A method for simplifying the integration of roads and residential areas

Abstract

This invention relates to a method for collaborative simplification of roads and settlements, belonging to the field of digital mapping technology. The invention first uses Delaunay triangulation to extract the contour segments of adjacent settlements and the corresponding road segments. Then, it performs node matching on the extracted settlement contour segments and their corresponding road segments. Finally, it simplifies roads using constraint points, synchronizing the node selection of roads to the corresponding settlement contours based on the node matching results, thus achieving collaborative simplification. This invention establishes node-level associations between roads and settlements in adjacent areas through node matching, synchronizing the node selection of roads to the adjacent settlement contours, thereby achieving collaborative simplification. Compared to traditional road and settlement simplification methods, this invention effectively maintains the shape similarity and topological consistency between features, significantly reducing topological and shape conflicts.

Description

Technical Field

[0001] This invention relates to a method for collaborative simplification of roads and residential areas, belonging to the field of digital mapping technology. Background Technology

[0002] In a broad sense, any phenomenon in a map that violates logical relationships and geographical significance can be termed spatial conflict, not just topological errors. Shape similarity is an important characteristic of line and surface elements in neighboring areas, possessing significant value in spatial cognition, feature identification, and correlation assessment. Shape similarity is a concrete manifestation of the spatial correlation of geographical elements in a local context. For example, rivers and roads on a map may not have a very strong correlation, but in some areas, roads may be built along rivers. In such cases, the more similar the shapes of the roads and rivers, the closer their association in that area. Settlements and roads are important socio-economic elements, closely related in terms of geographical origins and evolution. In urban areas, simplifying the overall morphology of settlements and selecting roads are the first comprehensive steps. These two operators work together to control the overall pattern of the road network and settlement clusters. Basic methods for simplifying the overall morphology of settlements include deletion, merging, segmentation, and exaggeration. After determining the overall pattern of the road network and settlement clusters, their respective shape details need to be simplified. After simplification, some residential areas exist as large, block-shaped blocks, whose outlines often share a high degree of shape similarity with adjacent roads, representing a strong correlation between the blocks and nearby roads. In this case, if the outlines of roads and residential areas are simplified independently, uncontrollable topological and shape conflicts can easily occur, seriously affecting the quality of map data, visual perception, and the expression of spatial correlation.

[0003] The spatial relationships between map elements should be kept as consistent as possible before and after aggregation; otherwise, the accuracy and readability of the map will be affected. As the scale decreases, buildings are gradually merged into larger blocks. Normally, residential areas are tangent to or separate from roads, and the outlines of areas near roads often have a high degree of shape similarity to the roads themselves. Figure 1 As shown, the strong correlation between roads and residential areas is the fundamental reason for the similarity between the outlines of residential areas and the shapes of adjacent roads. Different studies have different definitions and descriptions of shape similarity. Distance is a basic characteristic for evaluating shape similarity; the smaller and more balanced the spatial distance, the more similar the similarity. Angles, node curvature, and bending levels are also commonly used characteristics for evaluating shape similarity. Overall, roads and residential outlines with similar shapes have small and balanced spatial distances, similar node angles and curvatures, similar degrees of tortuosity, and approximately parallel relationships.

[0004] Line features on a map consist of nodes and connecting segments. Simplification operators change the number and position of nodes, thereby altering the spatial location and overall shape of the line features. When simplifying adjacent and similarly shaped road and residential area outlines separately, the changes in nodes for each type of feature are independent, potentially altering the spatial relationships between features. Based on the type of relationship involved in road and residential area simplification conflicts, they can be categorized into topological conflicts and shape conflicts, such as... Figure 2a and Figure 2b As shown. Topological conflicts involve topological errors, specifically manifesting as "disjoint → intersecting". Shape conflicts mainly involve inconsistencies between distance and direction relationships, specifically manifesting as "approximately parallel → significantly non-parallel".

