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6.5 Exercises 299

2. Detect and match feature points across neighboring frames and chain them into feature
tracks.
3. Compute homographies between overlapping frames and use Equations (6.56–6.57)to
get an estimate of the focal length.

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4. Compute a full 360 panorama and update your focal length estimate to close the gap
(Section 9.1.4).
5. (Optional) Perform a complete bundle adjustment in the rotation matrices and focal
length to obtain the highest quality estimate (Section 9.2.1).

Ex 6.7: Target-based calibration Use a three-dimensional target to calibrate your camera.
1. Construct a three-dimensional calibration pattern with known 3D locations. It is not
easy to get high accuracy unless you use a machine shop, but you can get close using
heavy plywood and printed patterns.
2. Find the corners, e.g, using a line finder and intersecting the lines.

3. Implement one of the iterative calibration and pose estimation algorithms described
in Tsai (1987); Bogart (1991); Gleicher and Witkin (1992) or the system described in
Section 6.2.2.

4. Take many pictures at different distances and orientations relative to the calibration
target and report on both your re-projection errors and accuracy. (To do the latter, you
may need to use simulated data.)

Ex 6.8: Calibration accuracy Compare the three calibration techniques (plane-based, rotation-
based, and 3D-target-based).
One approach is to have a different student implement each one and to compare the results.
Another approach is to use synthetic data, potentially re-using the software you developed
for Exercise 2.3. The advantage of using synthetic data is that you know the ground truth
for the calibration and pose parameters, you can easily run lots of experiments, and you can
synthetically vary the noise in your measurements.
Here are some possible guidelines for constructing your test sets:

1. Assume a medium-wide focal length (say, 50 field of view).
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2. For the plane-based technique, generate a 2D grid target and project it at different
inclinations.

3. For a 3D target, create an inner cube corner and position it so that it fills most of field
of view.

4. For the rotation technique, scatter points uniformly on a sphere until you get a similar
number of points as for other techniques.

Before comparing your techniques, predict which one will be the most accurate (normalize
your results by the square root of the number of points used).
Add varying amounts of noise to your measurements and describe the noise sensitivity of
your various techniques.