The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
order to assess equivalence, the same dataset from the same 
camera was calibrated three times, each time using a different 
distortion model. If the distortion models are equivalent, the 
resulting IOP should be equivalent. In order to compare the 
three sets of IOP, the stability analysis software was used to 
assess the IOP similarity. 
Ax = K,(r 2 -R„)x + fC 2 (r 4 -R^)x + P,(r 2 + 2x 2 ) + 2P 2 xy-A,x +A 2 y 
Ay = K,(r 2 -R 2 )y+K 2 (r 4 -Ro)y + P 2 (r 2 +2y 2 ) + 2P,xy +A,y (1) 
Ax = x(K 0 + K,r 2 + K 2 r 4 + K 3 r 6 ) + (1 + P 3 r 2 )(P, (r 2 +2x 2 ) + 2P 2 xy) 
Ay = y(K 0 + K,r 2 + K 2 r 4 + K 3 r 6 ) + (1 + P 3 r 2 )(2P,xy + P 2 (r 2 + 2y 2 )) ( 2 ) 
^ (R 0 + R,r +R 2 r + R,T + R„r 4 + R 5 r 5 + R 6 r 6 R 7 r 7 ) — 
“ X (3) 
+ (1 + P 3 r 2 + P 4 r 4 )(P, (r 2 + 2x 2 ) + 2P 2 xy) 
^ (R u + R,r+R 2 r‘ + R 3 r 3 + R 4 r +R 5 r +R 6 r + R 7 r )_ 
r 
+ (1 + P 3 r 2 + P 4 r 4 )(2P,xy + P 2 (r 2 + 2y 2 ) 
The results from this equivalence analysis are presented in 
Table 6. The RMSE values are all well under the size of a pixel. 
From these experiments, we can thus conclude that the tested 
distortion models are equivalent. 
Distortion models: 
Camera 1 
RMSE (mm) 
Camera 2 
RMSE (mm) 
Krauss vs. SMAC 
0.0012 
0.0009 
Krauss vs. PCI 
0.0010 
0.0011 
SMAC vs. PCI 
0.0017 
0.0004 
Table 6: Equivalence analysis 
5.4 Photogrammetric Reconstruction 
Sections 5.1 and 5.2 have dealt with the calibration and stability 
of the investigated cameras. In this section, the achievable 
accuracy that can be obtained using the investigated terrestrial 
cameras is analyzed. To assess the accuracy, the point targets 
on the calibration test field were surveyed to millimetre 
accuracy, using a Total Station. Photogrammetric 
reconstruction was then performed, using the IOP from 
calibration session 1 for Camera 1, and the imagery data 
collected from session 3. The point targets were extracted 
automatically from the imagery, using the procedure outlined in 
Section 2.1. An RMSE analysis was performed between the 
surveyed and reconstructed points. The mean, standard 
deviation, and RMSE results are tabulated in Table 7. From 
these results, it can be concluded that the achievable accuracy 
of these cameras has been determined to be within one 
millimetre of the results obtained using a Total Station. In 
addition, considering the average object space pixel size is 2.3 
mm, the RMSE from the reconstructed object space compared 
to the Total Station survey results are less than half a pixel size 
in the object space. 
Mean AX± o x (mm) 
-0.38 ±0.87 
Mean AY ±0Y (mm) 
-0.38 ± 1.04 
Mean AZ± <i z (mm) 
-0.38 ±0.77 
RMSE X (mm) 
0.92 
RMSEy (mm) 
1.07 
RMSE Z (mm) 
0.83 
RMSEmtai (mm) 
1.64 
Table 7: Mean, standard deviation, and RMSE for the comparison 
between the reconstructed and surveyed coordinates 
6. CONCLUSION 
This paper has addressed several issues that are coming to 
surface with the increase in adoption of amateur digital cameras 
for photogrammetric mapping applications. In particular, the 
method and quality of camera calibration, as well as long-term 
stability has been investigated. First a low cost and efficient 
calibration technique was outlined, in which a test field 
composed of linear and point features was utilized. An 
automated method for the extraction of the point and line 
features was then summarized, after which several stability 
analysis methods were presented. The stability analysis was 
then used to evaluate the equivalency of different distortion 
models. Finally, the achievable accuracy of the tested terrestrial 
cameras was investigated. These procedures were performed on 
two Prosilica GC1020 CCD cameras, and the experimental 
results were presented in Section 5. Based on these results, it 
was determined that the tested amateur digital cameras 
remained stable over time, and provided an accuracy of one 
millimetre. These results can be used to promote the use of 
small format digital cameras as an attractive alternative for 
convenient and inexpensive close-range applications, such as 
deformation monitoring of building structures. Furthermore, 
although the tests conducted in this work were performed on 
small format digital cameras for close-range photogrammetric 
applications, the outlined calibration and stability procedures 
and tools are valid for use in analysis for aerial applications. 
ACKNOWLEDGMENT 
The authors would like to thank the GEOIDE Network of 
Centres of Excellence of Canada (TDMASR37) and NSERC for 
their partial funding of this research. 
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