[0005] Simplification conflicts refer to spatial conflicts caused by the execution of simplification operators. Currently, methods for handling simplification conflicts fall into two categories: The first is to execute the simplification operator first, then detect spatial conflicts and handle them through operations such as shifting. Commonly used shifting methods include optimization methods and geometric methods. This type of method cannot control the generation of spatial conflicts during simplification; the principles and processes of detection and shifting are complex, requiring significant computational resources and easily generating new conflicts. The second approach aims to avoid spatial conflicts as much as possible during the simplification process. Based on the type of geographic element being processed, this can be divided into single-element-oriented and multi-element-oriented methods. Single-element-oriented simplification conflict handling methods aim to address spatial conflicts within an element but struggle with spatial conflicts between multiple elements. Multi-element-oriented spatial conflict handling requires design tailored to specific elements. Currently, there is considerable research on the coordinated simplification of contour lines and rivers, but no research on the coordinated simplification of roads and settlements.

[0006] Existing research focuses on maintaining the consistency of topological relationships before and after simplification, paying less attention to the shape similarity between adjacent line elements. This results in shape conflicts between adjacent line elements after simplification, which in turn affects the overall mapping effect. Summary of the Invention

[0007] The purpose of this invention is to provide a method for the collaborative simplification of roads and residential areas, in order to solve the problem of shape conflicts caused by the failure to consider shape similarity in the current collaborative simplification process of roads and residential areas.

[0008] To solve the above-mentioned technical problems, this invention provides a method for collaborative simplification of roads and residential areas, which includes the following steps:

[0009] 1) Use Delaunay triangulation to extract the outline segments of adjacent residential areas, insert constraint points in the corresponding roads according to the positions of the first and last nodes of the segments, and extract the road segments corresponding to the residential area outline segments.

[0010] 2) Perform node matching on the extracted residential area outline segments and their corresponding road segments;

[0011] 3) Simplify roads using constraint points. Based on the node matching results, synchronize the node selection of roads to the corresponding residential area outlines for collaborative simplification.

[0012] This invention establishes node-level associations between roads and settlements in adjacent areas through node matching, synchronizing the selection and rejection of nodes on roads with the outlines of neighboring settlements to achieve collaborative simplification. Compared to traditional road and settlement simplification methods, this invention effectively maintains the shape similarity and topological consistency between elements, significantly reducing topological and shape conflicts.

[0013] Further, the process of inserting constraint points in step 1) is as follows: the constraint points on the road are the projections of the endpoints of the residential land segments, and the constraint points on the residential land contours are the projections of the road intersections. If there exists a corresponding node whose distance from the endpoint of the residential land segment or the road intersection is less than the adjacent distance, then that point is set as a constraint point.

[0014] Furthermore, when a residential area is completely adjacent to a road, the adjacent roads of the target residential area are connected to form a ring road, the start and end points of the residential area outline and the start and end points of the ring road are reset to the adjacent positions, and the clockwise and counterclockwise coordinates of the residential area outline and the ring road are aligned.

[0015] When there are no nodes within the adjacent distance of the endpoint of the residential area outline segment of the neighboring road, insert a node as a constraint point at the nearest point from the neighboring road to the endpoint to provide reliable support for subsequent simplification.

[0016] Furthermore, in step 2), the road is used as a reference and the residential area is used as the target. The DTW algorithm is used to obtain the preliminary matching results of the nodes in the road and the residential area.

[0017] This invention uses the DTW algorithm, which can quickly match nodes in roads and residential areas.

[0018] Furthermore, step 2) also includes a step of optimizing the preliminary matching results based on the node angle, the length of the connecting line, and the direction of the connecting line.

[0019] To avoid potential mismatches or overmatches in the DTW algorithm during the matching process, this invention optimizes the initial DTW matching results based on node angle, connection line length, and connection line direction, thereby improving the accuracy of node matching.

[0020] Furthermore, when the initial matching result is 1:1, for the initially matched road nodes q i With residential node c j The following optimizations will be performed:

[0021] A. Calculate road node q i The node angle α, the node opening direction β, and the residential node cj The node angle α′, the direction of the node angle bisector β′, and the road node q i With residential node c j The direction of the connecting line between them is λ, α, λ∈[0,180°]°, β∈[-180°,180°];

[0022] B. Calculate road node q i With residential node c j The angle difference Δα between them, and the road node q i With residential node c j If the difference in the direction of the angle bisector between the two nodes Δβ and the deviation in the direction of the angle bisector between the connecting line and the node angle bisector of the road or residential area Δβλ, the two nodes cannot be matched if either difference is greater than the corresponding set threshold.

