# Semi-Automatic Extraction of Geometric Elements of Curved Ramps from Google Earth Images

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Localization of Road Centerline

_{0}, and the curve can be divided at this value using the de Casteljau algorithm Figure 2 [32], recursively applying the following equation to obtain the new control points:

- The values ${\mathrm{b}}_{\mathrm{i}}^{0}$ are the original control points of the curve.
- The value of the curve at parameter value ${\mathrm{t}}_{0}$ is ${\mathrm{b}}_{\mathrm{n}}^{\mathrm{n}}$.
- The curve is divided at parameter value ${\mathrm{t}}_{0}$ and can be represented as two curves, with control points (${\mathrm{b}}_{\mathrm{i}}^{0},{\text{}\mathrm{b}}_{1\text{}}^{1},\dots ,{\mathrm{b}}_{\mathrm{n}}^{\mathrm{n}}$) and (${\mathrm{b}}_{\mathrm{n}}^{\mathrm{n}}$,${\text{}\mathrm{b}}_{\mathrm{n}}^{\mathrm{n}-1}$,…,${\text{}\mathrm{b}}_{\mathrm{n}}^{0}$).

#### 3.2. PC and PT Station Identification

#### 3.2.1. Curvature Recognition

- $\mathsf{\rho}$: Curvature;
- ${\text{}\mathrm{y}\prime}^{2}$: First derivative;
- $\text{}\mathrm{y}\u2033$: Second derivative;
- $\mathrm{R}$: Radius of curvature;

#### 3.2.2. Linear Fitting Analyses for PC and PT Detection

#### 3.3. Curve Radius Calculation

## 4. Case Study

#### Test Sites

## 5. Results

#### 5.1. PC and PT Determination

#### 5.2. Curve Radius

## 6. Discussion

## 7. Conclusions

- The data points were first selected along the road trajectory using a graphics editor software and fitted with the best curve that passes through those points to generate a smooth curve that meets the horizontal curve conditions.
- The curvature analysis method was used for automatic PC/PT location search, and the linear fitting analysis method was applied for exact PC/PT localization. After the PC and PT were located, the road curves were measured using the total least-squares fitting method.
- The presented method was validated by comparing the estimated results against a road with known data. The results show that the proposed method successfully identified the spiral transition from circular curves and extracted their curve radii with an average error of 2.20% for simple curves and 6.35% for spiral curves. The proposed method presented a virtual extension to existing methods for obtaining horizontal curve information and should be of interest to surveying professionals. This helps reduce the burden associated with traditional surveying tools. The applications of the developed algorithm range from providing real-time information about curve geometry to drivers and autonomous vehicles to using the extracted data in safety-prediction models to improve safety on curves.
- The precision of GE images may contribute to the errors in the extraction of horizontal curve parameters. Future research focusing on a fully automatic extraction method might reduce the errors and increase the overall identification rate. Drone images may also be used to enhance the accuracy of obtaining the geometric information of horizontal curves.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CE | Curvature Extension |

CF | Curve Finder |

CS | Circular to Spiral |

FHWA | Federal Highway Administration |

GE | Google Earth |

GIS | Global Information System |

GPS | Global Position System |

IMU | Inertial Measurement Unit |

LE | Length of Strait Ling |

LiDAR | Light Detection and Ranging system |

LS | Least Squares |

PC | Point of Curvature |

PT | Point of Tangent |

SC | Spiral to Circular |

ST | Spiral to Tangent |

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**Figure 1.**Data point selection and centerline determination (Test site 4): (

**a**) selected data points (

**b**) determined ramp centerline.

**Figure 4.**Curvature sampling at different positions: (

**a**) curvature at 1 m position; (

**b**) curvature at 2 m position; (

**c**) curvature at 3 m position; (

**d**) curvature at 4 m position.

**Figure 6.**PC and PT determination (test site 4): (

**a**) curvature profile; (

**b**) PT and PT determination.

**Figure 7.**The geometry of fitting continuous horizontal curves to a sequence of selected data points.

**Figure 11.**Curvature profile: (

**a**) curvature profile of ramp 1; (

**b**) curvature profile of ramp 2; (

**c**) curvature profile of ramp 3; (

**d**) curvature profile of ramp 4.

**Figure 12.**PC and PT determination: (

**a**) PC and PT of ramp 1; (

**b**) PC and PT of ramp 2; (

**c**) PC and PT of ramp 3; (

**d**) PC and PT of ramp 4.

**Figure 13.**Curvature fitting result between actual and estimated curves: (

**a**) fitted ramp 1; (

**b**) fitted ramp 2; (

**c**) fitted ramp 3; (

**d**) fitted ramp 4.

Test Site | Highway | Length (m) | Location | Lanes | |
---|---|---|---|---|---|

Easting | Northing | ||||

1 | S 55 | 287.75 | 675,744.00 | 3,518,284.00 | 1 |

2 | S 88 | 282.51 | 679,060.00 | 3,514,339.00 | 1 |

3 | S 55 | 203.05 | 669,327.00 | 3,533,951.00 | 1 |

4 | S 88 | 298.91 | 671,488.00 | 3,524,935.00 | 1 |

Test Site | Curve Type | Curve Radius | ||
---|---|---|---|---|

Estimated (m) | Reference (m) | Errors (%) | ||

Test site 1 | Spiral | 75.43 | 79.77 | 5.44 |

Spiral | 58.61 | 64.61 | 9.28 | |

Simple | 51.44 | 50.00 | 2.88 | |

Test site 2 | Spiral | 50.94 | 55 | 7.38 |

Simple | 50.47 | 50.00 | 0.94 | |

Test site 3 | Spiral | 59.00 | 57.50 | 2.60 |

Spiral | 62.40 | 59.00 | 5.76 | |

Simple | 46.81 | 45.00 | 4.02 | |

Test site 4 | Spiral | 81.87 | 75 | 9.16 |

Spiral | 71.36 | 75 | 4.85 | |

Simple | 70.68 | 70 | 0.97 |

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**MDPI and ACS Style**

AL-Qadri, M.; Cheng, J.; Zhang, Y.
Semi-Automatic Extraction of Geometric Elements of Curved Ramps from Google Earth Images. *Sustainability* **2022**, *14*, 1001.
https://doi.org/10.3390/su14021001

**AMA Style**

AL-Qadri M, Cheng J, Zhang Y.
Semi-Automatic Extraction of Geometric Elements of Curved Ramps from Google Earth Images. *Sustainability*. 2022; 14(2):1001.
https://doi.org/10.3390/su14021001

**Chicago/Turabian Style**

AL-Qadri, Mohammed, Jianchuan Cheng, and Yunlong Zhang.
2022. "Semi-Automatic Extraction of Geometric Elements of Curved Ramps from Google Earth Images" *Sustainability* 14, no. 2: 1001.
https://doi.org/10.3390/su14021001