper junction points by
buffering the end points of the line feature. (2)TopologicaI
threshold: When adjacent buildings get too close, the above
distance check is inadequate to guarantee appropriate junction
points. A topological check (Jaw and Chen, 2007b) is therefore
implemented to identify those ambiguities. Figure 6 shows the
result after applying the aforementioned thresholds and Figure 7
depicts the algorithm of junction point determination.
Figure 5. Candidate junction points before applying thresholds
Input: 3D line features of building roof
Output: Reasonable Junction points
do 3D line feature projected onto XY plane,
do calculating the candidate junction points,
do the distance check and confirm if there is only
one junction point in this direction of 3D line features
if YES
Find the reasonable junction points. Output the result.
ELSE
do the topological check. Output the results.
Figure 7. Algorithm of thresholding junction points
3.1.2 Grouping the 3D Line Features and Constructing the
Topology: After obtaining the proper junction points, the 3D
line features that belong to the same building, each highlighted
with different colors as shown in Figure 8, can be grouped by
introducing the concept of cluster analysis, which is also
utilized in establishing the topology of roofs within the same
building.
Figure 8. Grouping 3D line features
3.2 Shape
At the shaping stage, the model of Conditions Adjustment with
Additional Parameters (as seen in Equation (2)) is used to
estimate the 3D coordinates of roof comers. Realizing that one
3D line features can be expressed by two plane equations, as in
Equation (1), the 3D coordinates of roof comers are treated as
unknown parameters and solved by employing least-squares
adjustment
a x X + b x Y - \ * (1)
a 2 Y + b 2 Z = 1
where c\ are the observations;
X, Y, Z are the unknown parameters of roof comers
when considering the intersection of two 3D line
features.
Figure 6. Junction points after applying thresholds
5 cx„ e „xi + 4x„Ci - Kxi = °cxi e ~ (0,1 = o- 0 2 p-') (2)
where A, B matrix are obtained by taking partial derivatives
of unknown parameters, observations,
respectively, with respect to Equation (1);