International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
  
> o 7j X Fs XY Org 7 Yin) 
Jen =X) +p — Yi) 
(1) 
  
  
Aix 
where / = the index of the edge line 
j = the index of the overlapped image 
k = the index of the edge pixel 
The photo coordinates vi (x;;, yı) and vix(xi», y;;) are functions 
of the unknown model parameters, comparatively the exterior- 
orientation parameters of photos are known. Therefore, dj; will 
be a function of the model parameters. Taking a box model for 
instance, d;; will be a function of w, 1, h, a, dX, dY, and dZ, 
with the hypothesis that a normal building rarely has a tilt angle 
(f) or swing angle (s). The least-squares solution for the 
unknown parameters can be expressed as: 
Yo = SF Ow lh a, 40 47 dDOF = win, (2) 
Eq.(2) is a nonlinear function with regard to the unknowns, so 
that the Newton's method is applied to solve for the unknowns. 
The nonlinear function is differentiated with respect to the 
unknowns and becomes a linear function with regard to the 
increments of the unknowns as follows: 
+ 0 ik OF oF, oF, jk 
da ESTA AN — | Mel —2 | Aa+ 
E ed Kt hen em ru. 0 
OF, oF, oF; 
© | AdX-4 —— | AdY+| — | AdZ 
aX J, adY J, 772 
  
  
in which, Fj) is the approximation of the function Fix 
calculated with given approximations of the unknown 
parameters. Given a set of unknown approximations, the least- 
squares solution for the unknown increments can be obtained, 
and the approximations are updated by the increments. 
Repeating this calculation, the unknown parameters can be 
solved iteratively. 
The linearized equations can be expressed as a matrix form: 
V=AX-L, where A is the matrix of partial derivatives; X is the 
vector of the increments; L is the vector of approximations; and 
V is the vector of residuals. The objective function actually can 
be expressed as q-VTV— min. For each iteration, X can be 
solved by the matrix operation: X-(AlAy'A!L. The iteration 
normally will converge to the correct answer. However, 
inadequate relevant image features, affected by irrelevant 
features or noise, or given bad initial approximations may lead 
the computation to a wrong answer. 
4. EXPERIMENTS 
The test data are aerial photos of the NCKU campus, digitized 
by the photogrammetric scanner in 254m resolution. The 
original photos are taken with a 305.1 1mm-focal-length aerial 
camera in the height about 1600m, so the average photo scale is 
about 1:5000. The end-lap between photos is more than 60%, 
and the side-lap is more than 30%. In the tests, buildings were 
extracted from the stereo image pairs formed by end-lap. Ten 
various buildings were arbitrarily selected for the test. All of the 
buildings are properly represented by a combination of box and 
gable-roof primitives, totally 23 primitives. For each primitive 
model, it takes about 20 sec to complete the fitting. Figure 9 
shows an example of the fitting results. To evaluate the 
accuracy of LSMIF, all of the visible building corners were also 
measured by an experienced operator with an analytical plotter. 
Table 2 lists the average and RMS differences. 
Table 2. The average and RMS differences of the building 
corner coordinates derived from LSMIF and manual 
  
  
  
  
measurements. 
X(m) Y(m) Z(m) 
Average Diff. 0.161 0.007 0.047 
RMS Diff. 0.330 0.277 1.034 
  
  
  
  
  
   
  
(b) 
Figure 9. (a) The image pair superimposed with the extracted 
edge pixels (red) and the projected wire-frame 
model (green) after manual approximate fitting. 
(b) The fitting result. 
5. CONSLUSIONS 
The objective of this study is to provide a semi-automated 
model-based building extraction system which can improve the 
efficiency of extracting and modelling buildings from multiple 
photogrammetric images. There are a number of characteristics 
of the proposed approach: 
€ The semi-automated strategy combines human ability on 
image interpretation and computer algorithmic potential. 
€ Compare to the traditional point-by-point mapping system, 
this approach provide floating models to extract data object- 
by-object. 
€ It is able to handle multiple images simultaneously, even 
combines aerial and close-range images. 
€ There is no need for stereo viewing. 
€ It complies with the constructive solid geometry, so the 
complex building can be modelled by a number of primitives. 
The experiments results have shown the reliability and potential 
of this approach. If introducing adequate constraints, the 
influence from irrelevant noise data can be decreased and the 
accuracy will be improved. Besides, the floating models are not 
only capable of extracting buildings, but also capable of 
determining image orientation. The ideal scenario would be 
integrating the aerial and close-range photogrammetry. First, 
   
  
  
  
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