The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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Since the value of building dimensions (IV, H) does not affect 
the building orientation, the only unknown parameter of 
building orientation is Of. At this stage, the camera orientation 
is known. The objective function of Equation (6) is employed to 
obtain an initial estimate for CL . The minimization of the 
objective function (6) sums the extents to which the model 
orientation v violates the constraints arising from Equation (2). 
Refinement of Building Orientation 
Once initial building orientation is obtained, a non-linear 
technique based on the Gauss-Newton method is applied to the 
minimization problem. Based on Equation (9), the minimization 
is straightforward since there is only one unknown 
parameter CL, 
-a^Wsina+ aJ 2 Wcosa = 0 
where a ] = m] R 
Given the initial building orientation obtained from the previous 
step, the Gauss-Newton algorithm computes the accurate 
building orientation within 2-3 iterations. 
Determination of Building Dimensions and Location 
The building dimensions and location is determined by 
minimizing objective function 0 2 as shown in Equation (7). In 
this stage, image norm vectors m, camera rotation R and 
translation t are known. The unknowns are points w, on the 
model edges which are expressed as linear functions of building 
dimension and location, and can be solved through a set of 
linear equations. The same way can be employed to reconstruct 
more buildings. 
2.3 Vanishing Points Based Algorithm 
The method (Zhang et al., 2001) proposed an adjustment model 
for computing vanishing points, and then determined camera 
focal length as well as camera orientation using calculated 
vanishing points. Given a dimension of the cubic building, the 
camera translation and other two dimensions of the building 
were determined. We also extended this approach to deal with 
multiple buildings using the topological representation as 
shown in Figure 1. Then we evaluated effectiveness of our 
method with this extended vanishing points based method. Due 
to the space limit, we do not include the details of their methods 
in this paper. 
3. EXPERIMENTAL RESULTS 
This section describes a series of experiments that were carried 
out in order to evaluate the effectiveness of proposed algorithm 
and the vanishing points based algorithm. Simulation is first 
used to systematically vary key parameters such as the camera 
parameters and measurement of the image segments; thereby 
enabling us to characterize the degradation of the algorithms in 
extreme situations. Real examples are shown to gauge practical 
results. 
3.1 Simulation Experiments 
The synthetic image data was generated with a virtual camera 
and two 3D cubic building models as shown in Figure 1. The 
camera parameters are listed in the Table 1, assuming that the 
image centre lies at the centre of the image frame. Table 2 
shows information about the two building dimensions, locations, 
and orientations. 
Focal Length 
(m) 
0.0798 
Pixel Size (um) 
12 
X 0 (m) 
-500.672 
O)(o) 
50.346 
Yo(m) 
100.317 
3.582 
Zo(m) 
650.783 
K(O) 
2.787 
Table 1. Camera intrinsic and extrinsic parameters 
Building 1 
Building 2 
Length (m) 
40 
26.41 
Width (m) 
20 
20.92 
Height (m) 
30 
22.31 
Orientation along X axis (°) 
0 
a = 30.856 
Location of a building model vertex (m) 
X 3 
100.512 
Y 3 
-200.217 
Table 2. Building parameters of dimensions, locations and 
orientations 
We evaluated how errors in measurements of image segments 
as well as camera parameters influence accuracy of the 
recovered camera pose and building model dimensions for both 
methods. In the following tables, entries in rows with “V” 
correspond to experiments from the vanishing points based 
method, with “M” correspond to experiments from our model 
based method. Entries in column with “0” correspond to 
experiments with correct image measurements or camera 
parameters. 
Errors from image noise 
A uniformly distributed random image error is added to the 
endpoints of the image segments. Entries in columns with 0 
random errors correspond to the experiments with the image 
segments without errors. Table 3 shows that the reconstruction 
errors increase as the random image errors are increased for 
both methods. However, the vanishing points based method is 
extremely unstable to those random errors in the endpoints of 
the image segments. The results from vanishing points based 
method shows a very bad reconstruction. The reason is small 
errors in endpoints of the image segments cause huge errors in 
the determination of vanishing points. Thereby, large errors in 
vanishing points cause huge errors in the resulted camera pose 
and buildings. While the model based approach is relatively 
stable to those random errors. The errors in the endpoints have 
much less effect on the accuracy of the reconstruction 
compared with vanishing points based method.