LCBRG: A lane-level road cluster mining algorithm with bidirectional region growing

2.1 Motivation

A cluster refers to a group of similar things that are close together. Lanes are always modeled as lines in the spatial database. Generally speaking, a lane-level road cluster is defined as a set of lane lines that are clustered into groups by some constraints such as distance and orientation. The lane lines in one cluster are not limited to these with strict parallel relationships. As shown in Figure 2, some short lanes are nonparallel but they are still regarded as a part of the cluster because they are located in the region of the existing cluster. However, the existing research cannot deal with these complex situations. For example, Luan and Yang [32] and Savino and Touya [10] provide methods for parallel line recognition, which are unable to handle complex line cluster with nonparallel sense.

Figure 2

Lane-level cluster in road networks of OpenStreetMap.

With the development and integration of mobile communication and wireless Internet, smart mobile devices, and mobile sensors and measurement, the spatial information is massively surging. The possible reasons for line cluster include at least the following aspects [33]:

1. In terms of user demands, the spatial data used for driving and riding navigation require that the geographical features should be detailed as precisely as possible, and that motorway, lanes, sidewalks, and so on should be modeled in detail.

2. From the view of data collection, Volunteered Geographic Information (VGI) systems are now important data source for spatial data updating. Some participants of VGI are short of professional cartographic knowledge (such as the concept of map scale), so they collect data according to their personal need and experience without authoritative supervision, strictly in accordance with neither the navigation data standards nor the topographic map standards. The subjectivity of the participants leads to the appearance of multiple inharmonious shapes and attributions of the same geographic object. This may lead to the existence of data repetition and multiple and inconsistent levels of details (LoDs) [34].

3. The reference dataset is of great variety, including existing map productions, different high resolution remote sensing image datasets, the US Census Bureau TIGER, Ordnance Survey OpenData, ArcGIS Open Data, open navigation data, VGI systems such as OpenStreetMap, and other open or authoritative data sources. These platforms are independent of each other, and there are no uniform data production specifications, resulting in spatial data inconsistency (in referencing system, data model, coding system, visualization, and so on). The location and geometric shape of different reference datasets are always inconsistent. In addition, the LoDs of some data sources are higher than the topographic map specifications, while others are lower or even short of.

4. New acquisition equipment such as vehicle-based GPS and smart mobile devices are widely used [35,36,37], resulting in the acceleration of the speed of data acquisition and the improvement of data currency, but the data quality is not always guaranteed: spatial and temporal accuracy of different receivers and positioning methods (such as GPS/Beidou satellite navigation system, mobile wireless positioning, or integrated navigation) are inconsistent; the storage formats and attributions of data collected by different equipment lack uniform standards; unprofessional operations such as arbitrary driving lead to irregular trajectory; and acquisition equipment is also greatly affected by platforms, weather, and other natural conditions [38]. The noises may make the road trajectory irregular.

A large amount of noises in spatial data not only increase the data redundancy but also affect the overall accuracy of the map production, which will increase the burden of the cartographers, thus affecting the quality of the map updating. For example, in the emergency mapping [39,40], noise information is a serious obstacle to the acquisition of fine information in the disaster area, which will delay the relief time and will directly bring great life and property damage. Therefore, it is necessary to quickly and automatically extract high-quality road information for cartographic mapping.

2.2 Characteristics of line cluster

The abovementioned investigation shows the following characteristics: (1) most of the line clusters in various reference datasets are always with multiple inconsistent versions; (2) they do not comply with the existing NMA cartographic specifications; and (3) the topological relationships of the line primitives in the lane-level road cluster are chaotic. Although the symbolized Digital Cartographic Model (DCM) map production appears to be correct, the Digital Landscape Model (DLM) dataset behind may be chaotically organized with disordered topological relationships. Figure 3a shows the DCM result from OpenStreetMap website after symbolized rendering, while Figure 3b shows the corresponding DLM dataset. It can be seen from the DLM dataset (and the five enlarged views) that the length and orientation of the lines in the lane-level road cluster are almost inharmonious, but the one or more line primitives together contribute to the geometric representation of the corresponding geographic object.

Figure 3

DCM and DLM of lane-level roads from OpenStreetMap: (a) DCM and (b) DLM.

