A New Typification Method for Combined Linear Building Patterns with the Resolution of Spatial Conflicts

Abstract

Typification is a crucial generalization operator for maintaining the structure of building patterns in map generalization. However, in densely built-up areas, the structure of building patterns is complicated, and spatial conflicts exist not only within building patterns but also between them. Applying typification solely to individual patterns fails to resolve conflicts between them and does not adequately preserve their spatial distribution. To address these challenges, this study proposes a new typification method that treats linear building patterns with common buildings as a whole named combined linear patterns, simultaneously resolving the spatial conflict both within and between combined linear patterns. Firstly, linear building patterns and combined linear patterns are recognized, respectively, using visual perception principles and the common elements of linear building patterns. Secondly, spatial conflicts within the combined linear pattern are resolved through the segmental building reconstruction of linear building patterns and a reduction in linear building patterns at junction buildings. Finally, spatial conflicts between combined linear patterns are solved based on the position and number of conflict buildings in the patterns. The proposed method is evaluated using a building dataset from OpenStreetMap. The experimental results indicate that the proposed method can preserve the spatial distribution of building patterns with better legibility than the usual typification method for individual linear building patterns.

1. Introduction

Urban spatial structures provide crucial information that reflects human activities [1,2]. This topographic map information is mainly represented by building arrangements and patterns [3]. Therefore, when a map’s scale is decreased through map generalization, the spatial distribution of building patterns should be maintained as crucial information. Typification is a generalization operator specifically used for these situations. It reduces the number of buildings in building groups while preserving the spatial distribution characteristics of these groups [4,5,6].

Linear patterns are some of the most common distributions in urban buildings, and some scholars have studied the typification of linear building patterns. For example, Gong and Wu [4] proposed a typification method for linear patterns with a progressive and iterative process, and Wang and Burghardt [5] developed a typification approach for linear patterns inspired by stroke simplification. In densely built urban environments, buildings may exhibit high density and complex spatial arrangements [7]. Linear building patterns might intersect due to sharing common buildings. Furthermore, there may also be spatial conflicts between linear patterns. Therefore, to achieve better urban map generalization, it is necessary to explore a new typification method that treats these intersecting linear building patterns as a whole. In this study, intersecting linear building patterns are grouped to form a combined linear pattern. Correspondingly, a linear building pattern without intersection is referred to as an individual linear building pattern.

We propose a new typification method for combined linear patterns to preserve the spatial distribution of building patterns while eliminating the spatial conflicts between buildings. Our work makes several contributions. Firstly, a detection method for combined linear patterns is proposed based on grouping detected linear patterns, and the significance of each linear building pattern within the combined linear patterns is calculated to evaluate their importance. Secondly, a method of solving spatial conflicts within combined linear patterns is proposed to maintain their spatial distribution, including their specific arrangement and overall outline. Finally, a method of solving spatial conflicts between combined linear patterns is provided to preserve the distinguishability between each one.

The remainder of this study is organized as follows: Section 2 reviews previous works on the recognition and typification of building patterns. Section 3 presents the details of the proposed typification methods for generalizing building groups with combined linear patterns. Section 4 demonstrates the proposed method using a building dataset from OpenStreetMap, and its effectiveness is discussed and analyzed. Section 5 concludes this study and looks forward to further improvements.

2. Related Work

Many studies have been carried out on building typification. Typification methods maintain the distribution of building groups by determining the number, positioning, and representation of buildings after generalization. These studies can be classified into global typification or local typification.

Global typification processes buildings in the whole region and recognizes structural characteristics from a global perspective. For example, Regnauld [6] used the principle of divide and conquer to segment building groups by street blocks. Then, harmonization functions and secondary positioning methods were developed to reconstruct each building group. Sester [8] selected optimization approaches for generalization and used self-organizing maps for building typification. The mesh simplification technique, derived from the computer graphics area, is used to rapidly typify buildings. Buildings are abstracted as a graph, and the vertices representing buildings with the shortest edges are iteratively replaced by a new vertex until the number of vertices meets a threshold value [9]. Yan et al. [10] used affinity propagation clustering to achieve building typification. Based on a sparse graph of an input building set, messages are passed between all potential buildings, and point-similar object selection generates exemplars in local building clusters as the typified result. Global typification can maintain the overall layout, including all buildings within the study area, although the local regularity of building groups is ignored.

