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Table 1: RanSac performance against random for multiple calibration datasets. ID is an identification number assigned to
each set. Valid Frames refers to the number of frames in the dataset that gave rise to valid left (L), right (R) or stereo (S)
images of the calibration target. RanSac RMS is the RMS projection error for one run of Algorithm 1, while Best, Mean and
Fails are the best and mean RMS values for the Random Algorithm while Fails is the percentage of calibration efforts that
resulted in a RMS error of three pixels or more. For some of the calibration sequences (e.g., 1886) random calibration sets
perform poorly over all three set sizes. While for others (e.g., 1906) smaller set sizes performed quite well almost always.
ID Valid Frames RanSac Random 15 Random 25 Random 35
L R S RMS Best Mean Fails Best Mean Fails Best Mean Fails
1886 689 680 680 8.48 1.14 35.3 96% 1.52 39.2 97% 2.14 31.5 90%
1887 768 744 744 2.06 0.63 18.1 56% 0.82 22.5 51% 0.81 20.9 72%
1895 687 694 687 0.48 0.47 9.40 43% 0.73 12.8 48% 0.51 4.47 9%
1896 596 593 589 32.1 0.76 15.1 77% 1.20 15.3 82% 1.36 5.50 54%
1905 932 929 929 2.25 1.13 30.8 87% 1.36 40.3 94% 20.8 43.6 100%
1906 538 505 498 0.52 0.40 2.86 9% 0.41 1.90 6% 0.43 4.28 19%
1915 636 636 636 5.40 0.74 13.7 89% 1.09 11.7 67% 1.46 21.3 81%
1916 736 733 733 1.15 0.65 12.3 39% 0.70 15.5 61% 0.72 20.8 72%
1923 402 401 401 1.98 0.82 2.29 16% 0.88 1.87 9% 1.01 1.86 18%
1940 217 225 213 0.44 0.42 16.0 29% 0.46 19.0 42% 0.44 12.16 27%
1941 469 497 468 1.08 0.84 4.92 19% 0.96 6.86 27% 1.13 3.23 9%
to obtain these sets could be used to choose multiple
sets of different sizes and then to just “take the best”
resulting set, this approach is not guaranteed to pro-
duce a good set of views. Rather, many of these cal-
ibration efforts will produce camera calibrations that
produce RMS errors much greater than three pixels.
An error that will lead to stereo misalignment or sig-
nificant error in recovered scene structure.
All that being said, in practice the calibration pro-
cess in the lab has the advantage of providing for the
calibration process to be run repeatedly until accept-
able calibration performance results. We have found
that a RanSaC greedy approach can be used to focus
such repeated searches for a good calibration set in a
way that does not require a predetermined calibration
set size and which can use a greedy approach to se-
lect elements of the calibration set so as to optimize
the RMS reprojection error.
The RanSaC algorithm (Algorithm 1) works to
minimize the projection error. This is not the only er-
ror metric that might be used. For example, it would
be possible to construct an error that not only sought
to minimize the reprojection error but at the same time
seeks to maximize the size of the calibration image
set, or the distribution of camera poses used for cali-
bration. This is the subject of ongoing investigation.
ACKNOWLEDGEMENTS
The financial support of the NCRN and NSERC
Canada is greatfully acknowledged.
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