# An Improved Hybrid Method for Enhanced Road Feature Selection in Map Generalization

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. An Improved Method of Road Selection

#### 2.1. An Improved Stroke Generation Method

#### 2.1.1. Overall Stroke Connection Rules

_{i}and S

_{i+}

_{1}.

_{i}is composed of N

_{i}(i = 1,2,...,n) nodes and n − 1 road segments. The (x

_{i}, y

_{i}) terms represent the coordinates of nodes N

_{i}, while the declination rate m of path R

_{i}was calculated using the following equation:

_{0}and TN

_{0}are nodes for the initial road segment S

_{0}, the number of road segments generated by the stroke from e node FN

_{0}(which satisfy the first connection rule at node FN

_{0}) is n. The declination rate for an initial road segment S

_{0}is m

_{0}, where m

_{i}(i = 1, 2, …, n) is the declination rate of paths formed by the n road segments linked to node FN

_{0}. If Δm = min |m

_{i}− m

_{0}|, the road segment S

_{i}corresponding to Δm is connected to the initial road segment S

_{0}. Before carrying out the next connection, new declination rates were set to the initial declination rate, namely m

_{0}= m

_{i}. Road segments linked to the nodes at road segment S

_{i}continue being updated using connection rules (1) and (2) until there is no road segment satisfying the first connection rule. A new stroke is then generated using the same method, processing the other nodes TN

_{0}.

_{0}, S

_{1}, and S

_{2}are linked to node SN

_{0}. Supposing that a stroke was generated from road segment S

_{0}, the deflection angles S

_{1}, S

_{2,}with S

_{0}, were calculated, respectively. Declination rates for nodes (SN

_{1}, SN

_{0}), (SN

_{1}, SN

_{0}, SN

_{2}), and (SN

_{1}, SN

_{0}, SN

_{3}), were m

_{0}, m

_{1}and m

_{2}, respectively. The following three situations could potentially occur when generating a stroke at node SN

_{0}: (1) if both of the deflection angles are less than θ, the absolute value of the difference of m

_{1}with m

_{0}and m

_{2}with m

_{0}was calculated, respectively. Without loss of generality, we assumed |m

_{1}− m

_{0}| < |m

_{2}− m

_{0}| and that road segment S

_{1}was selected to connect with road segment S

_{0}. We then set m

_{1}as the initial declination rate before connecting the road segments linked to node SN

_{3}; (2) if neither of the deflection angles are less than θ, the stroke generation algorithm is terminated at node SN

_{0}; (3) if only one road segment’s deflection angle is less than θ, the road segment can be directly connected with road segment S

_{0}.

#### 2.1.2. A Connection Strategy Based on Road Importance

#### 2.2. Stroke Order Based on Stroke Importance

_{1}, p

_{2}, p

_{3}and p

_{4}can be obtained using the CRITIC method; ${L}_{max}$, ${D}_{max}$, ${B}_{max}$ and ${C}_{max}$ are the maximum stroke length, degree, similarity, and closeness, respectively.

_{j}is the amount of information in indicator j; ${\sigma}_{j}$ is the standard deviation of indicator j; m is the number of stroke evaluation indicators, and ${r}_{jk}$ represents the linear correlation coefficient of indicators j and k.

#### 2.3. Road Density Based on a Weighted Voronoi Diagram

^{2}) and 23.1 (km/km

^{2}) based on an ordinary Voronoi diagram and a weighted Voronoi diagram, respectively. Under the control of the density threshold 25.5 (km/km

^{2}), road segment RS was deleted using an ordinary Voronoi diagram, while it was selected using the weighted Voronoi diagram. It can be seen from Figure 6 that the road segment RS in the road network plays a very important role in connectivity, and therefore it needs to be selected. In fact, weighted Voronoi diagrams take the road importance into account, as important roads occupy a larger area and thus result in lower road density. Therefore, an important road tends to be selected based on a weighted Voronoi diagram, which shows that a weighted Voronoi diagram is more reasonable than an ordinary Voronoi diagram in partitioning a road network.

_{m}[29,30]. Müller also suggested a value of 0.4 mm as being appropriate [31]. Considering the scale of the target map (1:50,000) and source map (1:10,000), a value of 0.4 mm was chosen to calculate the road density threshold, which equals 25.0 (km/km

^{2}) based on Equation (8).

## 3. Road Selection Based on Stroke and Voronoi Diagrams

- (1)
- Generate a stroke using the improved stroke algorithm and compute stroke importance using the CRITIC method based on the evaluation indicators in Table 2. Then sort strokes based on stroke importance.
- (2)
- Generate a weighted Voronoi diagram to partition the road network and calculate stroke density based on the partition. Then calculate a density threshold using the natural principle method.
- (3)
- Calculate the total length L
_{s}of the road selection using the radical law method. - (4)
- Make stroke a selection unit used to select road segments based on stroke importance as well as stroke density. The strokes were sorted based on stroke importance and selected the strokes according to order, from high to low. If a stroke density is lower than the density threshold, the stroke is selected. The selected algorithm continues until the total length of the selected stroke is larger than Ls. If the total length of the selected stroke is still smaller than Ls when all strokes are processed using the selected algorithm, the strokes whose densities are lower than the density threshold are continually selected based on stroke importance until the total length of selected strokes is larger than Ls.
- (5)
- If the selected road network is disconnected, then a minimum spanning tree method is used to connect the road network by adding a minimum number of nodes [33]. In order to ensure overall connectivity of the road network after selection, the shortest path is selected to connect pseudo nodes to newly added nodes until all pseudo nodes have been processed.

