Conformal Geometric Algebra in Stochastic Optimization Problems ...

8.2. POSE ESTIMATION 213
8.2.3 Experiments
The experiments presented here are throughout real world experiments. For both
methods no rigorous calibration was carried out. The only thing that was done was
to determine the focal length and the image center from the outline of the iris-like
image as described on page 208. For equation (8.4) the mirror radius rM = 40mm
and the focal length fmm = 16.7mm were used as intrinsic parameters. Note that
these values come directly from the manufacturer.
Throughout all experiments, observations were taken from the sensory data by
hand. The reason is a lack of sufficiently robust and accurate automatic methods
coping with sensitivity regarding lighting conditions, ‘curvy’ mappings of straight
lines, especially for loosely calibrated systems, and the related non-uniform imaging
resolution, which decreases towards the image center as demonstrated on the right
side of figure 8.6. Another issue is the correspondence problem, see item 2 of
the general pose estimation assumptions on page 136, which is likely the biggest
challenge in pose estimation. A human observer can, under these circumstances and
with some effort, ensure that the underlying assumptions are not violated. Thus
assessing the method as such, i.e. its consistency, is possible.
Point-Line
Two experiments were conducted using aSony DxC-151AP camera with a resolution
of 768 × 576 pixels.
In the first set of experiments, a pose estimation with respect
to a model house was done. Tags were attached to
the house at certain positions so as to allow for a smooth
feature point retrieval from the omnidirectional pictures;
each tag reflects one vertex in the known house model.
The image coordinates corresponding to these points of
interest were extracted manually. One illustrative view
of the model house and all visible feature points, as extracted,
is depicted on the left side of figure 8.8 (showing
only the relevant part of the sensed image). The house
dimensions in cm are approximately 21×15×21.
Fig. 8.7: Camera, but
with pinhole objective
Two sequences were conducted, one with 35.1 cm (A) and one with 52.4cm (B)
orthogonal distance between the house and the optical axis of the sensor. In order
to simplify the acquisition of ground truths the rotation plane was perpendicular
to the optical axis. The house was rotated in 10 ◦ steps from 60 ◦ down to 0 ◦ . The
respective errors relative to the 60 ◦ -rotation were measured.
The results are listed in table 8.1. Note that the house appears flat in the 0 ◦ -image,
i.e. the usable 3D-model points are nearly coplanar such that the estimation result
is affected. The mean error in the rotation was 1.65 ◦ and the mean error in the
planar distance was 0.43cm. The estimated height of the sensor relative to the
house was 27.5 ± 0.4cm, which is within the measurement error of ground truth
27.55 ± 0.4 cm.