Local typification concentrates on building groups with certain regular patterns. Therefore, building pattern recognition is always applied before typifying building patterns in these methods [11]. The building patterns for typification are mostly linear and grid patterns, in which linear patterns include collinear ones and curvilinear ones; collinear patterns can be further classified as straight-line ones and oblique ones. These linear patterns can be recognized through multiple methods. For example, Rainsford and Mackaness [12] matched building groups with defined templates based on structural parameters to detect linear patterns. Zhang et al. [13] used a minimum spanning tree with the theories of gestalt and the theories of association fields to identify collinear and curvilinear patterns, respectively. Wei et al. [14] combined convex polygon decomposition to recognize linear patterns more widely. Grid patterns can also be identified based on linear pattern recognition. Du et al. [3] extracted grid patterns by combining parallel and perpendicular groups of collinear patterns, and Gong and Wu [15] detected grid patterns via graph theory, with a graph operation involving multi-connected linear patterns. Yan et al. [16] modeled vector building groups as a graph and identified regular patterns using the graph convolutional neural network. These building patterns have been typified using various methods. Gong and Wu [4] developed a typification method for linear patterns with a progressive and iterative process consisting of elimination, exaggeration, and displacement. Wang and Burghardt [5] proposed a typification approach for linear patterns inspired by stroke simplification. Wang and Burghardt [17] developed a mesh-based typification that uses the center of each mesh to generate a new building to maintain grid patterns. Shen et al. [11] designed a typification method for raster building patterns based on superpixel analysis. Local typification generally applies to specific scenarios, and each method adopts a particular building pattern with a limited range of buildings, especially for linear patterns.

However, according to the theory of urban morphology, urban structures exhibit a hierarchy between the whole region and individual linear patterns [1,18]. Therefore, multiple intersecting linear building patterns will form different shapes. For example, alphabet-like X-shaped (Figure 1a), L-shaped (Figure 1b), and T-shaped (Figure 1c) patterns can comprise linear building patterns [5], as can grid patterns [3,15] (Figure 1d). Linear building patterns may also form more building groups with incomplete regular patterns, such as in Figure 1e. Furthermore, building patterns can form a network like a road network [19]. The above research shows that linear patterns can be fundamental alignments for many building patterns. However, existing typification methods for individual linear building patterns cannot be directly applied to other kinds of building patterns, such as those in Figure 1. Furthermore, spatial conflicts between buildings in different building patterns must be resolved. In summary, it is necessary to develop a new typification method for combined linear patterns to solve spatial conflicts and maintain their spatial distribution.

3. Methodology

Our method follows the local typification practice. Combined linear patterns are first recognized and then typification is achieved by resolving spatial conflicts inside and between them. A flowchart of combined linear pattern typification is shown in Figure 2, and the following sections describe the main methods proposed in this study.

3.1. Detection and Analysis of Combined Linear Patterns

3.1.1. Characteristics and Recognition of Linear Building Patterns

Linear building patterns can be defined as building clusters whose elements are similar and that are arranged along a line [13,14]. According to the gestalt principles of perceptual grouping, objects tend to be regarded as a whole when they are close, similar, and regularly aligned with each other. In other words, the distribution of buildings should follow proximity, similarity, and continuity [13].

Proximity between buildings can be reflected by proximity graphs [20,21]. Proximity graphs of buildings can be generated through constrained Delaunay triangulation. If two buildings are connected by a common triangle, a segment is drawn to connect the centroids of these buildings. These lines are considered the edges of the proximity graph. If two buildings are linked by an edge, they have a proximity relationship. The proximity graph G = (V, E) represents proximity relationships, where V refers to the set of buildings, and E refers to the set of edges representing proximity relationships between buildings. If there is an edge between building A and building B, then the proximity relationship between A and B is denoted as Proxi(A, B) = 1.

