# A Novel Method for Extracting and Analyzing the Geometry Properties of the Shortest Pedestrian Paths Focusing on Open Geospatial Data

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## Abstract

**:**

## 1. Introduction

- Which route shows the least curviness?
- How many twists and turns (or directional changes) and intersections exist on each route?
- Which route shows lower road gradients, making the walking experience more pleasant for pedestrians?

## 2. Methodology

#### 2.1. Shortest Path Analysis

- Is the chosen POI listed as a famous place by Google Maps and OSRM?
- Are the distances between POIs no more than the recommended walking distance per day (10,000 steps ≈ 8 km) [45]?
- How well are the POIs distributed uniformly within the study area?

#### 2.2. Geometry Analysis

#### 2.2.1. Similarity

- (a)
- Minimum distance$$\begin{array}{c}\hfill {D}_{min}(A,B)=\underset{a\in A}{\mathrm{min}}\left\{\underset{b\in B}{\mathrm{min}}\right\{d(a,b)\left\}\right\}\end{array}$$
- (b)
- Maximum distance$$\begin{array}{c}\hfill {D}_{max}(A,B)=\underset{a\in A}{\mathrm{max}}\left\{\underset{b\in B}{\mathrm{max}}\right\{d(a,b)\left\}\right\}\end{array}$$
- (c)
- Centroid distance$$\begin{array}{c}\hfill {D}_{c}(A,B)=d(\frac{1}{m}\sum _{i=1}^{m}{\nu}_{iA},\frac{1}{n}\sum _{j=1}^{n}{\nu}_{jB})\end{array}$$

#### 2.2.2. Route Curviness

#### 2.2.3. Road Turns and Intersections

#### 2.2.4. Road Gradients

## 3. Results

## 4. Discussion

- Road dataset’s characteristicsThe data-related dissimilarities in route length might be derived from (a) differences in road density of networks or/and (b) existent topological inconsistencies in the dataset, such as unidentified connections and intersections. Moreover, (c) the starting/ending edges of calculated routes might have been placed in different positions (i.e., behind or ahead of the POI) for Google’s road dataset and OSM project’s data. As a result, it can be expected that the start or end of the route has yet to reach the exact position of the POI, or it conversely has gone beyond that (Figure 13). Such a circumstance is more likely to occur to the POIs in areas inaccessible by the main street networks.
- Utilized routing algorithmAlthough both web mapping services use Dijkstra’s algorithm to calculate the shortest path between points A and B, the OSRM’s algorithm is a modified version of Dijkstra, namely, “MultiLevel Dijkstra (MLD)”, which works on the overlay graph (i.e., an approximation of the original graph with a reduced complexity) produced by a partitioning step. This could result in negligible differences in the lengths of the calculated routes.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANOVA | Analysis of Variance |

DEM | Digital Elevation Model |

GEE | Google Earth Engine |

GIS | Geographical Information System |

NSW | New South Wales |

POI | Point/Place of Interest |

ORS | OpenRouteService |

OSM | OpenStreetMap |

OSRM | Open Source Routing Machine |

OTP | OpenTripPlanner |

SRTM | Shuttle Radar Topography Mission |

TAZ | Traffic Analysis Zone |

VGI | Volunteered Geographical Information |

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**Figure 1.**The shortest path (

**a**) and alternatives (

**b**,

**c**) suggested by Google Maps (yellow and red markers: road turns and intersections).

**Figure 3.**Hausdorff distance [56].

**Figure 4.**The number of road turns and intersections (

**a**) and degrees of turns (

**b**) present different mobility problems for a wheelchair user (yellow and red markers: road turns and intersections).

**Figure 7.**An example of calculated shortest paths with slope profile (blue line: OSM, red line: Google Maps, and green/red placemark: origin/destination).

**Figure 8.**The selected OSM shortest paths with different dissimilarity ratios (blue line: OSM, red line: Google Maps, green/red placemark: origin/destination).

**Figure 13.**An example of the starting/ending edge problem (blue line: OSM, red line: Google Maps, black line: starting edge of the route, green/red placemark: origin/destination).

