Jorge Brito 
  
// Algorithm for Data Preparation for Analysis of Occlusions through a Bayesian Network: 
1) Select point pairs in the problem areas of original, digitized-frame images. 
2) Compute ground coordinates of point pairs selected in step 1 above. // Either from stereo model or (orthoimage and 
DEM.) 
3) Sort each point pair according to the *X" coordinate (ground coordinate system), so that X4 € Xg. 
4) Project each point onto the digital image space through the collinearity equations, and compute the respective 
variance-covariance matrices (V CM's) projected points “a” and “b”. 
5) Compute the direction of sight (0) for each point pair. The angle “0” ranges from -x/2 to + 71/2. It is computed by 
equation 2. 
6) Rotate the coordinates of each point pair (equations 3 and 4) so that the condition y’, = y’, (equation 1) is 
satisfied. 
7) Compute the new VCM's for the transformed coordinates of the points in each pair, by the General Law of Error 
Propagation (equation 5). 
8) Compute the eigenvalues of the transformed VCM's. // The computation of the eigenvalues is necessary to 
eliminate the covariance between x', and x',. 
9) Output the values computed in steps 6 through 8 to a file, which will be read as the input for computation of the 
Bayesian network. 
X X 
= R(0). (3) 
y y 
cos(0)  sin(0) 
R(0) - | | (4) 
—sin(0) cos(0) 
T 
SEI £s | 
ml-———l.Xyy.l ——— 
0 30 yy 36 (5) 
Yyy is the respective variance-covariance matrix of the differential rectification process. (Brito, 1997). 
2.2 Building the Bayesian Network 
Before going through the set up of the Bayesian network itself, it is necessary to simplify figure 3. This simplification is 
achieved by drawing only the projections of “a” and “b” along the “6” direction, x’, and x’, , respectively. Figure 4 
shows these projections, associated with their respective error regions. These error regions are represented by elliptical 
areas of constant probability, centered at each point. The axis x’ is enlarged for a better understanding of this situation. 
It is important to notice that these elliptical areas 
above represent the joint distribution of the “A” y 
and “B” coordinate errors, respectively, after the 
following transformations: 
e projection onto the digital image coordinate 
system; 
e rotation "0" applied to “a” and “b” coordinates 
and to their respective VCM's, and 
e computation of the eigenvalues of the rotated 
VCM's. 
One can conclude from figure 4 that only the error 
distribution of the x' coordinate is necessary for 
implementation of the Bayesian network. This is 
because the occlusion is being investigated along 
that direction. 
  
  
^ 
and "b" and their error 
Figure 4. The Rotation of points “a 
distribution regions, represented by elliptical areas. 
  
104 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.