magnitude of the parameter correction convergence 
criteria. 
RESULTS 
Basis of comparison are: 
. model redundancy; 
. camera axis convergences and base; 
. reference variance; 
. plate observation RMS residuals; 
. object coordinate RMS errors; 
. object coordinate RMS standard error ellipsoid: 
. camera position RMS standard error ellipsoid; 
NOOO, WON = 
1. The degrees of freedom is increased in the 
CONSTRAINED solution over the other two due to the 
nature of the constraint equations. 
2. The results for the camera base and orientation are the 
same for each treatment by the CONSTRAINED model but 
differs for the other two. At this stage it is not clear 
whether this is due to the action of the constraint equations 
or is merely coincidental. The MODIFIED model has larger 
base and convergence than the CONVENTIONAL model's 
mean values. The CONSTRAINED model has smaller base 
and convergence angles than the CONVENTIONAL model's 
mean values. 
3. The reference variance increases from the 
CONVENTIONAL to the CONSTRAINED to the MODIFIED 
models indicating progressively less flexible modelling. 
This should be expected as the CONSTRAINED and 
MODIFIED models effectively force the cameras into a fixed 
relationship whereas the CONVENTIONAL model allows the 
cameras to find optimum positions. Any constraining of 
the cameras will result in an increase in the plate residuals 
(see point 4.) and thus the reference variance. 
4. Plate observation RMS residuals of the CONVENTIONAL 
model reduced from the control to the unknown treatment 
as the points are free to find optimum locations. There was 
an expected increase in the RMS values for the other two 
models, however there was no change between the RMS 
values of the two treatments. An increase over the 
CONVENTIONAL model is to be expected as the cameras 
are not free to find optimum individual positions. 
5. Using the RMS point coordinate residuals as an indicator 
of accuracy the CONSTRAINED and MODIFIED models 
yield better results for both treatments than the 
CONVENTIONAL. Of the two new models presented the 
CONSTRAINED model producing the better results. For 
the CONVENTIONAL model there was an average of 560% 
increase in the RMS values from the control to the 
unknown treatments compared to only a 270% increase for 
the other two models. 
6. Using the RMS point standard error ellipsoids as an 
indicator of PRECISION the CONSTRAINED and MODIFIED 
models are similar but worse than the CONVENTIONAL 
model for both treatments. The CONSTRAINED model is 
slightly more precise than the MODIFIED model. 
NOTE: these values are generated from the inverted normal 
equation matrix multiplied by the reference variance. Any 
reduction in the reference variance of each model by better 
weight selection may correspondingly reduce these figures. 
The weights used for the CONVENTIONAL model were 
kept for the other models. 
7. There is an increase in the camera position RMS 
standard error ellipsoid for each model with the MODIFIED 
model having the highest values. In the MODIFIED model 
the right ellipsoid is relative to the left ellipsoid. 
CONCLUSIONS 
Two bundle adjustment models optimised for use with 
stereo photography have been developed. Initial testing of 
these models indicate that they both yield a greater 
accuracy than a conventional bundle adjustment using the 
accuracy of the object coordinates as that indicator. Using 
the error ellipsoids of the object points as an indicator of 
precision the two models presented do not compare as 
favourably with the conventional model. 
The constrained model has a higher degree of freedom 
than the conventional model due to the addition of the 
constraint equations. It also produces the same stereo 
camera invariant parameters whether the object points are 
treated as control or unknown. 
The modified model requires fewer parameters to be solved 
for than the conventional model giving a savings on 
computational power. 
ACKNOWLEDGMENTS 
The author wishes to acknowledge the assistance of Drs 
Harvey Mitchell, John Fryer and Eric Kniest of the 
University of Newcastle, New South Wales and ADAM 
Technology, Perth, Western Australia for their support of 
this research project. 
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