No. | Name | Category | X | Y |
---|---|---|---|---|

01 | Alan Davidson Oval | Sports Field | 151.187701 | −33.908699 |

02 | Australian Museum | Museum | 151.213034 | −33.874292 |

03 | Beaconsfield Park | Park | 151.199765 | −33.910976 |

04 | Chinese Garden of Friendship | Tourist Attraction | 151.202877 | −33.876583 |

05 | Curtin University Sydney | University | 151.202495 | −33.885293 |

06 | Elizabeth Bay House | Historic Site | 151.22428 | −33.870109 |

07 | Erskineville Oval | Sports Field | 151.190778 | −33.901992 |

08 | Glebe Library | Library | 151.184925 | −33.877996 |

09 | Hollis Park | Park | 151.186125 | −33.894647 |

10 | Museum of Sydney | Museum | 151.211414 | −33.863787 |

11 | National Art School | Education Facility | 151.218514 | −33.879836 |

12 | Powerhouse Museum | Museum | 151.199715 | −33.878096 |

13 | Queen Victoria Building | Tourist Attraction | 151.20668 | −33.871804 |

14 | Surry Hills Library | Library | 151.213734 | −33.885998 |

15 | Sydney Fish Market | Shopping Center | 151.192611 | −33.873051 |

16 | Sydney Opera House | Community Facility | 151.215356 | −33.85652 |

17 | Sydney Tower Eye | Tourist Attraction | 151.208945 | −33.870376 |

18 | Ultimo Community Center | Community Facility | 151.198198 | −33.877846 |

19 | Waterloo Library | Library | 151.206767 | −33.899361 |

20 | WILD LIFE Sydney Zoo | Tourist Attraction | 151.201812 | −33.869181 |

Shortest Path | Length (km) | S1 | S2 | S3 | S4 | S5 | S6 | Overall |
---|---|---|---|---|---|---|---|---|

A | 1 | 1.05 | 1.8 | 1.75 | 1.65 | 2.12 | 1.77 | 1.69 |

B | 1 | 1.25 | 1.14 | 1.95 | 2.18 | 2.8 | - | 1.86 |

OSM | Google Maps | |||||||
---|---|---|---|---|---|---|---|---|

Impedance | Sum | Mean | Max | Min | Sum | Mean | Max | Min |

Distance (km) | 1162 | 3.3 | 7.3 | 0.3 | 1115 | 3.1 | 6.9 | 0.3 |

Travel time (min) | 14,532 | 41 | 91 | 4 | 13,948 | 39 | 86 | 4 |

OSM < Google Maps | OSM > Google Maps | ||||||
---|---|---|---|---|---|---|---|

Freq. | Mean (m) | Max (%) | Min (%) | Freq. | Mean (m) | Max (%) | Min (%) |

148 | −116 | −12.5 | −2.9 | 232 | 201 | 14.5 | 2.1 |

**Table 5.**Geometry analysis of the route pair (part 1) (${d}_{H}$: Hausdorff distance, DR: dissimilarity ratio, and SI: sinuosity index).

Data | Distance (km) | Travel Time (min) | ${\mathit{d}}_{\mathit{H}}$ (m) | DR (%) | SI (%) |
---|---|---|---|---|---|

OSM | 2.5 | 33 | 89 | 3.56 | 1.38 |

GM | 2.4 | 31 | 1.42 |

**Table 6.**Geometry analysis of the route pair (part 2) (SL: straight line between turns, and Int.: intersections along the route).

Turn Types (Freq.) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Data | Turn (Freq.) | 30${}^{\circ}$ | 60${}^{\circ}$ | 90${}^{\circ}$ | 120${}^{\circ}$ | 150${}^{\circ}$ | 180${}^{\circ}$ | SL (m) | Int. (Freq.) | $\overline{\mathit{Slope}}$ (%) | Max Slope (%) |

OSM | 47 | 11 | 8 | 27 | 1 | 0 | 0 | 53 | 4 | 7.3 | 26.7 |

GM | 50 | 21 | 7 | 19 | 1 | 0 | 2 | 48 | 7 | 8.1 | 30.2 |

**Table 7.**Similarity classification of the route pairs (DR: dissimilarity ratio, $\overline{{d}_{H}}$: average Hausdorff distance, and $\overline{d}$: average distance between OD pairs).