Examining the different conditions of the lane-level road cluster, we found that the line primitives that make up the cluster have the following characteristics or relationships:

1. Condition C1: Distance. The distance between line primitives satisfies the certain prior threshold. In general, a semantic road entity (road sections that have the same semantic name) may be represented collectively by one or more lane-level primitives, but the distance between them is generally less than the road width w plus the data error δ, namely the sum (w + δ).

2. Condition C2: Parallelism. The orientation between line primitives is approximately parallel. Due to the practical factors such as traffic rules, vehicle driving safety, and so on, the lane-level road primitives that represent the traffic information are generally parallel to each other.

3. Condition C3: Containing relationship. The line primitives located in the region of existing clusters are regarded as a part of the cluster. This condition mainly deals with the nonstandard lane information such as overpass and footway with the corresponding steps. These facilities are usually modeled as lines and stored together in the road database, sometimes with attributions provided by conscientious and dedicated participants.

Of the three conditions above, not all the three relationships are necessary to be a lane-level road cluster. If conditions C1 and C2, or C1 and C3, or C1, C2, and C3 are satisfied, it is possible to determine those lanes as a cluster.

As we know, the distance between two intersecting lines is zero. So not all the lines with a distance of zero constitute a cluster. Either parallelism or containing relationship or both of them are required to be satisfied to be a lane-level road cluster. Take Figure 4 as an example. The red dotted line primitive in Figure 4a is not accepted as a part of the cluster for distance constraint. Though distance constraint is satisfied, the red dotted line primitive in Figure 4b is not accepted because neither parallelism nor containing relationship is satisfied, while the blue dotted line in Figure 4c satisfies containing relationship; therefore, it is accepted as a part of the cluster.

Figure 4

Three cases of cluster conditions.

In addition, the composition of a cluster has no direct relationship with the length of the line primitive. Even though the lengths of line primitives are uneven, which means failing to meet the spatial alignment [41], a cluster is possible if they satisfy the above relationships. This situation will be handled by the novel MD algorithm in Section 4.

According to the characteristics of the lane-level road cluster, the constraints condition of lane r _i and r _j to be a cluster can be formalized as the following three sub constraints:

• T1: the distance between r _i and r _j is less than the threshold T _d.

• T2: the orientation difference between r _i and r _j is less than the threshold T _dir.

• T3: though T2 is not satisfied, r _i (r _j ) is located in the region of any existing cluster.

A bidirectional region growing algorithm is proposed to lane-level road clustering in Section 3, and the involved quantitative constraints is descripted in detail in Section 4.

3.1 Method’s basic strategy

The lane-level road cluster can be extracted by geometric and semantic methods. The semantic information such as the street names is very efficient when extracting the lane-level clusters. In practical project, we prefer the semantic information in the extraction work when it is available and with high quality. However, there are still many difficulties when using the semantic information. For example, the semantic information may be omitted or uncompleted during the data acquisition. Another example is that, the semantic information may have different encoding methods and recording formats, which leads to more measurement difficulties in semantic similarity.

From the perspective of scientific research, geometric methods and semantic methods are two different categories, so the research objects are greatly different. In this article, we focus on the geometric information. From the perspective of practical application, the geometric method and semantic method complement each other and need to work together.

By analyzing the characteristics of the lane-level road cluster, the following strategy is proposed to identify the cluster: First, according to condition C1, the distance constraint is used to identify the initial cluster. Second, line primitives that do not meet the parallelism relationship in condition C2 are removed from the recognized initial clusters. Finally, for the remaining line primitive which has not been assigned to any cluster, check condition C3. If the line primitive is contained by the region of any existing cluster, assign it to the corresponding cluster.

Based on this strategy, a lane-level road cluster mining algorithm with bidirectional region growing (LCBRG) is proposed, which extracts clusters both horizontally and vertically. The algorithm steps are as follows:

1. Calculate the quantitative constraints of lines and capture the proximity relationships among line primitives.

2. Region growing cluster on the vertical (RGCV) examines the neighboring lines of the initial seed line along the line orientation and determines whether the line neighbors should be assigned to the existing cluster. Here the neighboring relationship means the connection between neighboring roads.

3. Region growing cluster on the horizontal (RGCH) examines the neighboring lines of the initial seed line which are perpendicular and adjacent to the seed line and determines whether the neighbors should be assigned to the existing cluster. Here the neighboring relationship means the proximity.