[0023] This invention further filters the matching results based on the angle difference between node pairs, the direction difference of the angle bisector, and the direction deviation of the connecting line from the angle bisector of the road or residential area, in order to improve the accuracy of the matching.

[0024] Furthermore, when the initial matching result is one-to-many or many-to-one, the matching node pair includes a matching node and a corresponding group of matching nodes. The optimization process for this matching node pair is as follows:

[0025] a. Calculate the length of all connecting lines in the matching node pair, and remove the nodes in the matching point group corresponding to the connecting lines with abnormal lengths. If there is only one node left in the matching point group, optimize it in a 1:1 optimization manner; otherwise, proceed to b.

[0026] b. Based on the node angles of each node in the filtered matching point group, search for the node set with the smallest difference between the angle of the matched node and the angle bisector direction difference and the angle bisector direction deviation in the filtered matching point group.

[0027] c. Compare the similarity between the node set and the matching point group and the matching node. If the similarity between the node set and the matching node is greater, only the matching relationship of the node set is retained; otherwise, the matching relationship of the entire filtered matching point group is retained.

[0028] This invention further filters the matching results for many-to-one or one-to-many matching results based on the length of the connecting line, the difference in the direction of the angle bisectors between node pairs, and the direction deviation of the connecting line from the angle bisectors of the road or residential area node, in order to improve the accuracy of the matching.

[0029] Furthermore, the collaborative simplification process employed in step 3) includes:

[0030] Using the nodes inserted into the roads when extracting adjacent segments of residential areas and the road endpoints as discontinuities, all roads are segmented and simplified.

[0031] Organize the road simplification results, extract the nodes that were deleted in the segmented simplification, and delete the residential nodes corresponding to the deleted road nodes according to the matching results.

[0032] Furthermore, step 3) also includes organizing the road simplification results, extracting the road nodes that were retained in the simplification, retaining the residential area outline nodes corresponding to the retained road nodes, and simplifying the unprocessed parts of the residential area outline segment by segment.

[0033] This invention synchronizes the node selection on the road with the outline of the adjacent settlement to achieve collaborative simplification. At the same time, it uses an appropriate algorithm to simplify the outline of the settlement in non-adjacent areas, ensuring the shape similarity and topological consistency of the road and settlement before and after simplification.

[0034] Furthermore, the segmented simplification is performed using a node-based simplification algorithm.

[0035] This invention employs a node-based simplification algorithm for segmented simplification, which effectively satisfies the need for simultaneous selection of road nodes and residential areas. Attached Figure Description

[0036] Figure 1 It is a schematic diagram showing the outline of residential areas and the shape of roads;

[0037] Figure 2a This is a schematic diagram illustrating topological conflicts during the simplification of residential area outlines and roads;

[0038] Figure 2b This is a schematic diagram illustrating the shape conflict in the simplification of the residential area outline and roads;

[0039] Figure 3 This is a flowchart of the method for simplifying the coordination between roads and residential areas according to the present invention;

[0040] Figure 4 This is a schematic diagram illustrating the adjacent state of residential areas and roads in an embodiment of the present invention;

[0041] Figure 5 This is a schematic diagram of the adjacent segment extraction process in an embodiment of the present invention;

[0042] Figure 6 This is a schematic diagram of node features in a 1:1 matching embodiment of the present invention;

[0043] Figure 7 This is a schematic diagram of the angle of the matching point group in an embodiment of the present invention;

[0044] Figure 8This is a schematic diagram of the road and residential area collaborative simplification process adopted in this invention;

[0045] Figure 9 This is a diagram illustrating the process of simplifying anomalies in an embodiment of the present invention;

[0046] Figure 10 This is a schematic diagram of the experimental data used in the experimental verification of this invention;

[0047] Figure 11 This is a schematic diagram of the node matching results during the experimental verification process of this invention;

[0048] Figure 12 This is a schematic diagram comparing the results of collaborative simplification and independent simplification during the experimental verification process of this invention;

[0049] Figure 13 This is a schematic diagram comparing the simplification results of the present invention and the ODP method during the experimental verification process of the present invention. Detailed Implementation

