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Three different methods of weighting the pixels were
used, being binary (Bl), grey value (GV) and grey value
squared (GV^2). The binary method applied a weight of
one to each pixel, the grey value method weighted each
pixel by its grey value and therefore, the brighter the grey
value the more importance was put on the pixel. The
grey value squared method used the square of the grey
value at the weight to be applied, thus exaggerating the
effect as described in the grey value method. Each
method produced a separate set of observations and
each was processed through the bundle adjustment. The
results from each method have been tabulated in
Section 5. However, only the binary results have been
graphed in Figures 5, 6, 7 and 8 as the results from each
method were very similar.
The program described above was customised to output
files in the format compatible with the bundle adjustment
being used. Three bundle adjustment programs were
used initially for comparisons, with SPGA (Fraser, 1982)
eventually being the sole bundle adjustment used as it
was flexible, fast and efficient.
Prior to processing the observations in the bundle
adjustment, the decentering distortion parameters P1 and
P2 were determined using a plumbline lens calibration.
These values were used as initial values in the bundle
adjustment, to overcome the correlation problems with
the offsets to the principal point, as previously
mentioned.
5. RESULTS
The results from the calibration procedure have been
tabulated and graphed in this section and include the
calibration parameters for each camera, an analysis of
the benefits of averaging images from video cameras,
and an analysis of the benefits of radiometric corrections
for ‘bad’ pixels and a comparison of the suitability of each
camera for close-range photogrammetric measurement.
The calibration parameters for each camera are shown in
Table 4. This table includes: the root mean square of the
image coordinate errors in x and y; the focal length; the
offsets to the principal point in x and y; lens distortion
parameters K; , Ke , P; and P» ; and the degrees of
freedom from each bundle adjustment. From this table,
it can be seen that the Single Frame of the Right Philips
camera is only marginally worse in image coordinate
RMS than the averaged binary, GV or GV squared,
however, the averaging does improve the visual quality of
the images, removing phase patterns and line jitter. The
focal length was determined consistently for each
camera. The Right Philips camera was shown to have a
relatively large x component in the principal point offsets.
The final values for P; as shown in Table 4 vary by only
5-1096 from the initial values determined by the
plumbline lens calibration.
The radiometric investigation, as described in
Section 3.2, determined that there were no 'bad' pixels in
these digital still cameras, and 'bad' pixels found in the
analog video cameras were more due to sampling and
signal transmission than problems in array. This was
141
concluded after many images were acquired to find the
'bad' pixels in the video cameras, and the results were
not consistent, but changed with each image.
The lens distortion parameters are graphed in Figures 5,
6, 7 and 8 in Section 5.3. The resultant values for the
binary, grey value and grey value squared methods were
all very similar, as can be seen in Table 4 and only the
results of the binary method are graphed. The large
radial distortion of the Apple Quicktake and the Logitech
Fotoman should be noted. At a radial distance of 2mm,
it is equivalent to a shift of 2 pixels, and at the edges of
the array amounted to approximately 6 to 7 pixels. This
would have to be considered when using the cameras for
photogrammetric applications. Any targets or objects to
be measured would best be situated close to the centre
of the image to ensure the best results.
5.1 Statistical Results of Target Centroiding.
Camera Average Average Average Pixels
Maximum Minimum Threshold above
GV GV (0-255) Threshold
Left Philips 253.54 6.92 167.19 117.10
Right Philips 253.79 2.92 165.72 131.48
Apple Quicktake 254.55 1.18 159.76 24.19
Logitech Fotoman 255.00 12.76 170.98 29.38
Table 2. Statistical Results of Target Centroiding
As referred to in Section 4, Table 2 shows that the
contrast between the targets (average maximum grey
value) and the background (average minimum grey
value) on the images was very high, which is beneficial
for the centroiding of the targets.
5.2 Additional Parameters. See Section 3.1 for a
mathematical description.
Camera Di b2 Ds ai
Left Philips
Binary 0.246E-3 0.0298 ** 0.452E-3 0.202E-2 *
GV 0.274E-3 0.0298 ** 0.351E-3 0.221E-2 *
GV^2 0.259E-3 0.0298 ** 0.427E-3 0.221E-2*
Right Philips
Binary 0.270E-3 0.0298 ** -0.302E-4 0.173E-2 *
GV 0.269E-3 0.0298 ** -0.859E-4 0.174E-2 *
GV^2 0.256E-3 0.0299 ** -0.721E-4 0.171E-2 *
Single Frame 0.112E-3 0.0298 ** 0.137E-3 0.191E-2 *
Apple Quicktake
Binary 0.273E-4 0.518E-4 -0.331E-4 -0.380E-4
GV 0.233E-4 0.448E-4 -0.210E-4 -0.484E-4
GV^2 0.267E-4 0.315E-4 0.249E-5 -0.418E-4
Logitech Fotoman
Binary 0.698E-4 0.729E-4 -0.716E-4 -0.933E-4
GV 0.689E-4 0.752E-4 -0.815E-4 -0.894E-4
GV^2 0.716E-4 0.720E-4 -0.770E-4 -0.830E-4
* Significant ** Very Significant
( Significance determined by Fisher statistical analysis,
see Fraser, 1982)
Table 3. Additional Parameters.
The most notable additional parameter in Table 3 is that
of b» for the Philips cameras, showing that the actual
size of the pixel in the y direction is 396 different from the
initial value used.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