4. Traverse all the remaining ungrouped line primitives and examine whether the line primitive is contained by any existing cluster. If yes, assign this line primitive to the corresponding cluster.

The complexity of LCBRG is O(n ²), where n denotes the lane number. In order to reduce the computational complexity, strokes are first constructed according to the principle of good continuation [42]. Line primitives with similar orientation at the touching endpoint are assigned to the same stroke. In fact, stroke construction is in some sense a sub-step of RGCV.

The two key sub-steps of LCBRG algorithm, RGCV and RGCH, are conducted in the Sections 3.2 and 3.3, respectively to recognize the lane-level road cluster.

3.2 RGCV

RGCV examines neighboring lines of the initial seed line along the line orientation and determines whether the line neighbors should be added to the existing cluster. Here the neighboring relationship means the connection between the neighboring roads. Considering the quality characteristics of lane-level road cluster, lines may have dangles or pseudo-nodes. As shown in Figure 5, the endpoints should be touched, but they are not due to the lack of professional knowledge of the participants. Hence, a buffer circle with the radius α is offered to cover the dangles or pseudo-nodes that are not connected to the seed line. That is, if two lines are connected by the same buffer circle, they are regarded as neighbors and will be assigned to the same cluster.

Figure 5

The buffer circle in RGCV.

Here the buffer radius α is critical. Figure 5a shows the case that buffer radius α is too small to detect the candidate neighbors, where line B is ignored which should be assigned to the cluster of line A. While Figure 5b shows the case that buffer radius α is too large that too many candidate neighbors are detected, where lines C and D are detected which should not be assigned to the cluster of line A. Considering the fact that the maximum distance between lanes is generally less than the road width, half of the road width is suggested for buffer radius α. Even in the case that candidate neighbors are excessively detected, the detected candidates are still located in the region of the road polygon, which will not affect the identification results of lane-level clusters. Thus, the maximum value of buffer radius α is suggested to be half of the road width.

Let the integer K denote the cluster number, the integer array cls() denote the cluster that a stroke belongs to, the list array clu(k) denote the objects that a kth cluster contains, and the Boolean array bVisited() denote whether the stroke has been visited. The RGCV is conducted by the following steps:

1. For the interested dataset, strokes are first identified using the method in research [32]. Initialize all the notation variables to 0.

2. For the identified strokes, select one of them (the first in this article) as seed stroke r ₀ .

3. If bVisited(r ₀ ) = false, query the candidate neighboring strokes set Cnt(r ₀ ) which are not disjoint with the buffer circles of the endpoints of stroke r ₀ . If cls(r₀ ) = 0, then K++; set cls(r₀ ) = K, and add r₀ to clu(cls(r₀)). Let bVisited(r ₀ ) = true.

4. For each stroke cr _i ∈ Cnt(r ₀ ), if cls(cr _i ) = 0, test the constraints condition c(r ₀ , cr _i ). If c(r ₀ , cr _i ) is satisfied to T2, then cls(cr _i ) = cls(r ₀ ), add cr _i to clu(cls(r ₀ )). Let bVisited(cr _i ) = true.

5. Let r ₀ = cr _i , recursively carry out step3 to step5 until all the strokes are visited.

3.3 RGCH

RGCH examines neighboring lines of the initial seed line which are perpendicular and adjacent to the seed line and determines whether the neighbors should be added to the existing cluster. Here the neighboring relationship means the proximity relationship. The methods to measure proximity include the topological method (such as Delaunay triangle) and metric method (such as buffer analysis). The topological method using Delaunay triangle captures proximity relationship without the limitation of distance, and two features are regarded as neighbors if they are connected by the same Delaunay triangle and are not separated by other features, which means that it is a qualitative approach. It can be seen that even if there is a street block between two lanes from different roads (the distance between them is larger than road width), they are considered adjacent. This is against our motivation. In fact, only the lanes with specific distance can be treated as a cluster. So the topological method using Delaunay triangle may fail to detect the correct candidate neighbors, thereby making the subsequent steps time-consuming. Taking the road width into account, this article uses the buffer analysis with fixed radius β to capture the neighbors. The buffer radius β needs to agree with traffic rules, driving safety, road design principles, and other related factors.