## 4. A Case Study

^{2}and was located in Neixiang County in Henan Province. As shown in Figure 8, the data scale was 1:10,000 and there were 422 nodes and 644 road segments. The total length of all road segments was 152.1 km.

#### 4.1. Analysis of Stroke Generation Results

#### 4.2. Road Density Result Analysis

_{1}, st

_{2}and st

_{3}are decreasing. Based on a given density threshold, road segments st

_{1}, st

_{2}and st

_{3}may not be selected. Therefore, it can be concluded from the road selection process that the weighted Voronoi diagram and the mesh method achieved essentially the same results for the road network with ordinary areal road segments. During the process of road selection, the mesh method needs to fully consider adjacent meshes, while the weighted Voronoi diagram directly compares the road density with a density threshold to determine whether a road segment is selected. The weighted Voronoi diagram method offers a simple calculation process (nearly equivalent to the selection accuracy) whose implementation is simpler than the mesh method.

_{v}is composed of four road segments but was deleted based on ordinary Voronoi diagram partition, because of density threshold limitations. In contrast, stroke S

_{v}was selected in the process of the weighted Voronoi diagram partition, because the importance degree of stroke S

_{v}was large and the density was larger than the threshold. Stroke S

_{v}was also selected by manual selection because it links several road segments and plays an important role in road network connections. In Neixiang case, the final selection accuracy of the weighted Voronoi diagram and the ordinary Voronoi method were 85.8% and 80.2%, respectively.

#### 4.3. Results Analysis for Road Selection

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 6.**Partition results for the ordinary and weighted Voronoi diagrams: (

**a**) weighted Voronoi diagram; (

**b**) ordinary Voronoi diagram.

**Figure 12.**A comparison of selection processes for the weighted Voronoi method and the mesh method; (

**a**) a schematic road network with areal road segments; (

**b**) selection results based on the mesh method for an areal road pattern; (

**c**) selection results based on the weighted Voronoi diagram for an areal road pattern; (

**d**) a schematic road network with hybrid road segments; (

**e**) selection results based on the mesh method for a hybrid road pattern; (

**f**) selection results based on the weighted Voronoi diagram method for a hybrid road pattern.

Set S = Sort (I_{segment}); //Sort the importance of road segmentIf (S! == NULL) { Bool IsSelected = False; Initial segment = max (S); //Select road segment that has the maximum importance as the initial road segment Initial segment_IsSelected = True; //Set the property of initial road segment as True. IsLinked (Initial segment); Update S (); } IsLinked (Initial segment) //Judge whether road segment connects { Get the neighbor segments’ number of Initial segment; //Get the linked road segment of initial segment If (k = 0) Set ST = ST + Initial segment; //Build a new Stroke For neighbor segment = 1 to k //k is the number of linked road segments Calculate the deflection angle; //Calculate deflection angle If (deflection angle <= θ) Δ m = |m _{segment} - m_{Initial segment}|;Else Return; Linked segment = min (Δ m) segment; Linked segment_IsSelected = True; //Mark the connected road segment Set Initial segment = Linked segment; } Update S () //Update the road network { Set S_selected = Initial segment; S = S - S_selected; } |

Stroke Evaluation Indicator | Explanation | Calculated Equation |
---|---|---|

Stroke Length (L) | The total length of road segments formed by stroke | $L\left({s}_{i}\right)={{\displaystyle \sum}}_{k=1}^{n}{l}_{ik}$, ${l}_{ik}$ is the length of kth road segment of ith Stroke. |

Stroke Degree (D) | The total number of road segment formed by stroke | $D\left({s}_{i}\right)={{\displaystyle \sum}}_{k=1}^{n}r\left({s}_{i},{v}_{k}\right)$ If road segment ${v}_{k}$ is part of Stroke ${s}_{i}$ then $r\left({s}_{i},{v}_{k}\right)$ = 1, or $r\left({s}_{i},{v}_{k}\right)$ = 0. |

Stroke Betweenness (B) | The probability of a stroke lying in the other strokes | $B\left({s}_{i}\right)=\frac{1}{\left(N-1\right)-\left(N-2\right)}{{\displaystyle \sum}}_{j,k\in N}\frac{{n}_{jk}\left(i\right)}{{n}_{jk}}$, (j ≠ k; j, k ≠ i), N is the number of node; ${n}_{jk}$ is the number of shortest paths between node j and node k; ${n}_{jk}\left(i\right)$ is the number of shortest paths between node j and node k that contains node i. |

