# Estimating Road Segments Using Natural Point Correspondences of GPS Trajectories
## 4 Experiments
### Results  
In the first experiment, the minimal version of the algorithm without DP, reversion of trajectory indices, and alignment reaches overall average HC-SIM of 0.53. Introducing the trajectory reversion step leads to an increased measure of 0.66. Finally, adding Douglas Peucker (\(\epsilon=0.15\)) both with and without alignment of the indices provides the same HC-SIM value of 0.67 (Figure 2).  
The averaged similarity over the whole data set occludes drawbacks and improvements in particular constellations of samples. Therefore, we take a more detailed look at 5 selected samples (ids: 9, 14, 20, 49, 95, see Figure 3). Adding the reversion (step 2) of the input trajectories leads to an improvement in three out of the five exemplary cases. The results of the trajectories 20 and 95 (Figure A4) do not improve, because the input trajectories have all been observed in the same  
Figure 2: Average HC-SIM over whole data set for the algorithm after introducing additional steps.  
direction. Among all 100 samples of the data set, there are no samples with a decreasing HC-SIM after the extension of the algorithm with reversion.  
The DP extension of the algorithm leads to an improvement for sample 9 (Figure A1) and sample 14 (Figure A2). While sample 14 improves due to the generalization of two input trajectories, sample 9 shows improved HC-SIM due to the simplification of the long input trajectory on the right side. This trajectory can be considered as an outlier and the reduction of the number of points of these trajectories by the DP reduced the influence of this outlier on the result. Samples 20 and 49 (Figure A3) were not influenced by applying DP simplification. In both cases, the reference segment, as well as the trajectories, were linear two-point segments. In that case, the approximation step has no influence. The DP has a negative impact on the segment with the id 95. This segment is U-shaped and reducing the number of input points makes the corners of the average drift away from the ground truth. The alignment of the trajectories has no influence on the result of any sample. For future work, we plan to allow segment models with constant curvature (e.g., polylines with bulges) as a generalization of line strings in order to simplify such curved road situations in a more sensible way.  
The results of the second experiment were presented in two blocks as well. The first block shows the average HC-SIM over the entire data set and in the second block, the similarity values of five selected examples are shown. The HC-SIM behaves mostly predictable, with initially rising similarity values and after the \(\epsilon\) of 0.15 reducing. There is still one outlier as the curve starts at 0.66 with no approximation and drops to a lower value near a value of \(\epsilon=0.04\) and starts to rise after that. The number of points after the approximation drops fast and converges to two (compare Figure 4).  
The samples with ids 49 and 26 have constant HC-SIM values of approximately 1.0 and 0.28. The minimum at \(\epsilon=0.04\) is, however, present at the graph for the samples 10, 14 and 95. The similarity value of the samples with id 14 and especially 95 suffers from increasing \(\epsilon\) (Figure 5).  
Figure 3: Similarity performance for five single samples.