Using the notations in RGCV, the RGCH is conducted by the following steps:

1. Perform RGCV. Reinitialize the Boolean array bVisited() to zero. Set variable k = 0.

2. While k ≤ K, visit the kth result clu(k) identified in RGCV. For each stroke r _i ∈ clu(k), go to step 3.

3. If bVisited(r _i ) = false, query the candidate neighboring strokes set Near(r _i ) which are not disjoint with the buffer of r _i . Let bVisited(r _i ) = true.

4. For each stroke nr _j ∈ Near(r _i ), if cls(nr _j )≠cls(r _i ), test the constraints condition c(r _i , nr _j ). If c(r _i , nr _j ) is satisfied to both T1 and T2, then add the list array clu(cls(nr _j )) to clu(cls(r _i )). For each stroke r _q ∈ clu(cls(nr _j )), set cls(r _q ) = cls(r _i ) and bVisited(r _q ) = true. Let bVisited(nr _j ) = true.

5. Let r _i = nr _j , go to step3.

6. Let k = k + 1, recursively carry out step 2 to step 5 until k > K or all the strokes are visited. The list array clu(k) with more than one object inside is regarded as a candidate cluster.

4.1 Distance metric strategy

First, the facing projection distance (PD) metric strategy is achieved by the following:

For the given two lines, noted as A = { a 0 , a 1 , … , a p } and B = { b 0 , b 1 , … , b q } , interpolation is conducted. For line A, for each vertex b _i on B, the travel distance between the b _i and b ₀ is noted as subLen(b ₀, b _i ) and the length of B is noted as Len(B). Create a new vertex on A at the location with the length subLen(b ₀, b _i ) × Len(A)/Len(B). Traverse all the vertexes on B, so that we get the interpolated A noted as A ′ = { a ′ 0 , a ′ 1 , … , a ′ t } , where t = p + q. Similarly, using the same strategy, interpolation on B is conducted and the interpolated B is noted as B ′ = { b ′ 0 , b ′ 1 , … , b ′ t } . The aim of interpolation is to reduce the effect of the unequal number and non-uniform distribution of vertexes.

With this, the distance between A and B is defined as

where MAX[·] means the maximum function, AVG[·] means the average function, and PD(A′, B′) denotes the average of facing PDs between each vertex of lines A′ and B′. ‖a − B′‖means the facing PDs between the vertex a and the line B′. The facing PD between a vertex and a line is the distance between the vertex and its projection point on the target line.

The projection point is calculated as follows. As shown in Figure 7, L ₁ and L ₂ are two lines and C (x ₁ , y ₁), D (x ₂ , y ₂), and B (x ₃ , y ₃) are the vertexes. The projection point z _t (x _t , y _t ) of source vertex B projected on the segment linking C and D is defined as:

where λ = Δ x 21 Δ x 32 + Δ y 21 Δ y 32 ( Δ x p q = x p − x q , Δ y p q = y p − y q ) and μ = Δ x 21 2 + Δ y 21 2 .

Figure 7

The calculation of projection point.

Here it is critical to find which segment the projection point is projected on. However, except the two endpoints, every vertex is shared by two segments. When the angle of the two touching segments is sharper, it is difficult to find which segment the projection point is on. For example, the projection point of vertex E in Figure 7 will fall beyond any segments of L ₂ but on the extension of the segment. Xing et al. [47] proposed the midpoint of the source segment as reference point to calculate the facing PD.

The method to find the projected segment is as follows: Taking Figure 8 as an example, midpoints of every segments of L ₁ are calculated first, and they are treated as reference points. Taking P ₂ as an example reference point, its projection point projected on L ₂ is noted as P′₂. Among the segments linking P ₂ and the vertexes of L ₂, the distance of P ₂ P ₆ is the minimum. Hence, the projection point certainly falls on either P ₅ P ₆ or P ₆ P ₇. According to the geometry characteristics of the triangle, if the perpendicular segment starting from one vertex of a triangle falls inside the triangle, the interior angles at the other two vertexes cannot be obtuse angle. As shown in Figure 8, both the interior angles at P ₆ and P ₇ of the triangle ΔP ₂ P ₆ P ₇ are not obtuse angle, so the segment linking P ₆ and P ₇ is suggested as the segment that the projection point P′₂ is projected on.

