International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
2.2.3 Patch Size Optimal Backprojection 
To reduce the interpolation error when terrain variation is 
considered, it would be better that the patch size changes 
according to the terrain characteristics. The patch size should 
be large for rolling terrain and, on the contrary, small for 
rugged one. Quadtree structure (Mather, 1999) that segments 
the terrain coverage with a given elevation range is a 
straightforward and yet effective way to characterize the terrain 
variations. Based on this consideration, we select quadtree 
structure to optimal the window size in the patch backprojection. 
The method discussed in this section is a modified one stated in 
the previous section. In the quadtree analysis, the allowed 
elevation range is selected according to that the model error 
will not exceed the tolerance. The analysis of the model errors 
will be given in the next section. After performing the terrain 
subdividing, tiles with different sizes are projected into the 
image space one by one using the process described in the 
previous section. Figure 3 illustrates the concept of the patch 
size optimal backprojection. 
  
  
  
  
  
  
  
  
  
  
  
  
  
Figure 3. Illustration of patch size optimal backprojection 
(a) Optimal tiles size by quadtree structure 
(b) Anchor point generation for the top layer 
(c) Anchor point generation for the bottom layer 
(d) Interpolation 
2.3 Model errors estimation 
Patch size is crucial when doing computation. The larger the 
patch size, the faster the computation time, but the model error 
increases as well. Hence, patch size optimal should consider 
the model error of the proposed method. Two steps, including 
affine transformation for anchor point sets and linear 
interpolation in patch backprojection could introduce model 
errors. Considering the imaging geometry, patch size, tilt angle, 
and elevation range are the three most important factors to be 
considered in the analysis of model errors. Simulations are 
employed on SPOTS supermode images. The model error is 
defined as the difference of the proposed method and the 
rigorous point-by-point backprojection. 
The evaluation items and parameters are shown in Table 1. The 
evaluation items includes: transformation model error, variation 
of terrain model error and tilt angle model error. The tilt angle 
is within 30?. The elevation ranges from 0m to 2000m. The 
patch size is within 40m by 40 m and 3000m by 3000m for each 
evaluation item. 
Table 1. SPOTS model error analysis 
  
  
  
  
  
  
  
  
  
  
  
Transformation Interpolation 
Model Error Model Error 
Evaluation Item Affine Variation of | Tilt angle 
Variable transformation terrain 
Tilt angle (deg 30 30 1-30 
Elevation (m) 0 and 2000 0~2000"" 0 and 1000 
Patch size (m * m) |80*80- 80*80~ 80*80~ 
2000*2000"* 2000*2000"'  |2000*2000'" 
"Tilt angle step (deg): 1, 2, 4, 8, 16, 20, 25, and 30. 
"Elevation step (m): 80, 160, 320, 500,640, 750, 1000, and 2000. 
"Patch size step (m*m): 80, 160, 320, 640, 1280, 1500, and 2000, 
  
588 
2.3.1 Affine transformation model error 
Given a tilt angle of 30? and elevation in 0m and 2000m, the 
errors due to affine transformation are shown in Figure 4. It 
indicates that when the patch size of 1500pixel by 1500pixel is 
selected, the model error is within the tolerance, i.e., 0.05 pixels 
in this investigation. 
, 
Transformation model error 
0.05 
Model Error(pixel) 
0.00 eet 
0 500 1000 1500 2000 
Patch Size(m*m) 
Figure 4. Transformation modcl error for SPOTS 
2.3.2 Variation of terrain model error 
Given a tilt angle of 30°, the errors due to terrain variation are 
shown in Figure 5. It indicates that when the variation of 
terrain is less than 1000m and patch size is less than 640m by 
640m, the model error is within the tolerance, i.e., 0.05 pixels, 
in this investigation. 
Model Error for Variantion of Terrain 
0.25 Patch Size 
(m*m) 
= 020 > 
e 
> 
a. | ? 160 
-— 0.15 
S 320 
= 
LL ne —610 
5 À 
= 
o —8—- 1280 
z 
0.05 , — 1500 
x —G-—- 2000 
0.00 SK : 
0 500 1000 1500 2000 
Variations of Terrain (meter) 
Figure 5. SPOTS model error for variation of terrain 
Intern 
2.3.3 
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