Similarity describes how regular the elements of a building pattern are. Similarity is reflected by three aspects: size, shape, and orientation [14]. These factors are parameter differences between buildings. Differences in size are calculated using the ratio of the larger area to the smaller area between two buildings. The difference in shape is evaluated through the ratio of the larger edge count to the smaller edge count between the two buildings. Differences in orientation are measured by the difference between the main directions of the smallest bounding rectangles of two buildings. There are two special circumstances in orientation calculation. If a building is square, it has two main directions. Both main directions calculate the square building’s orientation differences from other buildings, and the smallest is chosen as the final result. If a building is circular, it has no sole direction to compare with other buildings. In this situation, the orientation difference is set to 0. The similarity is only calculated between buildings with proximity relationships. If two buildings, A and B, satisfy Formula (1), then the similarity relationship between A and B is denoted as Sim(A,B) = 1.

$$Sim\left(A,B\right)=\max (A_A,A_B)/\min (A_A,A_B)<T_{si}\&\max (E_A,E_B)/\min (E_A,E_B)<T_{sh}\&|O_A-O_B|<T_{or}$$

(1)

where T_si, T_sh, and T_or refer to the difference thresholds in the sizes, shapes, and orientations of two buildings. A is the area of a building, E is the edge count of a polygon, and O is the main orientation of the smallest bounding rectangle of a building.

Continuity represents the arrangement and smoothness of a building pattern pathway. The pathway of a linear building pattern is a polyline formed by the continuous vertices of pattern elements, also known as successive proximity edges. The arrangement and smoothness of a pathway can be represented by three measurements of the angles and distances of the continuous elements in building patterns. First, the angle deviations between adjacent edges should satisfy the threshold of the path angle, T_pa. Second, the orientation deviations between elements and pathways should be less than the threshold, T_ma. The pathway’s orientation at vertices is calculated based on the orientation of the connecting line between the previous and next vertices. The pathway’s orientation at terminal vertices is the orientation of its terminal edges. Third, the length ratio of two consecutive edges should be less than the threshold value, T_el. Therefore, if A_i−1, A_i, and A_i+1 satisfy Formula (2), then the continuity relation between them is denoted as Conti(A_i−1, A_i, A_i+1) = 1.

$$Conti\left(A_{i-1},A_i,A_{i+1}\right)=pa\left(e_1,e_2\right)<T_{pa}\&pd\left(e_1,e_2\right)<T_{el}\&a{a}_i<T_{ma}$$

(2)

aa_i is the deviation of orientation between elements and the pathway (aa in Figure 3); pa(e₁,e₂) is the angle deviation between adjacent edges e₁ and e₂ (pa in Figure 3); and pd(e₁,e₂) is the ratio of the larger length to the smaller length between two consecutive edges, e₁ and e₂.

A_i−1, A_i, and A_i+1 refer to any three successive buildings in a building set {A}. If all of them satisfy Formula (3), this building set constitutes a linear pattern.

$$\left\{\begin{array}{c}Proxi\left(A_{i-1},A_i\right)=1\cap Proxi\left(A_i,A_{i+1}\right)=1\\ Sim\left(A_{i-1},A_i\right)=1\cap Sim\left(A_i,A_{i+1}\right)=1\\ Conti\left(A_{i-1},A_i,A_{i+1}\right)=1\end{array}\right.$$

(3)

There is no strict distinction between collinear patterns and curvilinear patterns. Collinear patterns are actually a particular kind of curvilinear pattern. Therefore, the above method can detect both types.

3.1.2. Recognition of Combined Linear Patterns

When there are common buildings between linear building patterns, these patterns form a more complex shape. In this study, these intersectional linear building patterns are referred to as combined linear patterns. If {lin₁, lin₂, lin₃…lin_m} refers to the set of linear building patterns and every linear building pattern in this set intersects with at least one other linear building pattern in this set, then this set is defined as a combined linear pattern, denoted as $cm{b}_A={\left\{li{n}_i^A\right\}}_{i=1}^M$. For typification in this study, a linear building pattern without any buildings in common with other patterns can also be regarded as a special combined linear pattern.

3.1.3. Significance of Every Linear Building Pattern in Combined Linear Patterns

The significance of each linear building pattern determines reservation or movement during the typification process. The significance of each pattern is proportional to the homogeneity value and the number of buildings in a linear pattern [22]. Therefore, the significance of a linear pattern is defined as Formula (4).

$${Sig}_L=Homo\times num$$

(4)

where num is the number of buildings in a linear pattern, and Homo is the homogeneity of a linear pattern, defined by Formula (5).

$$Homo={\displaystyle \sum w_i\times (1-{STD}_i/{Mean}_i)i\in \{\mathrm{spacing},\mathrm{size},\mathrm{shape},\mathrm{orientation}\}}$$

(5)

where i is the variable describing various aspects (spacing, size, shape, orientation, etc.) of a linear pattern. The spacing value is the minimum distance between two successive buildings. The remaining three aspects measure each building in linear patterns using the same parameters in similarity. STD_i is the standard deviation of differences between successive buildings in a linear pattern in i, and Mean_i is the average value of differences between successive buildings in a linear pattern in i.

