PHD Thesis - Institute for Computer Graphics and Vision - Graz ...

7.2. Localization 122
registration process. The 3D points are exactly located on a plane, because they are computed
by projecting 2D points onto a scene plane. Thus they do not contain noise. However the
2D − 2D point correspondences are obtained by correlation based matching and therefore are
assumed to be distorted by noise. We assume that the 2D points within the landmark from the
actual view are distorted by Gaussian noise. In the following we will check experimentally how
the Gaussian noise influences the pose estimation accuracy.
π 0
π 1
Figure 7.5: Pose estimation from 3D ↔ 2D point correspondences. The 3D points are exact,
the 2D points are assumed to be disturbed by Gaussian noise. The effect of the noise is that
the rays from the point correspondences do not intersect exactly at the camera center.
The influence of Gaussian noise distorted 2D points is evaluated with synthetic data. Figure
7.6 shows the results of the Lu and Hager pose estimation for our special situation. Pose
estimation for synthetic 3D − 2D point correspondences has been performed with noise added
to the 2D coordinates of the landmark points from the query image only. Gaussian noise of
standard deviation σ = 0.1, 0.3 and 0.7 (in pixel) was added to the 2D points. The experiment
has been repeated 1000 times. In Figure 7.6 each point denotes an estimated camera position.
Figure 7.6(a-c) show the distribution of the camera position for Gaussian noise with σ = 0.1
in different views. The blue cross marks the noise-free computed camera position. Noisy 2D
coordinates create a spherical distribution around the true position. Perpendicular to the line
connecting the true position and the 3D coordinates the points are spread out widely while the
depth distribution is small. This experiment shows that Gaussian noise influences the pose estimation
from a small number of point correspondences within a small image region (landmark)
significantly.
Next we investigate a solution to alleviate the influence of noise in the 2D − 2D point correspondences.
We analyze the effect of estimating the pose from a small sample of correspondences
only instead of using all 3D ↔ 2D correspondences. In the following experiment the pose is
estimated from 1000 random samples of size 5, 10, 20 out of 56 correspondences. The correspondences
are obtained by correlation based matching. The estimated poses are shown in
Figure 7.7. Sub-sampling generates a distribution of poses around the pose computed with all