AXE NAT NAT 6 VAT ; 
ARSENAL SY YAY 
(3-3) 
dy; dy; dy; 
Substituting equation (3-3) in (2-4) the linearization of the 
observation equations with respect to the coefficient vectors of a 
3-D B-spline curve can be obtained. For the same reasons as for 
2-D LSB-Snakes the equations are changed such that they can be 
expressed in matrix form as 
CÉmx 7 FyNAX ili > P , 
~€my = FyNAY -1,, , P. 2 (4-1) 
mé: FNAZ-l,.: , P 
i ay; 
FT 8605 3x t g( a 
Q ox; 0 dy; 
= ub em eer 4-2 
Fratris (n 
pA ax; à dy; 
z= Srna aay 932, 
The geometric observation equations (2-11), (2-15), (2-16) can 
be extended into three dimensions by introducing a new 
component for the Z-direction. Then the 3-D LSB-Snakes can 
again be solved by a combined least squares adjustment. That is, 
a 3-D linear feature is extracted directly from multiple images. 
The statistical analysis of the obtained results and the realistic 
evaluation of the algorithmic performance can be done through 
the use of the covariance matrix of the estimated parameters. 
  
  
  
(d) 
Fig. 3. Simultaneous 3-D extraction of a road segment from four images. Upper left: Location of seed points (0-iterations) and 
extracted road centre line. Rest: Extracted road centre line (after ca. 5 iterations). 
270 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
             
  
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