# Estimating Road Segments Using Natural Point Correspondences of GPS Trajectories

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## Abstract

**:**

## 1. Introduction

#### Task

## 2. Related Work

## 3. Method

- Generalize single trajectories using the DP algorithm. DP takes a curve composed of segments defined by 2D points and creates a sketch by repeatedly adding the point with maximal orthogonal error to the sketch unless this error falls below a fixed threshold $\u03f5$.
- Determine the trajectory ${T}_{max}$ that contains the most points. Reverse the order of the points in some trajectories to achieve identical orientation. The order of indices in a trajectory ${t}_{i}$ is reversed if the distance between the endpoint of ${t}_{i}$ and start point of ${t}_{max}$ is smaller than the distance between the start point of ${t}_{i}$ and the start point of ${t}_{max}$.
- Align indices of the points in trajectories with a smaller number of points along ${T}_{max}$ using linear interpolation. This step was part of the contribution to the contest, but as described in the Experiments and Discussion part this step is not always contributing to the performance improvement.
- Calculate the centroid of all points with the same index by averaging coordinates.

## 4. Experiments

#### 4.1. Results

#### 4.2. Competition Results and Relative Performance

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Algorithm applied to sample 9 with and without extensions. (

**a**) No extensions just the averaging based on corresponding ids; (

**b**) algorithm with reversion. The order of points in trajectory is reversed in order to group all starting points at one side; (

**c**) algorithm with DP and $\u03f5$ set to $0.15$; (

**d**) algorithm including the alignment of the shorter paths.

**Figure A2.**Algorithm applied to sample 14 with and without extensions. (

**a**) No extensions just the averaging based on corresponding ids; (

**b**) algorithm with reversion. The order of points in trajectory is reversed in order to group all starting points at one side; (

**c**) algorithm with DP and $\u03f5$ set to $0.15$; (

**d**) algorithm including the alignment of the shorter paths.

**Figure A3.**Algorithm applied to sample 49 with and without extensions. (

**a**) No extensions just the averaging based on corresponding ids; (

**b**) algorithm with reversion. The order of points in trajectory is reversed in order to group all starting points at one side; (

**c**) algorithm with DP and $\u03f5$ set to $0.15$; (

**d**) algorithm including the alignment of the shorter paths.

**Figure A4.**Algorithm applied to sample 95 with and without extensions. (

**a**) No extensions just the averaging based on corresponding ids; (

**b**) algorithm with reversion. The order of points in trajectory is reversed in order to group all starting points at one side; (

**c**) algorithm with DP and $\u03f5$ set to $0.15$; (

**d**) algorithm including the alignment of the shorter paths.

**Figure A5.**Algorithm applied to sample 95 with varying $\u03f5$. (

**a**) $\u03f5=0.0$, (

**b**) $\u03f5=0.04$, (

**c**) $\u03f5=0.15$, (

**d**) $\u03f5=0.4$.

**Figure A6.**Algorithm applied to sample 10 with varying $\u03f5$. (

**a**) $\u03f5=0.0$, (

**b**) $\u03f5=0.04$, (

**c**) $\u03f5=0.15$, (

**d**) $\u03f5=0.4$.

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Method | Rank | Training | Testing | Runtime |
---|---|---|---|---|

Karasek-2 | 1 | 0.671 | 0.620 | seconds |

Yang-2 | 2 | 0.704 | 0.618 | seconds |

Yang-1 | 3 | 0.680 | 0.618 | seconds |

Leichter | 4 | 0.666 | 0.615 | seconds |

Dupaquis | 5 | 0.674 | 0.612 | 10 min |

Amin | 6 | 0.666 | 0.612 | seconds |

Karasek-1 | 7 | 0.681 | 0609 | seconds |

Medoid | – | 0.619 | 0.567 | 1 h |

CellNeto | – | 0.664 | 0.612 | seconds |

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**MDPI and ACS Style**

Leichter, A.; Werner, M.
Estimating Road Segments Using Natural Point Correspondences of GPS Trajectories. *Appl. Sci.* **2019**, *9*, 4255.
https://doi.org/10.3390/app9204255

**AMA Style**

Leichter A, Werner M.
Estimating Road Segments Using Natural Point Correspondences of GPS Trajectories. *Applied Sciences*. 2019; 9(20):4255.
https://doi.org/10.3390/app9204255

**Chicago/Turabian Style**

Leichter, Artem, and Martin Werner.
2019. "Estimating Road Segments Using Natural Point Correspondences of GPS Trajectories" *Applied Sciences* 9, no. 20: 4255.
https://doi.org/10.3390/app9204255