Precision evaluation using measured distances #2
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This was referenced Oct 8, 2018
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Good validation results indeed. Still, they could get even better if the calibration plate was more tilted to obtain even more perspectively distorted images. Perspective distortion is needed to tell range from focal length after all, see Strobl et al.'s "On the Issue of Camera Calibration with Narrow Angular Field of View." |
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The precision evaluation was conducted with dataset1, dataset2 and
dataset3 of calibrel_testdata.
The three dataset were sampled from the same dataset actually which was
split into three parts. So camera parameters calculated from them should
be consistent to each other.
The calibration board has the following information. Pattern width and
height was 16 and 10 respectively. It's square size was 15mm ideally.
The chessboard pattern was printed with an ordinary office laser
printer and then pasted to a glass panel which was not so perfect planar
structure.
The following results were gotten with
test_calibrelwith arguments of-d=224.14 --winSize=7Camera parameters found with OpenCV's standard method
RMS reprojection errors
With k2 = p1 = p2 = 0 were set. We got the following.
RMS reprojection errors
Parameters such as fx, fy and k1 are so much different between the above
two circumstances (with and without k2 = p1 = p2 = 0).
Camera parameters found with refining 3D object points
RMS reprojection errors
With k2 = p1 = p2 = 0 were set. We got the following results.
RMS reprojection errors
We can see parameters (e.g. fx, fy and k1) found with this method are
more consistent and robust than OpenCV's standard method.
Refined 3D grid points
For the above 3 datasets, with and without k2 = p1 = p2 = 0, we got 6
list of refined 3D target grid points. Firstly, Situations with and
without k2 = p1 = p2 = 0 were compared. The following table shows the
coordinates delta between these two situations. And we can see the
coordinates are very consistent.
The delta between refined positions of three datasets were also
computed. In the following table,
d1 - d2means coordinates differencebetween refined positions generated with dataset1 and dataset2.
d1 - d3and
d2 - d3keep the similar meaning.The refined coordinates agree to each other very much.
Refined 3D grid corner distances compared to measured distances
We chose 4 corners p1, p2, p3 and p4 as shown below to evaluate the
accuracy of the refining process.
In board frame the coordinates of the 4 points are: p1(0, 0, 0), p2(x2,
0, 0), p3(x3, y3, z3) and p4(x4, y4, 0).
When Refining 3D grid points, p1, p2 and z4 of p4 are fixed according to
Strobl's paper. x2 was measured as the distance between p1 and p2. For
the board in dataset1, dataset2 and dataset3, x2 = 224.14.
The refined 3D grid corners are shown in the following table.
(x2 = 224.14).
We measured the distances between combinations of p1, p2, p3 and p4 with
a vernier caliper of 0.02mm resolution (The uncertainties of the
measurements are probably larger than 0.1mm I think). Then the computed
distances from above data were compared to measured one as the following
table.
The differences between hypothesis and measured values indicate that the
printed paper is not accurate at all. The computed distances agree very
well with measured values. The mean error is 0.0687mm with standard
derivation of 0.0435mm. The maximum error is 0.138mm.
In conclusion, this new extended camera calibration method is very
helpful when accurate calibration board is not available which is a very
common case for most people.
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