Full text: Proceedings International Workshop on Mobile Mapping Technology

3.4 Self-Calibration Model 
The additional parameter model for each of the two CCD cameras 
was as follows: 
Ax = - x p - (x/c) 5c + K] x r 2 + aix 
Ay = - y P - (y/c) 5c + K! y r 2 
where 5c is the correction to the estimate of principal distance, c, 
Ki is a coefficient of radial distortion, ai is the affinity term 
relating to differential scaling between the x and y image 
coordinates, x p and y p are the principal point coordinates, and r is 
the radial distance. Previous calibrations of the two Pulnix 
cameras had established that the radial distortion followed a near- 
cubic profile (hence the inclusion of K t only) and the level of 
decentering distortion was insignificant considering the degree of 
metric accuracy required. 
The presence of the affinity term aj was to prove problematic, as 
anticipated, especially in regard to the high projective coupling 
that existed between this parameter and the coordinates (x p , y p ) 
of the principal point. Even in instances when this term was 
suppressed, the recovery of interior orientation elements was 
quite weak. 
As a consequence, two basic self-calibration models were 
examined, one as represented by Eq. 1 and the other comprising 
principal distance (5c) and radial distortion (KO terms only. In 
the latter case, a^ x p and y p were suppressed to zero, with the 
image coordinate reference system being assumed to have its 
origin at the centre of the CCD array. Although this was unlikely 
to be the case in reality, the mildly convergent geometry of the 
two cameras offered the possibility of a significant level of 
projective absorption in the EO of errors arising from an 
erroneous interior orientation. 
Self-calibrating bundle adjustments for the 2-camera, 24-image, 
225-point network were performed for each additional parameter 
model, using both free-network datum constraints (no explicit 
control points) and a control configuration of 22 object target 
points. In terms of object space triangulation accuracy, all four 
adjustments yielded essentially the same results. Over 200 
ground checkpoints were available and in all cases the RMS 
coordinate discrepancies were within a centimetre or so of S x = 
0.15m, S Y = 0.17m and S z (vertical) = 0.16m. While this 
accuracy is somewhat less than the design precision of ct X yz < 
0.1m, the degradation was anticipated given both physical 
circumstances of the imaging configuration and concerns about 
the metric integrity of the analog-to-digital conversion of the 
SVHS video data. An RMS error of image coordinate residuals of 
approximately 5 pm was obtained in all four adjustments. 
In terms of the EO, the approaches of free-network and absolute 
ground control yielded basically the same solutions for camera 
position (X C ,Y C ,Z C ) and orientation (to, tp, k). This was 
understandable given that the preliminary object point 
coordinates employed in the inner-constraint adjustment were in 
fact the ‘true’ ground coordinates. 
As a result of the photogrammetric calibration process, the EO of 
each of the two CCD cameras was established with respect to the 
desired geodetic reference system. Aircraft position and attitude 
are also available at each exposure via the on-board kinematic 
GPS system coupled with the inertial positioning sensors. The 
nominally constant offset of position and orientation between the 
aircraft and the stereo camera set up was thus obtained and could 
be applied to determine the absolute object space coordinates of 
triangulated image features. This followed a two-stage process. 
In the first step the object space coordinates are determined with 
respect to the ‘relatively oriented’ stereo cameras. The final 
ground coordinate values are then obtained in a second step via a 
similarity transformation which takes into account the position 
and orientation measured by the onboard GPS/inertial system. 
It must be recalled that within the camera self-calibration network 
there was typically a dozen or more imaging rays to each target 
point. Routine application of RCAMS, on the other hand, 
involves only 2-ray intersection, often to features where it is 
difficult to precisely measure the corresponding coordinates of 
homologous image points. Coupled with this accuracy issue is 
the metric quality of the SVHS video imagery and the fact that 
the final EO cannot be assumed to be ‘fixed’ due to aircraft wing 
flexure and subsequent camera instability. A practical, analytical 
pre-analysis of object point intersection precision is therefore 
precluded to a large extent, for it could give only a vague 
indication of accuracy in the presence of such systematic error 
influences on the photogrammetric triangulation process. 
For the powerline mapping project, field accuracy checks were 
essentially the only feasible means to gain a reasonable estimate 
of the net impact of all error sources on the stereo triangulation 
process. Some 50 or more accuracy checks were performed on 
both powerline features (mainly pole locations) and adjacent 
trigonometrical survey markers. Positional errors were found to 
range up to 3.5m, with the achieved RMS positional accuracy 
(absolute position) of RCAMS being close to lm. This was 
consistent with the level of accuracy sought by the power 
company sponsoring the work. 
In the period following the field calibration process described, the 
airborne RCAMS was employed for ‘vegetation mapping’ of 
some 2300 km of 66 kv powerlines in the State of Victoria. The 
survey involved the positioning of 15,000 poles and the recording 
of countless instances of vegetation encroachment into the 
inspection and clearance space around the powerlines. This 
information is critical for fire risk assessment. The task

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