The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B5. Beijing 2008 
methods here. Interest readers may refer the paper (Guillou et 
al., 2000) for more information. 
1.2.2 Model-Based Methods: We regard model-based methods 
(e.g. Debevec et al. 1996, Wang and Ferrie, 2008) as evolution 
from line-based methods (e.g. Liu et al. 1990, Kumar and 
Hanson 1994). The model-based methods use structure 
information inherent in the objects which is ignored in the line- 
based approaches. Early attempt (Liu et al. 1990) solved for the 
camera rotation first and then the camera translation using both 
lines and points correspondence. They considered three camera 
rotation angles as obtained from a nominal orientation by small 
perturbations, e.g. 0 degrees. Based on this assumption, their 
algorithm only works if the three camera Euler rotation angles 
are less than 30 degrees. Kumar and Hanson (1994) solved for 
the rotation and translation simultaneously by adapting an 
iterative technique formulated by Horn (1990). They also 
reported that the initial rotation estimates for some data sets 
must be within 40 degrees for all the three Euler angles 
representing the rotation. When initial estimates for rotation and 
translation are not available, they sampled rotation space, and 
each of the samples was used as an initial estimate for the 
rotation estimation by a method akin to Liu et al. (1990). The 
estimated rotation and translation based on the rotation samples 
are then used as initial estimates for solving the camera rotation 
and translation simultaneously. Taylor and Kriegman (1995) 
estimated both the camera positions and the structure of the 
scene from multiple images. Based on a random initial estimate 
of rotation, the translation and model parameters are computed 
as initial inputs for the subsequent model-to-image fitting 
procedure. If the disparity between predicted edges and the 
observed edges is smaller than some preset threshold, the 
minimum is accepted as a feasible estimate. Debevec et al. 
(1996) argued that if the algorithm begins at a random location 
in the parameter space, it stands little chance of converging to 
correct solution. They developed a method to directly compute 
a good initial estimate for the camera positions and model 
parameters, and then use those estimates as initial inputs for the 
subsequent model-to-image fitting process. 
Our approach builds on this line of work. Described is a two- 
step iterative scheme for recovering camera orientation that, 
unlike existing methods, does not require a good initial guess 
for the rotation. Instead, the good initial estimate for the 
rotation is computed directly by using coplanarity constraints. 
The camera translation and predefined model parameters are 
determined based on the calculated rotation through a linear 
least squares minimization. The 3D reconstruction of buildings 
is based on the recovered camera pose and the assumption of 
flat terrain. Unlike existing methods, our method does not 
require a model-to-image projection process, and is particularly 
suitable for oblique images with large shooting angles in urban 
environments. 2 
2. THE METHOD 
2.1 Notation 
Figure 1 shows how a straight line segment, model edge 67, in a 
cube model (building 1) projects onto the image plane of a 
camera. The coordinates of two endpoints of the projected 
image edge 67 in the camera coordinate system can be 
represented as {(x h y h -f), (x 2 , y 2 , -/)}• The camera position 
relative to the object coordinate system is represented in terms 
of a rotation matrix R and a translation vector t. The straight 
line 67 can be defined by a pair of vectors (v, u) in the object 
coordinate system where v represents the direction of the line 
and u represents a point on the line, m is normal vector of the 
projection plane defined by the two lines (C 6 , C 7 ) and camera 
centre C in the camera coordinate system. The coplanar 
constraints derived in (Taylor and Kriegman, 1995) are outlined 
in the following. The fundamental relation of the imaging 
geometry can be represented by the equation (1), 
m = R(vx(u -/)) (1) 
Equation (1) is based on the fact that the 3D model lines (e.g. 
line 67) in the camera coordinate system must lie on the 
projection plane formed by lines (C6, C7) and camera centre C. 
m T Rv =0 (2) 
m T R(u-t) = 0 (3) 
Equations (2) and (3) are deduced from equation (1), which 
shows that the determination of camera rotation R can be 
independent from the estimation of camera position t and model 
parameters. Note v becomes a known vector in the object- 
centered coordinate system which is parallel to the Y axis, 
while u can be represented by the model parameters. 
onto a camera’s image plane and spatial relationship of 
buildings