[0050] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0051] This invention first uses Delaunay triangulation to extract adjacent residential area contour segments. Based on the start and end node positions of these segments, constraint points are inserted into the corresponding roads, and road segments corresponding to the residential area contour segments are extracted. Then, node matching is performed on the extracted residential area contour segments and their corresponding road segments. Finally, roads are simplified using constraint points, and the node selection / rejection of roads is synchronized to the corresponding residential area contours based on the node matching results, performing collaborative simplification. For example... Figure 3 As shown, this invention establishes node-level associations between roads and residential areas in adjacent regions through node matching, synchronizing the selection and rejection of nodes on the road to the contours of neighboring residential areas, thus achieving collaborative simplification. This algorithm effectively maintains the shape similarity and topological consistency of roads and residential areas before and after simplification, and the contours of residential areas in non-adjacent regions can reflect the characteristics of different simplification algorithms. The specific implementation process of this method will be explained in detail below with specific examples.

[0052] 1. Extract the outline fragments of adjacent settlements. Adjacent means adjacent to each other, in this case, meaning settlements are located right next to roads. If the distance between the target settlement and the target road is less than the adjacent distance pd and there are no other roads or settlements blocking the way, then they are considered adjacent. The adjacent status between different settlements and roads varies, such as... Figure 4As shown, residential area I has one continuous segment adjacent to the road, residential area II has multiple discontinuous segments adjacent to the road, and residential area III is completely adjacent to the road. Adjacent segments, i.e., the outlines of the parts of a road or residential area that are closely adjacent to each other, are the most direct links between entities. Only adjacent areas require collaborative processing; paired adjacent segments are the basis for subsequent processing. The process of extracting adjacent segments from residential areas and their corresponding segments on roads is as follows: Figure 5 As shown.

[0053] First, Delaunay triangulation is used to extract adjacent residential area contour segments. Constraint points are inserted into the corresponding roads based on the start and end node positions of each segment. Then, road segments corresponding to the residential area contour segments are extracted. Specifically, a Delaunay triangulation between residential areas and roads is constructed first. The adjacency relationship between roads and residential areas is clarified using the adjacency distance pd, connecting the adjacent roads of the target residential area into a complete long road. Second, Delaunay neighbor segments between roads and residential areas are extracted. The shortest distance from each residential area node in the Delaunay neighbor segment to the road is calculated, and outlier detection is performed to remove nodes with abnormal distances, obtaining the adjacent segments of the residential area. Third, constraint points are inserted on the road and residential area contours. Constraint points on roads are projections of the endpoints of residential area segments, and constraint points on residential area contours are projections of road intersections. If a corresponding node exists with a distance less than pd from the endpoint of a residential area segment or a road intersection, that point is set as a constraint point. Finally, road segments corresponding to the residential area segments are extracted, the starting points of the residential area segments and road segments are adjusted to adjacent positions, and the segment directions are aligned. For residential areas completely adjacent to roads, both the land segment and the adjacent road segment form a loop and do not require trimming. Only the starting point and direction of the segment need to be adjusted, such as... Figure 5 As shown.

[0054] 2. Perform node matching on the extracted residential area outline segments and their corresponding road segments.

[0055] In cartographic generalization, node matching is mainly applied to the Morphing transformation of line and surface features. Specific techniques include buffer methods, shape context, OptCor, and skeleton line features. These methods serve multi-scale interpolation in the Morphing transformation, where the scale of the matched objects varies greatly, and the level of detail differs, primarily emphasizing the matching of feature nodes. Collaborative simplification requires the simultaneous selection and rejection of some nodes from roads and residential areas, demanding high matching accuracy, which existing matching methods struggle to meet. Therefore, this invention designs a two-step matching method for high-precision node matching. First, the DTW algorithm is used for coarse matching, and then the matching results are optimized by combining the geometric features of the nodes and connecting lines.

[0056] 1) Coarse matching of nodes

[0057] The Time-Divergence (DTW) algorithm is a dynamic programming algorithm for calculating the similarity between two time series of different lengths. It is widely used in time series data processing such as isolated word speech recognition, gesture recognition, data mining, and information retrieval. The DTW algorithm constructs a distance matrix between the sequences and, under specific constraints, iteratively searches for the optimal matching path between the two sequences within the distance matrix. Line features have a similar structure and matching pattern to time series; therefore, this invention uses the DTW algorithm to perform node matching between residential area contour segments and their corresponding road segments.

