The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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(see figure 2) when there is an overshoot (case 1 in figure 2). If 
there is an undershoot, the values are defined as the value at 
+1.25 pixel from the edge center. As before, H is defined as the 
geometric mean of the overshoot in x and y directions. 
Figure 1. Calculation of H (Leachtenaucer et al., 1997) 
In order to calculate NIIRS through image analysis (Image- 
based NIIRS, INIIRS hereafter), we first selected points 
manually where intensities were changing rapidly. Edge 
profiles around the edge points provided were calculated. 
Figure 1 shows the example of edge points provided manually 
for edge response generation. 
Figure 3. Example of edge points used for edge profile 
generation 
For one image, around 20 edge points were provided and for 
each point, an edge profile was created. All edge profiles within 
one image were averaged out to create nominal edge responses 
for the image. Nominal edge responses were used to calculate 
RER and H values. 
It was difficult to have actual accurate values for G since this 
value was not provided within the metadata, For IKONOS we 
used the value published in the literature (Ryan et al., 2003) and 
for Quickbird we assumed the value for IKONOS. For SNR we 
assumed a constant value of 10. Although there are ways of 
analysing SNR from the image, this method was not hired in 
our experiments. 
Table 3 shows the NIIRS estimated through image analysis as 
explained so far. 
Image Type 
RER 
H 
G 
GSD 
INIIRS 
Quickbird 1 
0.2135 
0.7783 
4.16 
0.6994 
3.16 
Quickbird 2 
0.2043 
0.7735 
4.16 
0.6797 
3.15 
Quickbird 3 
0.2711 
0.7832 
4.16 
0.7509 
3.34 
Quickbird 4 
0.2515 
0.7668 
4.16 
0.7661 
3.23 
IKONOS1 
0.2444 
0.7939 
4.16 
0.9295 
3.01 
IKONOS 2 
0.2233 
0.7765 
4.16 
0.9099 
2.92 
Table 3. Estimation of Image-based NIIRS (INIIRS) 
Table 4 summarizes the three types of NIIRS: the NIIRS 
provided within image metadata (PNIIRS), the NIIRS estimated 
by human operator (TNIIRS) and the NIIRS estimated through 
image analysis (INIIRS). 
Image Type 
PNIIRS 
TNIIRS 
INIIRS 
Quickbird 1 
4.3 
3.71 
3.16 
Quickbird 2 
4.4 
3.75 
3.15 
Quickbird 3 
4.5 
3.93 
3.34 
Quickbird 4 
4.5 
3.75 
3.23 
IKONOS1 
(4.5) 
3.53 
3.01 
IKONOS 2 
(4.5) 
3.52 
2.92 
Table 4. Comparison of PNIIRS, TNIIRS and INIIRS 
We can observe that INIIRS values were significantly lower 
then PNIIRS and TNIIRS values. There can be many reasons 
for this error. The G and SNR values we used may not be very 
precise. (In fact SNR value of 10 was too small.) If we use 
larger SNR value and smaller G, INIIRS value will increase. At 
optimum situation, infinite SNR number can increase NIIRS 
value by 0.344. 
Also table 4 indicates that RER and H values we estimated may 
contain errors. There may be some errors in taking averages of 
edge responses and calculating nominal edge responses. This 
effect is currently under investigation. On the other hand, we 
estimated the edge responses (and RER and H) from natural 
targets. In this case, edge responses may not be in a perfect 
shape compared to the case tarps, for example, were used. RER 
values in ideal case should be larger than the ones estimated 
here. 
Figure 4 plots the three NIIRS values for the six images used 
for experiments. The figure shows very interesting results. As 
mentioned earlier, TNIIRS values were lower than PNIIRS 
values and there is no correlation between PNIIRS and TNIIRS 
(“NIIRS Inspection” in the figure). However INIIRS values 
(“NIIRS by hand” in the figure) showed strong correlation with 
TNIIRS. Although there were shifts between TNIIRS and 
INIIRS, the amounts of the shifts were almost constant. This