The typification of combined linear patterns is typified based on the significance of linear building patterns within it. Based on the basic significance of individual linear building patterns, in combined linear patterns, the importance of each building differs according to its position in a linear pattern. Buildings can be divided into three categories: junction buildings, terminal buildings, and internal buildings. If a building is an element in more than one linear pattern, it is defined as a junction building. Excluding junction buildings, if a building is the first or last building in a linear pattern, it is defined as a terminal building, and the remaining buildings are defined as internal buildings. Therefore, the significance of each linear building pattern is weighted based on different kinds of buildings. An improved significance equation is presented in Formula (6).

$${Sig}_C=Homo\times (w_n\times {num}_n+w_b\times {num}_b+w_c\times {num}_c)$$

(6)

where num_n, num_b, and num_c are the number of junction buildings, terminal buildings, and internal buildings, and w_n, w_b, and w_c are the weights of junction buildings, terminal buildings, and ordinary buildings. The larger the Sig_C value, the more important the linear building pattern is.

3.2. Typification of Combined Linear Patterns

3.2.1. Preconditions for Typification of Combined Linear Patterns

Before the specific typification method can be applied, some typification preconditions for combined linear patterns must first be defined: when to implement typification and what needs to be maintained during it.

The space between buildings in combined linear patterns is the key characteristic in triggering the typification method. The space between buildings is absolutely narrow locally but relatively loose globally. In other words, the former is measured by the minimum distance between buildings in patterns, and the latter is measured by the building density of patterns. The specific parameters of these two measurements are presented as follows.

(1) Density: The black–white ratio measures the density of building patterns. The black–white ratio of a linear pattern is defined as the ratio of the pathway length inside buildings to the total pathway length. In Figure 4, the black–white ratio of a linear pattern, denoted as D_l, is represented as the ratio of the total length of solid segments to the total length of all segments. The black–white ratio of a combined linear pattern is defined by Formula (7).

$$D_c={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{D}_l}$$

(7)

where n refers to the number of linear patterns in a combined linear pattern. The black–white ratio of a combined linear pattern should be less than the threshold, T_bw.

(2) Minimum distance: the minimum distance between one pair of buildings in a pattern should be less than the minimum separation threshold, T_md.

When building patterns meet these two conditions, typification algorithms can be implemented. Otherwise, other generalized operators should be considered, but this falls beyond the scope of this study and will not be elaborated on.

Combined linear patterns are hierarchical building groups, and the spatial distribution of building groups needs to be preserved after typification [23]. Therefore, the spatial characteristics and generalized ideas for combined linear patterns are proposed as follows.

Linear building patterns are the fundamental units inside combined linear patterns. As such, the linear distribution of buildings should still be preserved after generalization. Junction buildings are located at the intersection positions of linear building patterns. Therefore, junction buildings determine the main internal hierarchical structure of combined linear patterns. To keep the main structure in good condition, the junction buildings should be preserved. However, if there is not enough space to display multiple linear building patterns in a combined linear pattern—meaning there are spatial conflicts between the buildings in the same combined linear pattern—linear patterns and buildings with less significance must be discarded.

As building groups, combined linear patterns should maintain the independence of each individual pattern. Each building can only belong to one combined linear pattern at most, although a building can belong to multiple linear building patterns. In addition, there should be enough space between different combined linear patterns; that is, the distances between two buildings located in different combined linear patterns should be greater than the minimum separation threshold. Otherwise, spatial conflicts will arise between combined linear patterns.

Therefore, our typification method involves two parts: the resolution of spatial conflicts inside and between combined linear patterns.

3.2.2. The Resolution of Spatial Conflict Inside a Combined Linear Pattern

(1) Segmentation of linear building patterns

To maintain the position of a junction building, linear building patterns need to be divided into sub-linear alignments. Linear building patterns are separated at junction buildings that have at least one adjacent non-junction building. For example, in Figure 5, pattern 1 is separated at buildings b5 and b7 into sub-alignments 1a, 1b, and 1c. Although b6 is a junction building, adjacent buildings b5 and b7 are also junction buildings, so there is no separation.

