Page 114 - Rapid Learning in Robotics

100 Application Examples in the Vision Domain

z L h i h i h i h z i hj nji hj oji h n oi hj u ji hj u ji
P P
PSOM range L L
4 and 8 points are input
150 2 2.6 3.1 2.9 0.11 0.039 0.046 0.0084 given given

150 2 2.7 3.2 2.8 0.12 0.043 0.048 0.0084 0.010 0.0081

Learn only rotational part
3 3 3 150 2.6 3.0 2.5 0.046 0.048 0.0074 0.018 0.012
4 4 4 150 0.63 1.2 0.93 0.021 0.019 0.0027 0.013 0.0063
5 5 5 150 0.12 0.12 0.094 0.0034 0.0027 0.00042 0.0017 0.00089
Various rotational ranges
90 1 0.64 0.56 0.53 0.034 0.0085 0.0082 0.00082 0.0036 0.0021

120 1 1.5 1.5 1.4 0.037 0.021 0.021 0.0032 0.0079 0.0049

150 1 2.7 3.2 2.8 0.077 0.044 0.048 0.0084 0.013 0.010

180 1 6.5 5.4 7.0 0.19 0.079 0.098 0.014 0.019 0.016

Various training set sizes
150 2 2.7 3.2 2.8 0.12 0.043 0.048 0.0084 0.010 0.0081

150 2 2.6 3.2 2.8 0.11 0.043 0.048 0.0084 0.0097 0.0077

150 2 0.49 0.97 0.73 0.12 0.018 0.016 0.0030 0.0089 0.0059

150 2 0.52 0.98 0.71 0.035 0.017 0.014 0.0026 0.0082 0.0053

150 2 0.14 0.13 0.14 0.024 0.0033 0.0030 0.00043 0.0018 0.0011

Shift depth range z
150 1..3 3.8 3.4 3.7 0.12 0.061 0.064 0.0083 0.049 0.025

150 2..4 2.6 3.2 2.8 0.11 0.043 0.048 0.0084 0.0097 0.0077

150 3..5 2.6 3.2 2.9 0.15 0.042 0.047 0.0084 0.0050 0.0045

Various distance ranges
150 2 2.6 3.2 2.8 0.11 0.043 0.048 0.0084 0.0097 0.0077

150 4 2.6 3.2 2.8 0.20 0.042 0.047 0.0084 0.0068 0.0059

150 6 2.6 3.2 2.9 0.36 0.043 0.048 0.0084 0.0057 0.0052

150 6 0.65 0.73 0.93 0.39 0.016 0.013 0.00047 0.0070 0.0051

150 6 0.44 0.43 0.60 0.14 0.0097 0.0083 0.00042 0.0043 0.0029

Table 7.1: Mean Euclidean deviation of the reconstructed pitch, roll, yaw angles

, the depth z, the column vectors n o of the rotation matrix T, the scalar
o
product of the vectors n (orthogonality check), and the predicted image position
of the object locations P . PThe results are obtained for various experimental
parameters in order to give some insight into their impact on the achievable re-
construction accuracy. The PSOM training set size is indicated in the first column,

the intervals are centered around 0 , and depth z ranges from z min L,
where L denotes the cube length (focal length of the lens is also taken as L.)
In the first row all corner locations are inputs. All remaining results are obtained
using only four (non-coplanar) points as inputs.