International Archives of the Photogrammetry, Remote S 
43 Camera Rotation Accuracy 
Rotation parameters are estimated using a normalized quaternion 
d representation. As for the camera position, we can extract a 
variance covariance matrix from V. This matrix V4 will repre- 
sent the variance covariance matrix of the quaternion. Because of 
the normalization constraint, Vg does not provide any direct in- 
formation on the uncertainty of the rotation. Hence, we will use 
a backward transport of the covariance (Hartley and Zisserman, 
2002). We can define a rotation by an axis uo, y and an angle 6. 
Upp = (cos($) sin(s), sin($) sin (s), cos(1))' (25) 
LetQ: R^ — IR^ be a differential mapping taking a parameter 
vector 7 = (8, &, tb) to a measurement vector q. 
) j 0 
QU, 6,4) = (cosgsingugy) (26) 
Hence. we can deduce an approximation ofY 3.5 
Dogs 7 (JoV7 Je)" (27) 
With MT designing the pseudo-inverse of matrix M and Ja be- 
ing the Jacobian of Q. Again, given a significance number oa, 
we can associate a covariance ellipsoid to the estimated camera 
rotation £ (8, à, v, a). 
4.4 3D Points Accuracy 
We use the same method as in the Camera position Accuracy sec- 
tion. Again, given a significance number œ, we can associate to 
a tie point or a GCP a covariance ellipsoid £(f, o). One impor- 
tant application of this accuracy estimator is to predict roughly 
the accuracy of a 3D reconstruction. 
4.5 3D Lines Accuracy 
Line accuracy can be computed using our bundle adjustment 
technique. This part is still under development in our system. 
Some error propagation algorithms involving lines can be found 
in (Taillandier and Deriche, 2002) or (Heuel, 2001). 
5. EXPERIMENTS 
5.1 Test fields description 
Calibration polygon The first test field contains 16 images of 
a calibration polygon with 75 materialized GCP with an accuracy 
of 0.1 mm (see Figure 2). The polygon was created in order to 
precisely determine camera internal parameters. Here, it is used 
to assess the quality of accuracy prevision. 
Building facade The second test field is made of 16 images of 
a facade (see Figure 3) taken from a mobile vehicle using a stereo 
rig. It is representative of forthcoming image acquisitions from a 
vehicle. At a given instant £ two cameras along a vertical baseline 
take pictures of building facades. À more accurate description of 
the acquisition process can be found in (Bentrah et al., 2004). 
Nine tie lines have been manually selected. Thirty GCP have 
been measured by a surveyor using classical topographic tools 
with an accuracy of 0.25mm. 
5.2 Simulation 
In order to verify accuracy previsions coming from the Hessian 
matrix inversion, two different experiments have been carried out 
on each test field. In each case, a perfect solution has been cre- 
ated. The first experiment (A) adds simply a Gaussian noise on 
all observed value (tie points, tie lines and GCP). The second one 
ensing and Spatial Information Sciences, Vol XXXV, Part B3. Istan 
bul 2004 
1 m. 
  
Figure 2: Calibration polygon test field. 75 materialized GCP 
have been measured with an accuracy of 0.1 mm. 
  
Figure 3: Building facade test field. A stereo rig mounted on 
a mobile vehicle has taken 16 images of a facade. 30 GCP are 
available. 8 vertical and one horizontal tie lines have been manu- 
ally selected. 
      
International Ai 
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much more real 
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