Stroke Closeness (C) | The minimal connection number of a stroke to other stroke, reflecting the probability of a stroke being close to the another stroke | $C\left({s}_{i}\right)=\frac{n-1}{{{\displaystyle \sum}}_{k=1}^{n}d\left({s}_{i},{v}_{k}\right)}$, $d\left({s}_{i},{v}_{k}\right)$ represents the shortest distance of Stroke ${s}_{i}$ and Stroke ${v}_{k}$. |

Method | Number of Correct Types | Number of False Types | Sample Size | Accuracy Rate (%) |
---|---|---|---|---|

Improved algorithm | 92/178 | 8/22 | 100/200 | 92/90 |

Every-best-fit | 83/158 | 17/42 | 100/200 | 83/79 |

Self-best-fit | 79/150 | 21/50 | 100/200 | 79/75 |

Self-fit | 72/138 | 28/62 | 100/200 | 72/69 |

Sum | 326/624 | 74/176 | 400/800 | 82/78 |

Sample Size | Chi-Square | Degrees of Freedom | Significance |
---|---|---|---|

100 | 15.2 | 3 | 13.8 > 7.82, Yes |

200 | 24.7 | 3 | 24.7 > 7.82, Yes |

Methods | Absolute Difference | Critical Range | Significance |
---|---|---|---|

Improved algorithm and Every-best-fit | 0.09/0.11 | 0.065/0.051 | Yes/Yes |

Improved algorithm and Self-best-fit | 0.13/0.15 | 0.078/0.059 | Yes/Yes |

Improved algorithm and Self-fit | 0.20/0.21 | 0.087/0.063 | Yes/Yes |

Study Area | Stroke Generation Method | Length of Selected Road Segment (Km) | Length of Identical Strokes with Existing Map (Km) | Length of Identical Road Segments/Existing Map (%) | Length of Identical Road Segments/Automated Algorithm Result (%) | Accuracy of Road Selection (%) |
---|---|---|---|---|---|---|

Neixiang County (The length of existing map is 72.3 (Km)) | Improved Method | 74.8 | 65.4 | 90.1 | 87.4 | 88.8 |

Every-best-fit | 76.1 | 62.2 | 86.0 | 81.8 | 83.9 | |

Self-best-fit | 77.4 | 60.8 | 84.1 | 78.5 | 81.3 | |

Self-fit | 79.2 | 58.0 | 80.2 | 73.2 | 76.7 | |

Tianjin City (The length of existing map is 108.7 (Km)) | Improved Method | 111.4 | 96.4 | 88.7 | 86.5 | 87.6 |

Every-best-fit | 113.7 | 89.6 | 82.4 | 78.8 | 80.6 | |

Self-best-fit | 114.2 | 86.7 | 79.8 | 75.9 | 77.9 | |

Self-fit | 110.5 | 93.0 | 85.6 | 84.2 | 84.9 | |

Shanghai City (The length of existing map is 214.5 (Km)) | Improved Method | 217.7 | 185.5 | 86.5 | 85.2 | 85.9 |

Every-best-fit | 216.3 | 174.1 | 81.2 | 80.5 | 80.9 | |

Self-best-fit | 220.2 | 181.7 | 84.7 | 82.5 | 83.6 | |

Self-fit | 218.4 | 171.2 | 79.8 | 78.4 | 79.6 |

Road Selection Method | Length of Selected Road Segment (The length of Selected Road Segment by Manual Selection is 72.3 (Km)) | Length of Identical Strokes with Manual Results | Length of Identical Road Segments/Manual Result (%) | Number of Identical Road Segments/Automated Algorithm Result (%) | Accuracy of Road Selection (%) |
---|---|---|---|---|---|

Stroke-Based Method | 78.9 | 60.9 | 84.2 | 77.2 | 80.7 |

Mesh Density-Based Method | 76.7 | 61.2 | 80.2 | 79.8 | 78.5 |

Improved Method | 74.8 | 65.4 | 90.1 | 87.4 | 88.8 |

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**MDPI and ACS Style**

Zhang, J.; Wang, Y.; Zhao, W.
An Improved Hybrid Method for Enhanced Road Feature Selection in Map Generalization. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 196.
https://doi.org/10.3390/ijgi6070196

**AMA Style**

Zhang J, Wang Y, Zhao W.
An Improved Hybrid Method for Enhanced Road Feature Selection in Map Generalization. *ISPRS International Journal of Geo-Information*. 2017; 6(7):196.
https://doi.org/10.3390/ijgi6070196

**Chicago/Turabian Style**

Zhang, Jianchen, Yanhui Wang, and Wenji Zhao.
2017. "An Improved Hybrid Method for Enhanced Road Feature Selection in Map Generalization" *ISPRS International Journal of Geo-Information* 6, no. 7: 196.
https://doi.org/10.3390/ijgi6070196