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

7.2. Localization 124
(a)
(b)
(c)
Figure 7.7: Effect of pose estimation from random samples. The blue dot marks the pose
estimate using all available correspondences. (a) Sample size = 5 (b) Sample size = 10 (c)
Sample size = 20
A re-projection error ɛ can be defined as the distance between q ↔ ˆq.
ɛ = ∑ ‖q i − ˆq i ‖ (7.22)
Given multiple pose estimates the most accurate one can be identified as the one with the
smallest re-projection error ɛ. We analyzed the re-projection error for the pose estimates shown
in Figure 7.7. The re-projection error is coded in the point color. A dark green coded pose has
a re-projection error smaller than the median re-projection error. For a light green coded pose
the re-projection error is bigger than the median error. The results are shown in Figure 7.8.
The pose estimate using all available point correspondences is marked as blue dot. The pose
estimated with the smallest re-projection error is the red dot. It is evident that the best pose
estimate does not coincide with the all-points solution. Furthermore, the color coding reveals
the area in 3D space where the best pose estimate is located. The figure also reveals that the
distribution gets more compact when bigger sample sets are used. A small sample size will
create widely spread out hypotheses.
The conclusion is now, that the all-points solution will not guarantee the best pose estimate.
A sub-sampling scheme computing multiple pose estimates will in any case contain a better
pose estimate as the all-points solution. Scoring the different hypotheses with the re-projection
error the best hypotheses can be selected. However, when dealing with a single landmark match
additional 3D −2D point correspondences will not be available to compute a re-projection error.