Category | DR (%) | Freq. | $\overline{{\mathit{d}}_{\mathit{H}}}$ (m) | $\overline{\mathit{d}}$ (km) |
---|---|---|---|---|

Well matched | 0–10 | 197 | 171 | 3.26 |

Moderately matched | 10–20 | 130 | 341 | 2.51 |

Slightly matched | 20–30 | 46 | 394 | 2.08 |

Not matched | 30–40 | 7 | 468 | 1.35 |

**Table 8.**Description of selected OSM shortest paths categorized under different similarity clusters (${d}_{H}$: Hausdorff distance and DR: dissimilarity ratio).

ID | Origin | Destination | ${\mathit{d}}_{\mathit{H}}$ (m) | DR (%) | Category |
---|---|---|---|---|---|

a | Elizabeth Bay House | Glebe Library | 40 | 0.87 | Well matched |

b | Powerhouse Museum | WILD LIFE Sydney Zoo | 157 | 10.47 | Moderately matched |

c | Queen Victoria Building | Sydney Opera House | 480 | 20.87 | Slightly matched |

d | Queen Victoria Building | Surry Hills Library | 835 | 37.56 | Not matched |

**Table 9.**Overall statistics of the geometry analysis (SL: straight line between each turn and Int.: intersections along the route).

$\overline{\mathit{Turn}\phantom{\rule{0.277778em}{0ex}}\mathit{Types}}$ (Freq.) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Data | $\overline{\mathit{Sinuosity}\phantom{\rule{0.277778em}{0ex}}\mathit{Index}}$ (%) | $\overline{\mathit{Turn}}$ (Freq.) | 30${}^{\circ}$ | 60${}^{\circ}$ | 90${}^{\circ}$ | 120${}^{\circ}$ | 150${}^{\circ}$ | 180${}^{\circ}$ | $\overline{\mathit{SL}}$ (m) | $\overline{\mathit{Int}.}$ (Freq.) | $\overline{\mathit{Slope}}$ (%) | $\overline{\mathit{Max}\phantom{\rule{0.222222em}{0ex}}\mathit{Slope}}$ (%) |

OSM | 1.58 | 52.1 | 19 | 8 | 19 | 3 | 1 | 2 | 58.7 | 3.9 | 7.7 | 18.1 |

GM | 1.41 | 46.6 | 15 | 11 | 17 | 1 | 1 | 1 | 62.9 | 4.3 | 8.4 | 21.4 |

Source of Variation | SS | df | MS | F | p-Value | F Crit |
---|---|---|---|---|---|---|

Between Groups | 0.001507 | 2 | 0.000754 | 0.130351 | 0.927821 | 3.019664 |

Within Groups | 2.179306 | 377 | 0.005781 | - | - | - |

- | - | - | - | - | - | - |

Total | 2.180814 | 379 | - | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Hosseini, R.; Tong, D.; Lim, S.; Sun, Q.C.; Sohn, G.; Gidófalvi, G.; Alimohammadi, A.; Seyedabrishami, S.
A Novel Method for Extracting and Analyzing the Geometry Properties of the Shortest Pedestrian Paths Focusing on Open Geospatial Data. *ISPRS Int. J. Geo-Inf.* **2023**, *12*, 288.
https://doi.org/10.3390/ijgi12070288

**AMA Style**

Hosseini R, Tong D, Lim S, Sun QC, Sohn G, Gidófalvi G, Alimohammadi A, Seyedabrishami S.
A Novel Method for Extracting and Analyzing the Geometry Properties of the Shortest Pedestrian Paths Focusing on Open Geospatial Data. *ISPRS International Journal of Geo-Information*. 2023; 12(7):288.
https://doi.org/10.3390/ijgi12070288

**Chicago/Turabian Style**

Hosseini, Reza, Daoqin Tong, Samsung Lim, Qian Chayn Sun, Gunho Sohn, Gyözö Gidófalvi, Abbas Alimohammadi, and Seyedehsan Seyedabrishami.
2023. "A Novel Method for Extracting and Analyzing the Geometry Properties of the Shortest Pedestrian Paths Focusing on Open Geospatial Data" *ISPRS International Journal of Geo-Information* 12, no. 7: 288.
https://doi.org/10.3390/ijgi12070288