In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 
Paris, France, 3-4 September, 2009 
A rectangle classifier and a modified k nearest neighbours 
(KNN-) classifier are used. The result of the classification 
shall be unambiguously. 
k-nearest neighbours algorithm (KNN) is a method for classi 
fying objects based on closest training examples in the fea 
ture space. 
A data set of 414 different trajectories (Total) has been proc 
essed using different functions within the test data set. A total 
of 62 trajectories could not be classified (NC). A summary is 
given in table 2. 
The results shall be represented in greater detail by the hy 
perboles in the following. 
The rectangle classification (also cuboid classification) is a 
distribution free, nonparametric and supervised classification 
method (see figure 4). 
A 
V 
2 
Klaise 2 
i ** 
Merkma; 1 ^ 
Figure 4. A simple rectangle classification in a 2D feature 
space 
The KNN classification needs a training data set. It is a non 
parametric method for the estimate of probability densities. 
The operation of the classifier is steered by k (number of 
regarded neighbours, a free selectable parameter) and 8 (used 
metric). Figure 5 shows the approach. 
© 
& 
■M A 
© ® 
Figure 5. Visualization of the KNN classification. The k=7 
nearest neighbour are used. The object g is as 
signed to the class B 
The metric 5 defines the reliable determination of the dis 
tances to adjacent elements. The result of the classification 
depends substantially on the density of the learning set and 
the choice of the metric. Here the Mahalanobis distance was 
used. 
4. RESULTS 
To- 
N 
WR 
WR 
R 
R 
RW 
RW 
tal 
C 
R 
L 
O 
W 
R 
L 
Ref 
414 
62 
117 
59 
72 
26 
33 
54 
Circ 
414 
62 
119 
59 
68 
21 
34 
51 
Elli 
410 
51 
117 
58 
72 
28 
34 
50 
Hyp 
410 
51 
117 
58 
72 
28 
34 
50 
Str 
413 
50 
125 
56 
70 
28 
35 
49 
Table 2. Summary of complete occurrence and the class oc 
currence of different trajectory types. Ref - refer 
ence, Circ - circle, Elli - ellipse, Hyp - hyper 
bola, Str - straight lines 
4.1 Hyperbola 
Figure 6 shows examples of the approximation of hyperbo 
les. 
Figure 6. Approximation of hyperboles 
In addition to the parameters of the conical sections the di 
rection of motion was uses for the classification. Figure 7 
shows the plot of the rotational angle cp (X) and the delta in 
degrees (<J>) where the trajectory adapts to the hyperbola: 
Figure 7. Classification results 
Class 
Cuboid Classifier 
KNN-Classifier 
Total 
92.9% 
97.8% 
No_Class 
84.3% 
98.0% 
WRR 
95.7% 
99.1% 
WRL 
93.1% 
99.0% 
RO 
97.2% 
99.5% 
RW 
96.4% 
96.4% 
RWR 
85.3% 
91.2% 
WRL 
92.00% 
94.0%