[0058] In the collaborative simplification of roads and settlements, roads have a higher priority. Therefore, roads are set as the reference and settlements as the target. The DTW algorithm is used to obtain the preliminary matching results of nodes in roads and settlements.

[0059] Given a road segment (reference sequence) Q = {q1, q2, ..., q...} m} and the residential area segment (target sequence) C={c1,c2,...,c n The matching path is W = {w(1), w(2), ..., w(N)}, where w(t) = (i(t), j(t)) represents the t-th matching point pair, which is a matching point pair consisting of the i-th point of the road segment and the j-th point of the residential area segment, with a local matching distance d between the two points. i,j This invention uses Euclidean distance to calculate the local matching distance.

[0060] The following constraints must be observed when executing the algorithm in this invention:

[0061] (1) Monotonicity: Matched points cannot participate in subsequent matching, i.e., i(t)≥i(t-1) and j(t)≥j(t-1).

[0062] (2) Boundary conditions: The two sequences must match at the beginning and end, i.e., w1 = (1,1) and w N = (m, n).

[0063] (3) Continuity: No point can be skipped, i.e., i(t)-i(t-1)≤1 and j(t)-j(t-1)≤1.

[0064] Construct a distance matrix D and recursively calculate the cumulative distance, as shown in formula (1). The smaller the cumulative distance, the better the matching path. After calculating the minimum cumulative distance, backtrack to find all matching point pairs on the path as the matching result.

[0065] g i,j =d i,j +min{g i-1,j ,g i,j-1 ,g i-1,j-1} (1)

[0066] In the formula, d i,j g is the Euclidean distance from node i to node j; i,j This represents the cumulative matching distance of the best path among all possible paths from the start of the sequence to the matching point pair (i,j).

[0067] 2) Optimize coarse matching results

[0068] The DTW algorithm achieves good overall matching results. However, because it only utilizes the distance between nodes during the matching process and neglects the geometric features of line element nodes, and because all nodes must participate in the matching, there may be anomalies such as mismatches or overmatches, which require correction. Based on coarse matching, this invention also needs to integrate information such as node angles, connecting line lengths, and connecting line directions to optimize the matching results.

[0069] When performing matching optimization, the matching results are divided into 1:1 and 1:n according to the correspondence between nodes, and different optimization strategies are adopted for different matching results.

[0070] For a 1:1 matching result, that is, a road node matches a residential node, let's assume the road node q i With residential node c j To optimize the matching relationship obtained by the DTW algorithm, it is necessary to determine the direction deviation between the line connecting the two nodes (angle difference and angle bisector direction difference) and the angle bisector of the road or residential area node. The specific optimization process is as follows:

[0071] (1) Calculate q i The node angle α and the node opening direction β, c j The node angle α′, the direction of the node angle bisector β′, and the direction of the connecting line between nodes λ, where α,λ∈[0,180°], β∈[-180°,180°], are as follows: Figure 6 As shown.

[0072] (2) Calculate the node angle difference Δα. If the value is greater than the threshold v1, then a match cannot be made. Figure 6 If the angles of q1 and c1 are too different to match, then execute (3).

[0073] (3) Calculate the angle bisector direction difference Δβ. If the value is greater than the threshold v2, then a match cannot be made. Figure 6 The node angles of q6 and c6 are similar, but the angle bisectors are in opposite directions, so they cannot be matched; otherwise, (4) is executed.

[0074] (4) Calculate the direction deviation Δβλ between the connecting line and the angle bisector of the road or residential area. If the value is greater than the threshold v3, then a match cannot be made; Figure 6The difference in nodal angle and the difference in angle bisector direction between q5 and c5 are both acceptable, but the two points are not adjacent points, and the direction of the connecting line deviates significantly from the direction of the angle bisector. Therefore, the two points cannot be matched.