Figure 8

The position judgment of facing projection points.

More details about facing PD can be found in our previous research by Xing et al. [47]. Existing research about the line distance is based on the set of the line vertexes, while the PD metric is based on every vertex of the line to another line, which makes it outstanding in dealing with inharmonious spatial alignment [47].

4.2 Moving strategy

The spatial alignment is of great importance in measuring distance and orientation between lines. When the spatial alignment suffers a greater difference (twice as suggested), the true distance and orientation may become greater than they are. Hence, we give more attention to spatial alignment by employing the proposed moving strategy and define a novel MD metric. The intended purpose is to get the minimum orientation and distance between two lines with large differences. The moving strategy is performed when the length of the longer line is greater than or equal to twice the length of the shorter one [49]. The moving step length, noted as stepLen, is set by the user. It is suggested as 1 m in this work. The comparison in Section 5.1 shows that the MD metric is more capable than PD with the situation of heterogeneous length.

Let Len() denote the length function. Referring to Figure 9, the moving strategy is carried out by the following steps to get the MD and orientation:

1. Let A be the longer line and B the shorter. Set interpolation step length as stepLen and interpolate A and B.

2. Calculate the ending condition N, N = (Len(A)-Len(B))/stepLen. Set variable i = 0.

3. Select a ₀ as the starting seed vertex (i = 0), get the sub-curve A′ _i with the distance of Len(B), and calculate the distance PD _i and orientation θ _i between A′ _i and B.

4. If i < N，then move A′ _i along A with the distance of stepLen. That is, move A′ _i to the next interval location, so that A′ _{i + 1} is obtained. Calculate the distance PD _{i + 1} and orientation θ _{i + 1} between A′ _{i + 1} and B. i = i + 1. Execute step 4 until i ≥ N. If i ≥ N, then go to Step 5.

5. Find the minimum value of PD _i . The corresponding PD _i and θ _i are regarded as the moving distance and orientation difference, respectively, between A and B. That is, the moving distance MD(A, B) = MIN(PD _i ).

Figure 9

The moving strategy schematic of MD metric.

The computational processes of MD mainly include point distance, point interpolation, facing PD, and the moving strategy. The computational complexities are O(1), O(t), O(t ²), and O(t ³), respectively. So the computational complexity of MD is O(1 + t + t ² + t ³) = O(t ³).

5.1 Validation of MD

To check the validation and compatibility of the proposed MD for line clustering, five examples are provided, as shown in Figure 10. The dashed line is the buffer region with a distance of 5 m. From the perspective of human visual perception, it can be qualitatively found that the distance between lines in the experimental examples is approximately 10 m. Four sets of comparison experiments are designed. Compared with Figure 10a, the length of the line below in Figure 10b is smaller, the shape complexity is less in Figure 10c, the vertex number of the line below in Figure 10d is less, and the spatial alignment in Figure 10e is more heterogeneous. With the line distance, these examples include the aspects of length, shape complexity, vertex distribution, vertex number, and spatial alignment. Actually, Figure 10b–d collaboratively contribute to the shape complexity to some extent.

Figure 10

Example for the validation of MD.

Besides the classic ED, HD, and FD, other two recently introduced distance metrics from Huang et al. [46] and Xing et al. [47] are employed to compare with the MD method proposed in this article. More details of these five distance methods can be found in refs [43,44,46,47]. For short, these five metrics are noted as ED, HD, FD, HBHD, and PD. For the five examples in Figure 10, the distance results calculated by these five methods are shown in Table 1.

To understand Table 1, the readers have to compare both different rows and columns. Different columns demonstrate the different metric capabilities with the same factors. Different rows demonstrate the different metric stabilities with different factors. For example, the HD and MD in Figure 10a are 25.487063 and 10.745835. In Figure 10e, the line below only moves right side, and the spatial alignment is the more heterogeneous, While the HD and MD are 54.021876 and 9.679917. The rates of value change are |25.487063 − 54.021876|/25.487063 and |10.745835 − 9.679917|/10.745835, that is, 111.958027% and 9.919359%, respectively. This means that when measuring distance, MD has a better stability and is more robust to the heterogeneous spatial alignment.