(2) Reconstruction of buildings in a combined linear pattern

Buildings in a combined linear pattern need to be reconstructed through re-positioning and re-representation during building typification [9]. Typification should follow legibility constraints and preserve the constraints of map generalization [24]. Legibility for building patterns requires typified buildings to meet the minimum building size and minimum distance between buildings in the target scale. The original structure of the linear building pattern and the building characteristics should be preserved as much as possible. Furthermore, the homogeneity of building patterns will increase with decreasing scales, rather than in the opposite direction [22]. Therefore, the reconstruction of buildings in combined linear patterns must consider the shape, size, number, position, and orientation of buildings as follows:

• ①

  Shape: Building shape in linear building patterns is usually simple, but simplification needs to be considered for complex buildings. Thus, a rectangle is an ideal shape representation after typification. In addition, the elongation of buildings should remain the same before and after typification.

  ②

  Size: Given the rectangular shape after typification, the length and width of typified buildings are two shape parameters that must be confirmed. The initial building sizes within the same combined linear pattern are similar, so these buildings will adopt a uniform size after typification. According to the minimum size and average elongation, the uniform size is calculated using Formulas (8) and (9).

$${W_b}^a=\max ({\displaystyle \frac{1}{mn}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^n{w_i}^j}},minSize)$$

(8)

$${L_b}^a=\max ({\displaystyle \frac{1}{mn}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^n{l_i}^j}},minSize\ast Elg)$$

(9)

$$Elg={\displaystyle \frac{1}{mn}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^n{l_i}^j}}{\displaystyle /}{\displaystyle \frac{1}{mn}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^n{w_i}^j}}$$

(10)

where ${l_i}^j$ is the length of an original building, b_i, in lin_j; ${w_i}^j$ is the width of an original building, b_i, in lin_j; n is the number of buildings in lin_j; and m is the number of linear building patterns in a combined linear pattern.

• ③

  Orientation: Building orientation should reflect the direction of the linear pathway. However, there are angle differences between the buildings and the pathway. After typification, angle differences should be maintained but unified between buildings. Therefore, the orientation of a typified building is calculated per Formula (11).

$$ori\left(A_a\right)=ori\left({P_a}^v\right)+{\displaystyle \frac{1}{mn}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^{n}a{a_i}^j}}$$

(11)

where ori(P_a^v) is the pathway orientation at point v on the pathway, and aa_i^j is the deviation of orientation between the original building and the pathway, lin_j. For a junction building, ori(P_a^v) depends on the linear building pattern with a larger Sig_C.

• ④

  Number: The number of buildings in the combined linear pattern is calculated separately for each linear building pattern or sub-alignment. According to the definition of typification, the number of buildings should be decreased or remain the same after typification. The specific number is calculated using the target map scale and black–white ratio.

For an original sub-alignment or individual linear building pattern, the total length of the pathway is determined by Formula (12).

$$\left(D_0+S_0\right)\ast \left(n-1\right)={\displaystyle \sum _{i=1}^{n-1}{e}_i}$$

(12)

where D₀ refers to the average length of the pathway inside each building before typification; S₀ denotes the average length of the interval between neighboring buildings of the sub-alignment or the individual linear building pattern before typification; and e_i is the length of the edges in the sub-alignment or the individual linear building pattern. D₀ can be calculated by Formula (13).

$$D_0={\displaystyle \frac{1}{(n-1)}}{\displaystyle \sum _{i=1}^{n-1}l{b}_i}$$

(13)

where lb_i refers to the length of pathways inside each building of a sub-alignment or an individual linear building pattern, which are shown as solid segments in Figure 4. Thus, S₀ can be calculated using Formula (14).

$$S_0={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{j=1}^m{\displaystyle \sum _{i=1}^{n-1}{e_i}^j}}-D_0$$

(14)

Given the similar black–white ratio, the number of buildings in the linear building patterns is calculated per Formula (15).

$$N_j=floor({\displaystyle \frac{{\displaystyle \sum _{i=1}^{n-1}{e_i}^j}-D_1+D_0}{D_1+S_1}}+1)$$

(15)

$$D_1={L_b}^a\ast cos\left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^{n}a{a}_i}\right)$$

(16)

$$S_1=\max (D_1{\displaystyle \frac{S_0}{D_0}},T_{minDis})$$

(17)

where D₁ is the average length of the pathways inside each building after typification; S₁ denotes the average length of the interval between neighboring buildings in linear building patterns after typification; and N_j is the number of buildings in sub-alignments or individual linear building patterns.

