International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
outline edge of objective, to make simulation image to 
approach real image rapidly. 
  
   
Figure 3 The Sketch map of the plane's : 
outline and the ParaPoint. 
As shown in Figure 3, there are differences between outline 
edges L1 of real aircraft image and outline edges L2 of aircraft 
produced by simulation system because they are not matched 
completely. The difference shows in X direction and Y 
direction. For instance, the different distance between P point 
and real image in X direction dx = -PP1, in Y direction dy = 
-PP2, P point is any point in simulation image, it is a projection 
reproduced in simulation image plane from aircraft model. 
Object-space coordinate (X, Y, Z) of P point corresponding to 
aircraft model can be calculated, but we don't know the 
coordinate of the corresponding point (P^) of P point in real 
image, the main aim of this method is to eliminate dx and dy 
gradually, finally, to obtain position of P point in real image. In 
fact, the point position of outline edges vary with pose changes 
of simulation aircraft, therefore, while iteration eliminates dx 
and dy gradually, it is not to adjust difference of one point in 
the model, but is to adjust changing trend to whole simulation 
model. We call outline edge points used in adjustment 
calculation Parapoint. There are two reasons for this name: one 
reason is that position of P' calculated by us is very different 
from position of P on the model at the beginning of calculation, 
during the process of iteration, it is not to eliminate errors of P 
point located in outline of simulation images, but to approach 
outline edge of real image; the other reason is that when we 
conduct calculation by using these outline points, we use all 
outline points not only one point, and we carry out calculation 
by use of only the smaller of distances in X and Y direction. 
The whole process of FPE method can be divided into several 
steps as following: 
Stepl: first of all, a piece of clear image is found out at the 
beginning of the image sequences, then several feature points 
(for example, aircraft head, aircraft wing and aircraft trail, etc) 
are selected manually. Finally using these feature points’ 
image-space coordinates and its corresponding object-space 
coordinates, initial values of aircraft pose are measured by 
DLT. 
Step2: Outline points collection (S0) of aircraft objectives in 
this frame of image sequences is extracted, and the gross points 
in outline points collection {SO} are removed by use of 
. RANSAC, local spline fitting is conduct to produce new 
outline points collection {S1}. 
Step3: Initial values of aircraft poseare input into simulation 
system to produce a simulation image with OpenGL. Then 
aircraft outline point collection {S2} is extracted in this 
simulation image. 
Step4: Distance dx in X direction and distance dy in Y direction 
between each point in points collection S2 and its 
corresponding point in {S1}, that is, to calculate the 
coordinate(X, Y, Z) of P point in three dimension model, then, 
then establish error equation are established with formula (5), 
so two error equations can be established in X and Y direction 
for each point, here according to the amount of | dx | and| dy| ; 
only one error equation whose correction is smaller are used to 
conduct calculation of least square iteration. 
Step5: New pose of aircraft is obtained by solving the 
equations. 
Step6: if correction values between aircraft pose and space 
position is lager than the set threshold values, to return step3 to 
start a new loop, otherwise go to next step. 
Step7 To output pose data of current images, to judge if there 
are also image to be conducted in image sequence, if NO, to 
quit the calculation, otherwise, to get next image in image 
sequence to carry out the calculation. Two kinds of methods 
can be used to identify initial values of aircraft pose in next 
image. When frame number of image sequence conducted is 
less than three, the calculation value of former aircraft pose can 
be taken as initial values of aircraft pose in current frame of 
image. When frame number is greater than three, initial values 
of aircraft pose in new frame of image can be estimated by 
using KALMAN filter, then return to step2 to calculate aircraft 
pose in current frame of image. 
PEI method established by using parapiont solved successfully 
rapid match between image in simulation model and real image. 
It is a new application of traditional least square in the field of 
photogrammetry and computer vision. The method also can be 
applied to pose measurement of other crafts except of aircraft 
and check the quality of industry parts which geometry model 
data is known, etc. 
2.3 Calculation of image point coordinates 
It is necessary to know object-space coordinates of outline 
point of simulation image during pose of aircraft model is 
measured by using PFI method. Though outline points of 
aircraft in simulation image are acquired by projection of three 
dimension model, the deepness calculation of each point during 
projection spend not only a lot of EMS memory, but also a lot 
of time to calculate visibility of each point. So it is necessary to 
calculate dynamically three dimension point corresponded to 
outline points that is used in adjustment calculation. 
Suppose coordinate of photography center is(Xs, Ys,Zs) and the 
coordinate of image point is (X,y,-f), the beam vector 
crossing photography center can be expressed as: 
     
   
    
   
  
  
  
  
  
  
  
  
  
  
  
  
  
     
   
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   
  
    
   
    
   
    
    
   
  
  
    
    
   
    
   
    
    
   
    
   
   
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