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3.2.3 Image Coordinate Measurements. The image
coordinates are the basic input for the self-calibration bundle
adjustment and their accuracy directly influences the final
results. Thus, accurate determination of the image point
location is necessary for better evaluation. Although many
automatic techniques were developed for this purpose (Chen
and Schenk, 1992; Edmundson et al, 1991; Heipke et al,
1992; Paquette et al, 1990; Stefanidis et al, 1990; Vosselman
and Fórstner, 1988), this research is based on existing readily
available and low-cost software and hardware. Thus, the
following solution was adopted: Firstly, due to the lack of
fiducial marks of the digital camera and the poor definition of
the corners and edges of the obtained images, the pixel
location of each image point relative to the top left corner of
the sensor plane was determined. Then, with known pixel
size, the image coordinates of the image points can be easily
obtained by a simple multiplying operation. An assumption is
made here that all elements of the CCD sensor have uniform
size and are evenly distributed.
The digital images are originally stored in the slide-in memory
card supplied with the digital camera. To measure the image
coordinates, the images have to be transferred from the card
to a DVP via a DP-100 Card Processor connected to the
DVP. DVP is a low cost Digital Photogrammetric
Workstation(DPW) based on a PC computer (Nolette, 1992).
It can be employed to measure the location of image points
in pixel units with its interior orientation function, which is
essentially a manual screen digitization process. This
technique seems like a step backwards, but is appropriate
for certain cases where no other special image point
determination tools are available and the number of image
points is not large. Furthermore, to successfully apply existing
software and equipment to arrive at a solution is useful as far
as project cost is concerned. The resulting accuracy of
repetition was 0.4 pixels, equivalent to 3.88 um.
3.2.4 Evaluation of the Calibration Tests. After the image
acquisition and image measurement, the self-calibration can
proceed straightforward. To determine the geometric
characteristics of the digital camera, the following tests with
different APs were designed and carried out for both models:
Table 2. Calibration Tests
Test Description
1 without any interior orientation parameters
2 With X,, y; and c
3 with Xo, yo, C, K,, K;, K;
4 with Xo, Vo» C, k, Ko Ks, pi po
5 with Xo, yo, C, K,, Kj, Ks, pi, pa, A, B
For model |, some of the coordinated points were used as
control points, and the others were treated as check points.
This was also true for model Il; in addition, some of the
unknown intersection points were included in the adjustment
to improve the calibration results.
Due to the absence of the full variance-covariance matrix,
statistical tests cannot be implemented to check the
significance of the individual additional parameter. The
evaluation of the effects of APs, therefore, is based on the
63
root mean square errors(«RMSE) of the image coordinates (o,
and o,) and root mean square discrepancies (o x, 0 y and oy)
for the check points between the resulting photogrammetric
coordinates and the ECDS determined ones.
Since the number and distribution of the control points have
a certain influence upon the final results, the control and
check points in this project were kept fixed for all tests; thus
a comparison can be made for different tests based on the
same reference. The results of all tests from the two models
are tabulated in Tables 3 and 4.
Table 3 RMSE of Image Coordinates After Self-Calibrating
Bundle Adjustment
unit : um (photo scale)
Test Model I Model II
oO, 9, o, 9,
1 78 61 61 49
2 11 11 4 4
3 10 10 2 3
4 4 3 2 3
5 1 2 2 1
Table 4 RMS Discrepancies for the Check Points
unit : mm (object scale)
Test Model | Model II
( photo scale : 1 / 50) ( photo scale : 1 / 300)
Ox O, 0; Ox Oy Oz
1 1.87..,:04.46.. 4,77 28.98 11.33 31.93
2 0.20. 0.53 0.34 108 1.77 4.92
3 0.19 0.26 0.36 1.1811. 1.08 5.86
4 0.16. 0.10, 0.08 056 0095. 497
5 0.05 0.07 0.05 0.50 0.44 0.43
The above results show the following:
. With the self-calibration method, the final accuracy
can be improved significantly. The larger the object
distance, the bigger the improvement that can be
achieved.
° The basic interior orientation parameters play the
most important role in the data evaluation. Without
them, the results are too inaccurate to meet
industrial application requirements.
° The digital camera tested does not have a large
radial lens distortion, which was verified by test 3
where the inclusion of k,, k,, k, does not show
much improvement, with the accuracy gain in Y
direction slightly better than for other two directions.
. The adoption of parameters p,, p,, A, B further
improves the accuracy, which suggests that
decentering lens distortion and certain
imperfections related to the CCD senor plane and
the DVP digitization process were successfully
compensated by these parameters.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