[0075] The angle difference Δα can take values ​​within the interval (0, 30°], i.e., v1 ∈ (0, 30°]; the angle bisector direction difference Δβ can take values ​​within the interval (0, 90°], i.e., v2 ∈ (0, 90°]; the direction deviation Δβλ between the connecting line and the angle bisector can take values ​​within the interval [0, 60°), i.e., v3 ∈ (0, 60°). Specific parameter thresholds need to be set based on application requirements and data conditions.

[0076] Through the above process, the 1:1 matching results can be further filtered based on the node angle difference, angle bisector direction difference, and the direction deviation between the connecting line and the node angle bisector of the road or residential area, and node pairs that do not meet any conditions can be deleted from the matching results.

[0077] The matching results also contain numerous 1:n and n:1 cases, commonly seen in matching regions with varying levels of detail. Taking the matching of a road node with multiple residential outline nodes as an example, we will illustrate the optimization method for this type of matching result. Let there be a matching relationship between road node q0 and residential outline nodes c1 to c7, such as... Figure 7 As shown. The optimization process is as follows:

[0078] (1) Calculate the length of all connecting lines and eliminate those with abnormal lengths, i.e., those whose length values ​​deviate from the average length of all connecting lines in the matching pair by more than two standard deviations. As another implementation method, other outlier detection methods can also be used. If only one connecting line remains, execute the 1:1 optimization strategy; otherwise, execute (2).

[0079] (2) Calculate the angle α″ formed by several residential outline nodes. α″ is the angle between the line segment c0c1 and the extension line of line segment c8c7 on the side of the matching point.

[0080] (3) Calculate the node angle of each matching point, and search for the node c with the smallest angle difference with road node q0 and whose Δβ and Δβλ are both less than the given threshold. t .

[0081] (4) Compare c t and the difference in node angles between the matching point group and road node q0, if c t If the angle difference with q0 is smaller, then only point c is retained. t If the matching relationship is not specified, then the matching relationship of the entire matching point group is retained.

[0082] 3. Based on the node matching results, the node selection of the road is synchronized to the corresponding residential area outline for collaborative simplification.

[0083] After node matching between roads and residential outlines is completed, the relationships between features are established, allowing for collaborative simplification. Collaborative simplification applies to all roads and residential areas within the study area, not just adjacent segments. In terms of geometry, road features have higher priority; the collaborative simplification sequence is to simplify roads first, followed by coordinated simplification of residential outlines, as follows: Figure 8 As shown.

[0084] (1) Using the nodes inserted in the road when extracting adjacent segments of residential areas and the road endpoints as discontinuities, all roads are simplified in segments. Since it is necessary to simultaneously select and discard road nodes and residential areas, a simplification algorithm based on node selection is required when simplifying roads, such as the vertical distance method, the Douglas-Peucker algorithm, or a simplification algorithm based on curvature, etc.

[0085] (2) Organize the road simplification results, extract the nodes that were deleted in the simplification, and delete the residential nodes corresponding to the deleted road nodes according to the matching results;

[0086] (3) Organize the road simplification results, extract the road nodes that were retained during the simplification, and retain the residential area outline nodes corresponding to the retained road nodes. Using the segment endpoints, constraint points, and "retained" nodes as discontinuities, the residential area outline is simplified segment by segment. When simplifying the residential area outline, the algorithm selection is relatively free and not limited to the node selection method. In addition to the traditional line simplification algorithm, the nearest four-point method, the least squares method, and mathematical morphology and other building simplification algorithms can also be selected.

[0087] After simplifying residential areas, abnormal line segments are detected and processed. When some well-matched nodes with large turning angles are removed synchronously, the positional changes of road and residential area line segments differ, resulting in poor preservation of the relative positional relationships and shape similarity between features, and even topological conflicts. To solve this problem, the endpoints of residential area line segments that are not parallel to adjacent roads are appropriately shifted away from the road along another connecting line segment, such as... Figure 9 As shown.

[0088] Through the above process, the present invention can synchronize the node selection on the road with the contours of the adjacent settlements to achieve collaborative simplification. Moreover, the method can effectively maintain the shape similarity and topological consistency of the road and settlements before and after simplification. The contours of settlements in non-adjacent areas can reflect the characteristics of different simplification algorithms.

[0089] To verify the effectiveness of the present invention, the method of the present invention will now be described in detail through specific examples.

