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Ground Truth
X
Z PCA estimate
Projection
Euclidean Distance
Figure4.VisualizationofcalculationoftheEuclideandis-
tance between the ground truth vector and the vector esti-
matedby thePCA
ally, with machine learning approaches, the error in
the 2D projection of the 3D bounding box is mea-
sured [13]. Since the estimation error can be mea-
sured directly in this case, the Euclidean distance is
used as a metric instead. To ease the calculation of
the ground truth vector, environment knowledge has
been used to eliminate one dimension out of the 3D
vector. Since the target3Dmodel isguaranteedtoal-
ways be parallel to the ground, as is the camera, the
rotationaround theZ-axisdefined inFigure1canbe
ignored. Furthermore, as this approach is being used
in an industrial grasping use case where the indus-
trial robot has to grab the target object perpendicular
to the estimated plane, the Y-component of the esti-
mated PCA vector can be ignored and therefore set
to 0. In order to get two vectors of the same length
for further correct calculation, both, the ground truth
vector and the vector estimated by the PCA have
to be normalized. This results in an Euclidean dis-
tancebeingcalculatedbetween twovectors in theX-
Zplane. Thisprocess is shown inFigure4.
Equation (7) shows the calculation of the ground
truth vector, where the ~gtvector is the ground truth.
The X and Z components of the ground truth vector
can be obtained by calculating the direction of the
ground truth vector rotated byβ depicted in Figure
3.
~gt= ( sin(β)
0
cos(β) )
(7)
Equation (8) shows the calculation of the error in
formof the Euclideandistance.
r= √
(x1−x2)2+(z1−z2)2 (8)
x1 andz1denote therespectivecomponentsof the
ground truth vector. x2 and z2 denote the respective Table 1. List of positions that were used for the experi-
ments.
Angle [°] Distance [cm]
+/-0
30,35,40,45,50,75+/-10
+/-20
+/-40 30,35,40,45,50
+/-10aroundcamera
30,35,40,45,50,75+/-20aroundcamera
+/-30aroundcamera
30 35 40 45 50 75
Object Distance [cm]
0.0
0.1
0.2
0.3
0.4
0.5 Boxplot - Angle +/- 0°
Figure5.Visualizationof the resultswith theobjectbeing
placedon the optical axis
components of the calculated normal vector by the
PCA, thathasbeenprojectedonto theX-Zplane.
The measurements were taken in distances and
orientations that relate to the industrial grasping use
case. The target object has been moved to several
fixed positions in front of the camera. Table 1 lists
thepositions thatwereused for themeasurements.
Figure5showstheresults formeasurements taken
with theobjectbeingplacedon theoptical axis.
Both of the anomalies at 40 and 45cm can be ex-
plainedduetopoorlyselected templates. Thiscanbe
mitigatedbyusingadvancedapproachesfor template
matching [5][17]. Those rely on scaling of the tem-
plate to get a more accurate match and also address
the rotational limitations.
Figure 7 shows an example disparity image of the
object viewed by the Intel RealSense camera. It can
be argumented that the anomalies are induced be-
cause of the dark areas in the disparity image, which
canbemostly tracedback toocclusionsof thestereo
vision system. This has an even larger effect when
16
Joint Austrian Computer Vision and Robotics Workshop 2020
- Title
- Joint Austrian Computer Vision and Robotics Workshop 2020
- Editor
- Graz University of Technology
- Location
- Graz
- Date
- 2020
- Language
- English
- License
- CC BY 4.0
- ISBN
- 978-3-85125-752-6
- Size
- 21.0 x 29.7 cm
- Pages
- 188
- Categories
- Informatik
- Technik