• ⑤

  Position: The centroids of typified buildings are located on the original pathway. To ensure the outline of the linear building pattern, the first and last buildings in linear building patterns are located on the pathway slightly away from the end of the pathway. The centroids of the remaining buildings are evenly distributed on the pathway between the centroids of the first and last buildings in the sub-alignments of the individual linear building patterns.

(3) Reduction in linear building patterns at junction buildings for a sub-alignment

For a sub-alignment, if linear building patterns intersect at junction buildings, and the number of junction buildings in this sub-alignment is reduced after reconstructing the buildings, they need to be reduced simultaneously.

Linear building patterns at junction buildings can be reduced by merging or selecting these patterns. If the sub-alignment only retains one building after reconstruction, but there are multiple original linear building patterns at junction buildings before typification, the original linear building patterns are merged. If the sub-alignment retains more than one junction building, the linear building patterns at junction buildings are selected.

Before describing the reduction method, the move vector needs to be defined. In a sub-alignment, if the coordinate of a centroid for one original junction building is (x₁, y₁) and the coordinate of the centroid coordinate of the reconstructed building closest to (x₁, y₁) is (x₂, y₂), the moving vector of the linear building pattern at this junction building is represented by Formula (18).

V = (x₂ − x₁, y₂ − y₁)

(18)

When merging linear building patterns at junction buildings, only one intersectional pattern can be retained. In this situation, the merged linear building patterns at junction buildings should express the characteristics of all original intersection patterns. Firstly, each original linear building pattern at junction buildings in the current sub-alignment is subdivided into two sub-alignments based on its junction building in the current sub-alignment. Secondly, the sub-alignment with the largest significance on each side is selected to be displaced by its moving vector. Finally, the two sub-alignments on different sides of the sub-alignment are combined into a new intersection pattern. An example of merging linear building patterns at junction buildings is shown in Figure 6.

To select linear building patterns at junction buildings, the similarity of the original linear building patterns at these junction buildings must first be calculated based on the differences between a linear building pattern and its neighboring patterns, as shown in Formula (19).

$${Sim}_A={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n|{{Sig}_C}^A-{{Sig}_C}^i|}$$

(19)

where Sig_C^A is the target linear building pattern, and Sig_Cⁱ is the neighboring linear building pattern of the target linear building pattern. If a junction building is the previous or next building of another junction building in a sub-alignment, the two linear building patterns at these two junction buildings are considered neighboring patterns. Then, the linear building patterns with the highest similarity value at the junction buildings are selected. The number of selected linear building patterns at the junction buildings equals the number of junction buildings in the current sub-alignment after reconstructing the buildings. Finally, the selected linear building patterns at the junction buildings are displaced by moving vectors. An example of selecting linear building patterns at junction buildings is shown in Figure 7.

(4) Typification procedure for a combined linear pattern

The algorithm for typifying a combined linear pattern is as follows.

• ①

  The unprocessed linear building pattern with the largest Sig_C is selected as the current linear building pattern. If there is no unprocessed linear building pattern left, the algorithm ends.

  ②

  The current linear building pattern is segmented into sub-alignments based on the junction buildings within it.

  ③

  Buildings in all sub-alignments are reconstructed. The current linear building pattern is marked as processed.

  ④

  When the number of junction buildings in sub-alignments decreases, linear building patterns at these junction buildings are reduced. The deleted linear building pattern is marked as processed.

  ⑤

  The unprocessed linear building pattern at the junction buildings with the largest Sig_C value in the current linear pattern is selected as the current pattern, and we return to step ②. If there are no unprocessed linear building patterns at the junction buildings, we return to step ①.

3.2.3. Resolution of Spatial Conflict Between Combined Linear Patterns

(1) Resolution of spatial conflicts between buildings at different positions in linear building patterns

When the minimum distance between two buildings from different combined linear patterns (including independent linear building patterns) is less than the minimum separation threshold, T_md, there is a spatial conflict between these two combined linear patterns (including independent linear building patterns). In building pattern generalization, data quality focuses on the existence and spatial distribution of patterns rather than individual buildings. Therefore, buildings with such spatial conflicts should be adjusted. These buildings can be located at the terminal, junction, or internal parts of linear building patterns. The resolution and priority of spatial conflicts for buildings in different positions are different.

