Applications to Industrial Quality Inspection - 3D Computer Vision: Efficient Methods and Applications - page 245

off the halogen lamp does not affect the pose estimation results. The computation
time of the system amounts to about 200 ms on a Pentium IV 2 . 4 GHz proces-
sor.
As the described system aims at distinguishing incorrect from correct poses, i.e.
performing a corresponding classification of the inspected object, the rate of cor-
rectly recognised faults (the rate of incorrectly assembled oil caps which are recog-
nised as such by the inspection system) is determined vs. the rate of correctly as-
sembled objects erroneously classified as incorrectly assembled (false positive rate).
This representation of the system behaviour is termed the receiver operating char-
acteristics (ROC) curve. We determined the recognition behaviour of the system for
three different camera viewpoints. Here we concentrate on a typical fault situation
showing angle differences ρ 3 . 5 ◦ with respect to the

reference pose. In the production environment, the engine and thus the attached oil
cap are positioned with a tolerance of about 1 cm with respect to the camera. This
positional variation was simulated by acquiring 125 different images of each exam-
ined fault situation from 125 camera positions inside a cube of 1 cm size which are
equally spaced by 2 . 5 mm in each coordinate direction. This offset is taken into ac-
count appropriately in the pose estimation based on the measured position of the oil
cap in the image. As a first step, a fault is assigned based on each of the three angles
separately if the corresponding angle deviates from the reference value by more than
a given threshold. By varying this threshold, an ROC curve is generated for each an-
gle separately, as shown in Figs. 6.3 a-c. We then generate a combined ROC curve
by assuming that the oil cap is assembled incorrectly if the deviation of at least one
of the pose angles is larger than the corresponding threshold. These thresholds are
then adjusted such that the area under the ROC curve becomes maximum. This com-
bination generally yields an ROC curve showing very few misclassifications on the
acquired test set, as illustrated in Fig. 6.3 d. Both with template hierarchy 1, which
covers a wide range of pose angles with a large grid size, and with hierarchy 2,
covering a region on the viewing sphere close to the reference view with a small
grid size (cf. Table 6.1 ), very high recognition rates close to 100 % are achieved.
With hierarchy 3, which is identical to hierarchy 2 except that the writing on top of
the oil cap has been omitted, the performance decreases, but not significantly: At
a false positive rate of zero, a rate of correctly recognised faults of 98.4 % is still
achieved.
In the second scenario, dealing with the inspection of an ignition plug, we regard
three fault configurations in addition to the reference configuration: The clip is not
fixed, the plug is loose, and the plug is missing (Fig. 6.4 ). The connector and the plug
are modelled as two separate objects such that the offset of the plug in the vertical
direction can be used to distinguish fault configurations from the reference config-
uration. The matching results in Fig. 6.4 show that the vertical position of the plug
relative to the connector can be determined at an accuracy of about 0 . 5 mm, which
is sufficient to faithfully distinguish correctly from incorrectly assembled ignition
plugs.

0 ◦ , ε 2 . 5 ◦ , λ

= = =−

Comparison with Other Pose Estimation Methods At this point, a compar-
ison of the achieved pose estimation accuracy with other systems is illustrative.