Page - 16 - in Joint Austrian Computer Vision and Robotics Workshop 2020

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