C. Vincent Tao 
  
One ratio of polynomial model can be used for all types of images. 
The same ratio model can be used by all exploitation software, producing the same errors and error estimates. This 
commonality will make enterprise wide error analysis easier. 
e Exploitation software using the ratio model can be completely ignorant of the rigorous image geometry model used 
to create it. The rigorous image geometry model is thus easier to update as sensors evolve, since changes to it do 
not cascade into the exploitation software. 
€ Usually fit to a rigorous image geometry model with limited accuracy (not triangulated with several overlapping 
images). 
e (Complex fitting process, to avoid a denominator polynomial function going to zero within the image segment 
extent (producing excessive errors). 
4 TEST RESULTS AND EVALUATION 
4.1 Test Data Set 
The test data set is provided by Intermap Technologies. A total 
of 50 control coordinate pairs well distributed in the image were 
manually collected from an ortho-rectified aerial image with 2.5 
meters resolution (shown in Figure 1). Figure 2 provide a 3-D 
view of the distribution of these selected control points (marked 
by “e” dots). In Figure 2, the terrain was generated using a 
cubic interpolation based on a Delaunay triangulation of these 
points. An independent set of 49 points was collected as 
checkpoints from an ortho-rectified aerial image with 1 meter 
resolution, marked as “+” in Figure 2. 
  
Figure 2 The distribution of control/check points in 3-D 
DIN 
Hp 
N 
2+* 
2 
to 
Il 
A 
  
Table 1 Test configuration of the RFM 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Solution four-degree six-degree 
ü at CCPs at CKPs at CCPs at CKPs 
Direct 1.06e+00 | 2.62e+00 | 1.15e+00 | 3.45e+00 | 8.42e-01 | 2.05e+00 | 1.40e+00 | 3.68e+00 
Iterative 9.32e-01 | 2.34e+00 | 1.02e+00 | 2.80e+00 | 8.39e-01 | 2.09e+00 | 1.42e+00 | 3.81e+00 
PCI 1.05e+00 | 2.50e+00 | 1.19e+00 | 3.59e+00 | 8.77e-01 | 2.40e+00 | 1.28e+00 | 3.01e+00 
Direct 1.24e+00 | 2.73e+00 | 1.11e+00 | 3.27e+00 | 9.05e-01 | 2.26e+00 | 1.28e+00 | 3.14e+00 
Iterative 1.05e+00 | 2.14e+00 | 1.03e+00 | 2.50e+00 | 9.03e-01 | 2.29e+00 | 1.29e+00 | 3.11e+00 
Direct 1.17e+00 | 2.50e+00 | 1.10e+00 | 3.06e+00 | 9.78e-01 | 2.23e+00 | 1.24e+00 | 3.90e+00 
  
  
Table 2 Residuals in image with the test data set (unit: pixel) 
4.2 Results and Evaluation 
In order to compare the solution methods to RFM, both direct and iterative solutions were tested. We have also tested 
the RFM performance under the different parameter configurations. As shown in Table 1, third-order RFM (i.e., degree 
is 6) and second-order RFM (i.e., degree is 4) are tested under the following cases: (a) p2# p4 with 78 or 38 unknown 
RFCs; (b) p2=p4 with 59 or 29 unknowns; and (c) p2=p4=1, regular polynomials with 40 or 20 unknowns. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 879