Guehring, Jens
In a previous paper (Brenner et al., 1999) we have compared polynomial depth calibration, a standard direct calibration
technique to model based photogrammetric calibration. As a conclusion, we found that both calibration procedures
yield comparable accuracies. However, in our opinion it is advantageous to obtain the model parameters explicitly. The
fact, that model parameters hold true for all the measurement volume of the sensor omits problems with measurements
lying outside the volume originally covered by calibration. In addition, residuals and the covariance matrix give a clear
diagnosis for the determination of the calibration parameters and object point coordinates. Finally, point
correspondences that have been established between multiple cameras can increase redundancy and thus give more
accurate results.
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Figure 9. Calibration plate with automatically detected target points as seen by the camera (a) and by the projector (b).
4.2 Photogrammetric Calibration
Since the projector is able to project horizontal and vertical patterns, it can be modeled as an inverse camera. Two-
dimensional image coordinates can be obtained by phase shift and line shift processing. Thus, the projector can be
calibrated using a planar test field and a convergent setup.
The test field we use consists of an aluminum plate, on which we fixed a sheet of self-adhesive paper showing white
dots on a black background. Five of those targets are surrounded by white rings. These rings allow to determine the
orientation of the test field. In the next step all visible target points are measured and identified fully automatically.
Then, image coordinates for the camera are obtained by computing the weighted centroid. After that, corresponding
projector coordinates are computed with sub-pixel accuracy by a sampling at the centroid positions.
At present, we export these measurements and compute the bundle solution for the calibration parameters externally
using the “Australis” software package from The Department of Geomatics of The University of Melbourne.
We use a camera model with 10 parameters, namely the focal length c, the principal point offsets Ax and Ay, Kj,
K, and K, for radial symmetric distortion, P,, P, for decentering distortion and finally B, and B; for scale and shear
(Fraser, 1997).
—
With X=x-Ax, y 2 y—Ay and the square of the radial distance r^ 2 X^ y^, the radial symmetric distortion is
computed by evaluating the polynomial
dr-rK,*r'K,*r*K,
and applied to the x and y coordinates in the following way:
dr, =x dr
dr, =ydr.
Decentering distortion is modeled by
dd, =(r* +2X")P +2xyP,
dd =337R+0"+24)R,.
336 Ë International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.