To resolve spatial conflicts at terminal buildings, displacement and deletion operations are considered for implementation. Terminal buildings can be displaced (TD1) along the pathway toward the interior of linear building patterns (e.g., building A in Figure 8b). The displacement distance equals the minimum separation threshold, T_md. If the displacement of terminal buildings resolves the spatial conflict, the linear building pattern containing these terminal buildings needs to be typified again (e.g., pattern 1 in Figure 8c). Otherwise, the terminal building is deleted (TD2) to resolve the spatial conflict (e.g., pattern 1 in Figure 8e).

To resolve spatial conflicts at internal buildings, internal buildings will be processed only if there are no other building types in the spatial conflict (e.g., building B in Figure 8b). Displacement of the internal building (ID) will change the linear building pattern’s distribution. In this study, deletion is used to solve spatial conflicts for internal buildings. After deletion, the remaining buildings in the sub-alignments or independent linear building patterns where the deleted internal building belonged need to be evenly distributed (e.g., pattern 2 in Figure 8c).

To resolve spatial conflicts at junction buildings, displacement is not considered because junction buildings connect more than one linear building pattern. Deletion (JD) is used to solve the spatial conflict for junction buildings in this study (e.g., building C in Figure 8b).

(2) Resolution of spatial conflicts between two linear building patterns at different positions

For two linear building patterns in different combined linear patterns, if the closest distance between buildings from different linear building patterns is less than the minimum separation threshold, T_md, according to the number and position of buildings with spatial conflicts, the resolution can be implemented as follows.

①

Terminal-to-terminal type

In this case, each of the two linear building patterns has a building with a spatial conflict; both of them are terminal buildings. TD1 is first executed on the terminal building with the spatial conflict from the linear building pattern with less significance. If the spatial conflict remains, TD1 is executed on the terminal building in the other pattern. If the spatial conflict is not resolved after two displacements, we roll back to the state without displacement, and then, TD2 is executed on the terminal building from the linear building pattern with less significance. An example of resolving a spatial conflict in the terminal-to-terminal type is shown in Figure 9.

②

Terminal-to-internal or terminal-to-junction type

In this case, each of the two linear building patterns has a building with a spatial conflict; one is a terminal building, and the other is either an internal building or a junction building. At this point, TD1 is used first. If the spatial conflict remains after the displacement, we roll back to the state before TD1 and then use TD2. An example of resolving a spatial conflict in the terminal-to-internal type is shown in Figure 10.

③

Internal-to-internal type

In this situation, each of the two linear building patterns has a building with a spatial conflict, and both are internal buildings. In this case, at least one linear building pattern is curvilinear. At this point, ID is used on both linear building patterns. An example of resolving a spatial conflict in the internal-to-internal type is shown in Figure 11.

④

Junction-to-internal type

In this case, each of the two linear building patterns has a building with a spatial conflict, one of which is an internal building and the other is a junction building. JD is used on the junction building. An example of resolving a spatial conflict in the junction-to-internal type is shown in Figure 12.

⑤

Junction-to-junction type

In this situation, each of the two linear building patterns has a building with a spatial conflict, and both of them are junction buildings. JD is executed on the junction building with less significance to resolve the spatial conflict. An example of resolving a spatial conflict in the junction-to-junction type is shown in Figure 13.

⑥

Multiple conflicts

In this case, there is more than one building with spatial conflicts in at least one linear building pattern in two linear building patterns with spatial conflicts. At this point, the buildings with spatial conflicts of less significance are deleted. An example of resolving multiple spatial conflicts is shown in Figure 14.

(3) Spatial conflict resolution procedure

The algorithm for resolving spatial conflict between combined linear patterns is as follows.

① The set of buildings with spatial conflicts is obtained by determining whether the minimum distances between any two buildings from different combined linear patterns are less than the minimum separation threshold, T_md.

② The set of linear building patterns with spatial conflicts is obtained using the set of buildings with spatial conflicts.

③ The spatial conflicts are resolved for each pair of linear building patterns according to the positions of conflicting builidngs.

4. Experiment and Analysis

4.1. Experiment Data and Parameter Settings

To verify the effectiveness of the proposed typification method, the experimental data are a building dataset downloaded from OpenStreetMap for Wuhan City, China. There are 410 buildings in the study area, as shown in Figure 15a. Due to their similarity to 1:10 K authoritative spatial data with more detail [25], the original scale of OpenStreetMap is considered to be 1:5 K.

