Figure 1a AR display showing a computer-generated grid (orange) superimposed onto a real-world grid, using uncorrected position and orientation readings from an Ascension Flock of Birds magnetic tracker. The poor registration is due partly to the difficulty of calibrating a camera with anything other than a perfect tracker.
Figure 1b AR display using high-precision Faro Technologies Metrecom arm for camera tracking. The foreground elements on the right belong to the mechanical arm. Note the correct registration of both the grid and the arm's coordinate system at the center of the metal sphere (thick white lines).
Figure 2a AR display using partially corrected Ascension Technology Flock of Birds tracking system. Two beacons (marked by small white cross hairs) are used to correct camera orientation. The position reading from the tracker is used for the viewpoint for the computer graphics. Note the poor registration due almost entirely to the incorrect position reported by the magnetic tracker.
Figure 2b AR display using fully corrected Ascension Technology Flock of Birds tracking system. Two beacons (marked by small white cross hairs) are used to correct camera orientation. The position readings from the magnetic tracker are first corrected by the look-up table method.
Figure 3 Setup for collection of samples in our lab, annotated with transformations used. The FOB-to-receiver transformation is reported by the FOB. The Faro-to-rod transformation is reported by the Faro arm. All other depicted transformations are determined by calibration procedures (see text).
Figure 4a Noise from the FOB with no motion of Faro arm (red) and motion of Faro arm (green): relative position error (mm) versus time (sec).

Hash marks are every 0.2 mm and 0.5 sec.

Figure 4b Noise from the FOB with no motion of Faro arm (red) and motion of Faro arm (green): relative orientation error (deg) versus time (sec).

Hash marks are every 0.5 deg and 0.5 sec.

Figure 5a 3D view of the position error at the collected samples.
Figure 5b Noise in position readings from the FOB as a function of distance from the transmitter.

Hash marks are every 0.2 m (starting at 0.4 m) for distance and every 0.01 m (starting at 0.0 m) for noise.

Figure 5c Noise in orientation readings from the FOB as a function of distance from the transmitter.

Hash marks are every 0.2 m (starting at 0.4 m) for distance and every 0.01 m (starting at 0.0 m) for noise. See text for how the orientation noise is measured.

Figure 6a Calibration table at half resolution, with the same viewpoint as in Figure 5a.
Figure 6b The y=0 plane of the table.
Figure 6c The x=0 plane of the table.
Figure 7a Verifying the validity of the correction method. This graph shows only that the table accurately reflects the raw samples. Position error as a function of distance before and after correction. Before correction, the average position error is 38.1 mm and the maximum position error is 238 mm. After correction, the average is 5.0 mm and the maximum is 149 mm.

Hash marks start at 0.4 m and increment by 0.2 m for distance from transmitter, and start at 0.0 m and increase by 0.05 m for orientation error.

Figure 7b Verifying the validity of the correction method. This graph shows only that the table accurately reflects the raw samples. Orientation error as a function of distance before and after correction. Before correction, the average orientation error is 3.1 deg and the maximum orientation error is 8.1 deg. After correction, the average error is 1.3 deg and the maximum error is 7.1 deg.

Hash marks start at 0.4 m and increment by 0.2 m for distance from transmitter, and start at 0 deg and increase by 1 deg for orientation error.

Figure 8a Results from the correction method. Position error as a function of distance before and after correction. Before correction, the average position error is 28.7 mm and the maximum position error is 108 mm. After correction, the average is 6.1 mm and the maximum is 23.1 mm.

Hash marks start at 0.4 m and increment by 0.2 m for distance from transmitter, and start at 0.0 m and increase by 0.05 m for orientation error.

Figure 8b Results from the correction method. Orientation error as a function of distance before and after correction. Before correction, the average orientation error is 3.5 deg and the maximum orientation error is 6.64 deg. After correction, the average error is 2.1 deg and the maximum error is 6.55 deg.

Hash marks start at 0.4 m and increment by 0.2 m for distance from transmitter, and start at 0 deg and increase by 1 deg for orientation error.

Figure 9 Picture of support structure used to conduct the experiment outside.
Figure 10 Apparatus to allow (limited) freedom in orientation while maintaining (nearly) constant position.
Figure 11 Graph of orientation error as a function of the azimuth and elevation angles of the receiver. The longer axis of the reference grid is the azimuth angle, ranging from -180 degrees to 180 degrees with lines every 20 degrees. The shorter axis is elevation, ranging from -90 degrees to 90 degrees, with lines every 20 degrees. The hole in the graph corresponds to the position of a wooden support structure used; no significance should be attributed to it.

This work is part of the UNC Ultrasound Visualization project.

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Last Modified: 15 May 98 by Mark A. Livingston