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);