To detect linear building patterns, the similarity parameters are selected as follows: the shape difference threshold, T_sh, is 1.5; the size threshold, T_si, is 1.9; and the length difference between two segments, T_el, is 1.8. For collinear patterns, the orientation threshold, T_or, is 10°; the angle difference threshold, T_pa, between two pathway segments is 10°; and the angle difference threshold between the pathway and buildings, T_ma, is 90°. For curvilinear patterns, T_or is 38°, T_pa is 50°, and T_ma is 15°. All parameters are determined via the trial-and-error method. The minimum length for building edges (minimum size) is 0.5 mm, and the minimum distance between buildings is 0.2 mm. The target scale of the map is 1:30 K.

4.2. Results and Analysis

The 44 linear building patterns detected are shown in Figure 15b. In total, 13 blue linear building patterns compose a grid-like combined building pattern. However, 28 red linear building patterns need to be typified, and 3 green linear building patterns are not typified because one does not conform to the threshold of the black–white ratio (pattern A in Figure 15b), and the other does not conform to the minimum distance threshold (patterns B and C in Figure 15b).

Figure 15c shows the typification results of the proposed method. Ten linear building patterns remained in a grid-like combined building pattern after typification, and spatial conflicts between building patterns were resolved.

To validate the effectiveness of the typification method in resolving spatial conflicts, two methods for individual linear building patterns are implemented for the experimental data, as shown in Figure 16. Figure 16a shows the result of using the building reconstruction method proposed in this study for linear patterns, and Figure 16b shows the result of using Gong and Wu’s method [4]. The results indicate that the proposed method can better maintain the spatial structures of combined linear patterns.

Quantitative analysis can further demonstrate the validity of our method.

Table 1. Performance evaluation for typification methods.

Typification Method	Number of Conflicting Building Pairs	Number of Linear Patterns
Typification method of Gong and Wu [4]	9	17
Typification method for individual linear patterns	14	22
Typification method for combined linear patterns	0	19

shows the number of building pairs with conflicts and the number of linear building patterns in the typification method for combined linear patterns proposed in this study, as well as two comparison methods.

The disappearance of linear building patterns is due to their reduction at junction buildings (pattern D in Figure 15b) or the resolution of spatial conflicts between combined linear patterns (pattern E in Figure 15b). The number of buildings in these linear building patterns is not equal to or greater than three after typification (pattern F in Figure 15b).

4.3. Adoption of Parameters

Given that the detection of linear patterns involves many parameters, it is necessary to analyze the influences of these parameters on the extracted results. T_si, T_sh, and T_or are the similarity thresholds between buildings in terms of size, orientation, and shape. T_pa T_ma, and T_el are the thresholds used to determine whether the buildings are distributed along a defined line. All these parameters are less affected by scale changes. If these parameters are large, buildings recognized in a linear pattern will not comply with the visual perception of a human. For example, if T_sh = 2, the two buildings connected by the purple line in Figure 17a will be recognized as a linear pattern; if T_el = 2.3, the two buildings connected by the purple line in Figure 17b will be recognized as a part of a linear pattern. If these parameters are small, some human perceptual patterns may fail to be recognized. For example, if T_si = 1.5, the two buildings connected by the purple line in Figure 17d cannot be recognized, and if T_ma = 5° for curvilinear patterns, the pattern in Figure 17c cannot be recognized. For the angle difference threshold of T_pa, the permissible range is from 40° to 60°. Zhang [13] believed that the two values for their test cases showed almost no difference. Therefore, we chose 50 as a compromise value.

5. Conclusions

Linear building patterns intersecting with each other can form more complex combined linear patterns, increasing the difficulty of typifying these buildings. In this study, combined linear patterns are recognized using the common buildings in linear patterns, and the significance of each linear pattern in a combined linear pattern is analyzed. Then, to maintain spatial distribution characteristics, relevant buildings are typified. Finally, to preserve the distinguishability of each building pattern, conflict buildings from different combined linear patterns are resolved. The experimental results show that linear pattern characteristics can be preserved. Furthermore, the particular structures and hierarchical characteristics of the combined linear patterns can be captured and preserved in the typification results. In future research, more effort will be made to focus on the collaboration between typification and other map generalization operators for building groups.