Babak Ameri 
  
where 
be -ROGY, Z) = —(aÿas + bÿb5 + eic, 
Therefore, introducing an equation of the type (15) as a weighted observation equation for every model point which 
satisfies the orthogonality conditions, and formulating them in a matrix form will result in the well known formulation 
of a Gauss-Markov model such as equation (6), except that z is the vector of unknowns consisting of the corrections to 
the coordinates of the model points {AX ;, AY;, À Z;).The other conditional constraints can be implemented in the same 
manner as discussed for the orthogonality constraint and integrated into the estimation model. 
Based on the assumption that all the parameters involved in the estimation model are considered observations, and conse- 
quently equations arising with the constraints or conditions are introduced into the total system of equations as weighted 
Observation equations, then we are able to join the different estimation models which are formed by the (5), (7), (11), 
(12), (15), or any other equations into a unified combined least squares adjustment process where its solution gives the 
correction to the initial parameters of the model. 
  
  
  
Figure 7: Reconstructed fine building models: a, e, f) reconstructed coarse building model overlaid on aerial image, - b, f, 
m) perspective view of the reconstructed 3D coarse building model, - c, g, n) reconstructed fine building model overlaid 
on acrial image, - d, h, q) perspective view of the 3D fine building model. 
4 EXPERIMENTS AND RESULT 
Three representative buildings of the Avenches data set (Mason et al., 1994), are selected to represent the performance of 
the proposed method and to visualize the outcome of the FBMV algorithm. It should be noted that the whole process of 
model verification is only applied on the roof structure and the vertical walls are added to the building model at the final 
stage. This is performed based on the analysis of the bounding edges and points of the verified fine roof structures. The 
first building shown in first row of the figure 7 is a simple gable roof structure, The reconstructed coarse model (figure 7-b) 
indicates that the reconstruction process (Ameri and Fritsch, 1999), recovered the fundamental structure of the building. 
However, due to the presence of a dormer window on top of the roof and also the low contrast of the roof outline, the 
bounding edges of the building are broken into the small pieces and are very rugged. The FBMV approach successfully 
verified the model and removed the redundant edge segments. Furthermore, imposing the orthogonality constraints during 
  
32 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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