For further analysis, statistical indicators, i.e., maximum (Max), minimum (Min), average (Avg), median (Med), and standard deviation (SD), are calculated, as shown in Table 2. Box plot is also employed to visualize the range, distribution, central value, and variability of each metric, as shown in Figure 11. The box ranges from 25 to 75%. The whisker indicates variability outside the upper and lower quartiles such as the most extreme values in the dataset (maximum and minimum values).

Figure 11

Box plot to display the range of each metric.

In order to measure the deviation between the distance of different metrics and that of human visual perception, the deviation between the average and 10 m (visual distance) is calculated, noted as avg-10 in Table 2. The dashed line standing for the distance of 10 m is also illustrated in Figure 11 to visualize the deviation. It can be found that the deviation (avg-10) of MD is the smallest in Table 2, which means it is closest to the distance of human spatial cognition as shown in Figure 11.

On one hand, as stated in refs [46,47], ED measures the minimum distance between point sets without the consideration of shape, size, order, and alignment of object groups. On the other hand, though the SD of ED is the smallest, the avg-10 deviation is larger than that of MD. Among the other four, the variation range of MD is the smallest, which means that MD has better stability when dealing with the situation of non-uniformly distributed vertexes, heterogeneous length, inharmonious spatial alignment, and complex shape.

Actually, HBHD and PD are improved based on HD and FD. The results also reflect the fact that they perform better than the latter. On the state of the art, the applicability for line clustering from large to small is MD, PD, HBHD, FD, HD, and ED. The theory analysis, measuring stability, and visual reliability jointly proved that the proposed MD method is suitable for line clustering.

5.2 Lane-level road clustering

To verify the effectiveness of the proposed method, a real dataset from OpenStreetMap is used in the experiments. The experimental region is located in the east of Beijing City, between 39°56′25.30″ N to 39°54′24.40″ N latitude and 116°29′3.22″ E to 116°32′14.60″ E longitude, as shown in Figure 12. The semantic information of the region is uncompleted and fails to conduct the extraction work, so lane-level road clusters are extracted using the proposed LCBRG method. The distance threshold is critical and it is necessary to consider traffic planning, road design, and other factors. The lane width is the width required for safe and comfortable driving on the road, which considers the vehicle width and the extra width that is necessary for the overtaking or parallel driving. In general, the width of motorway in the city’s main road is 3.5–3.75  m, and the width of the sidewalk varies from 3 to 10 m [50,51]. The width of the central isolation zone ranges from 1 to 10 m [50,51]. There may also be overpasses, toll stations, and so on. Accordingly, the distance threshold T _d of lane width in this article is set to 25 m. Therefore, the buffer radius α in RGCV is 12.5 m and the radius β in RGCH is 25 m. The orientation difference threshold T _dir is set to 30°. The parameter table is shown in Table 3.

Figure 12

Lane-level road cluster input data and result. (a) The input strokes labelled with strokes IDs; (b) Lane-level road cluster result.

There are 119 road lanes in the experimental area, as shown in Figure 12. Because of the good organization of road networks, we use the method in ref. [42] to identify the strokes. Fifty-two strokes are recognized including the stroke-structured road group and single road lane. Using the proposed LCBRG method to mine the lane-level clusters from Figure 12, eight lane-level clusters are obtained, where 38 strokes are involved, as the colored solid class 1–8 shown in Figure 12. The details of the lane-level road clusters are listed in Table 4. Also, the statistics of lane-level road cluster result are shown in Table 5. It can be seen that 73.08% strokes are recognized as lane-level clusters. There are still 14 (52-38, as shown in Table 5) single road strokes that are not involved in the lane-level clusters, shown as the dashed class 0 in Figure 12.

In addition, there is one undesirable phenomenon in the recognized result, the cluster A shown in Figure 12, which is surrounded by the dotted line. Cluster A contains strokes {#45, #46, #47, #50, #51}. The overlap proportion of stroke {#45} and strokes {#46 and #47} is consistent with the constraint of lane-level constraint condition and therefore they are identified as part of the same cluster. There are at least the following two reasons responsible for this undesirable phenomenon:

1. Stroke construction algorithm. The experimental dataset does not have semantic information, so strokes are geometrically identified mainly according to the principle of good continuation. Hence, two lanes may be regarded as parts of a stroke because of their good local continuation, leading to the fact that the lanes may have large curvatures, such as the strokes #45, #46, and #47. In other applications, users should take into account both semantic information and good continuation principle to identify a stroke.

2. Lane-level road cluster recognition. In order to be compatible with the situation of heterogeneous length and inharmonious spatial alignment, the radius β in RGCH is relaxed. The advantage is that short lanes, such as those in the region C in Figure 13, are also identified as parts of a cluster, which will greatly increase the robustness and universality. But the drawback is also clear that there will be some undesirable lanes such as those in the dotted region A in Figure 12. On the whole, this relaxation is worthy, because the number of short lanes is far more than the number of that with large curvature (at least 10 times in general). In other applications, the threshold of the length constraint should be set based on user demands, data characteristics, and actual situation.

Figure 13

Enlarged view of lane-level road cluster result.

An enlarged sub-view of Figure 12 is shown in Figure 13. It can be seen that the proposed method can not only extract the regular two-lane road, but also the irregular lane-level road. However, the method by Zhang et al. [48] uses a strict parallel coefficient as a quantitative indicator to extract only two-lane roads, while the proposed method uses the distance, proximity, and orientation relationships; hence, it is more advantageous in robustness. Consequently, some noise lanes that satisfy T1 or T2 are assigned to clusters, for example, the region C in Figure 13. This means that the proposed method is more general that Zhang et al. [48]. Assigning these noise lanes to clusters makes the concept of semantic road entity more sufficient.

It should be noted that the overpasses are usually modeled as lines and stored together in the road database, as the region D shown in Figure 13, which is enlarged and shown in Figure 14a. This may lead to the fact that parts of the facilities such as steps or escalators along the road may be identified as parts of lane-level clusters. Although it is reasonable in geometry and social function, it destroys the semantic integrity of overpass, and will affect the actual width of the detected road clusters. An overpass is a bridge, road, railway, or similar structure that crosses over another road. The steps or escalators are components of overpass structure and cannot be individually assigned to the cross road. Hence, steps or escalators should be treated as a whole according to their semantic information or other more excellent methods.

Figure 14

Two undesirable examples: (a) overpass in lane-level road cluster dataset and (b) lane involved in the composition of multiple clusters.

In addition, due to data collection, data quality, and other reasons, some lanes may be visually involved in the composition of multiple lane-level road clusters. In the “L” shaped #43 lane shown in Figure 14b, the corner vertex at the right angle visually turns the lane into two parts, the horizontal part of #43 lane is visually adjacent to the cluster C3, while the vertical part is visually adjacent to the cluster C8. The length proportion that each part falls into the corresponding cluster is approximately the same. Since the distance between the road and the cluster C3 is smaller, it is recognized as a part of cluster C3. In other applications, distance, length proportion of each cluster, and other factors may be taken into account.

The validation of the proposed method is verified using the local region of Beijing City. The undesirable phenomenon and possible affecting factors are also discussed. Furthermore, experiments are carried out on the whole city of Beijing. In the result shown in Figure 15, the red lines are the clusters recognized using the proposed method, while the gray ones are unassigned roads. It can be seen that the recognized lane-level clusters act as the skeleton and framework of road networks.

Figure 15

The lane-level road cluster result of Beijing City.

In urban planning, the lane-level roads are always the ones that are important due to the amount of traffic flow and the aim is to relieve the traffic pressure. It means that compared with single road, the lane-level roads reflect the importance and capacity to some extent. The characteristics of lanes measure the hierarchy of the road networks. In general, the more the number of the lanes is, the greater the capacity of the road is, and the more important the road is. Hence, the lane-level road always has high priority in cartographic generalization and multi-scale representation.

The experiment is conducted on a laptop equipped with a Microsoft Windows 10 64-bit operating system. The central processing unit (CPU) is an Intel Core i7-8750H, and the memory (RAM) is 32 GB in size. The total computation time of the Beijing case is 311.22 s. The proposed algorithm with high complexity is still time-consuming and may affect the scalability. For example, when the data volume is very large, it may run timeout and fail to get the result. Spatial partitioning and indexing strategy such as hashing, trees, and Morton index may be referred to speed up the searching process and reduce the number of candidates for testing.