[0090] This experiment used roads and settlements from a 1:50,000 map of a region in Zhejiang Province as experimental data, including 114 roads and 128 settlements. The linear features in regions A, B, and C are relatively rich in detail, such as... Figure 10 As shown.

[0091] 1) Node matching analysis

[0092] Let the adjacent distance pd be 20 meters, the threshold v1 for the node angle difference Δα be 20°, the threshold v2 for the angle bisector direction difference Δβ be 90°, and the threshold v3 for the direction deviation Δβλ between the connecting line and the node angle bisector of the road or residential area be 20°. Taking region A as an example, adjacent segments are extracted and node matching is performed. The matching results are as follows: Figure 11 As shown. Figure 11 In region a, the coarse matching results show one-to-many matching, but the residential node in the middle is sufficient to match the road node, and the connecting lines on both sides can be deleted. Figure 11 In region b, two points on the residential area outline have significant differences from their corresponding road nodes; therefore, the connecting line between the two residential area nodes is deleted. Figure 11 In region c, there is an overmatch. The target residential node is a right-angle turning point and only matches with road intersections. The connection line with another road node is deleted. The DTW algorithm matches all nodes of roads and residential areas in adjacent regions according to distance. Further optimization is then performed on this basis, resulting in more accurate matching results, which can be used for collaborative simplification.

[0093] 2) Comparison with independent simplification methods

[0094] Setting the simplification threshold to 10 meters, the Douglas-Peucker algorithm (DP) is used to simplify the road into segments. After considering the linked selection of residential area nodes, the Douglas-Peucker algorithm and the four nearest neighbor method (AF) are used to simplify the residential area outline into segments. The simplification results for regions A, B, and C are as follows: Figure 12 As shown in the diagram, observation and analysis reveal that independently simplified roads and residential areas generally exhibit shape inconsistencies in adjacent regions. The approximate parallel relationships in the original data are not effectively preserved, and numerous topological errors exist. Cooperative simplification, on the other hand, better maintains the shape similarity between roads and residential areas in adjacent regions, and the approximate parallel relationships between roads and residential areas are significant. The simplification style of residential areas in cooperative simplification is the same as that of roads in adjacent regions, while in non-adjacent regions, it reflects the characteristics of its own simplification algorithm.

[0095] Further quantitative analysis was conducted on the simplification results. The parallel coefficient shown in Equation (2) was used to evaluate the shape similarity of adjacent areas, and the results are shown in Table 1. The parallel coefficient is the degree of fluctuation of the minimum distance from a node in one line feature to another line feature, reflecting the shape similarity between line features. The degree of similarity is inversely proportional to the value. The parallel coefficient of independent simplification increased significantly, indicating that the shape similarity between roads and residential areas in adjacent areas was severely damaged, and the simplification quality was poor. The parallel coefficient value of collaborative simplification was less different from the original data, indicating that the collaborative simplification method can better maintain the shape similarity between features. In addition, the parallel coefficient value of the collaborative DP algorithm was slightly smaller than the original data because some residential contours adjacent to roads lacked matching road nodes or their shapes were not similar to those of adjacent roads. Therefore, the simplification algorithm of the residential area itself was used. The DP algorithm reduced the details of this part of the contour, improved the straightness of the line, and thus increased the parallel coefficient value. The four-point neighbor method mainly deals with concave and convex structures and has little impact on the straightness of non-concave and convex structures. Therefore, its parallel coefficient value is slightly larger than the original data.

[0096]

[0097] In the formula, P CQ is the parallelism coefficient of segment C to segment Q, reflecting the fluctuation of the minimum distance from nodes in C to segment Q. The smaller the value, the higher the parallelism, and vice versa; n is the number of points in segment C; d i Let C be the minimum distance from each point in segment C to segment Q. It is the average of the minimum distances from the midpoint of segment C to segment Q.

[0098] Table 1

[0099]

[0100] 3) Comparison with other collaborative simplification methods

[0101] To further verify the effectiveness of this invention, it is compared with the DP collaborative simplification algorithm (ODP) constrained by the target displacement safety zone. Setting the simplification threshold to 20 meters, the DP and AF algorithms are used for collaborative simplification of roads and residential areas, and the ODP algorithm is used for two-stage simplification of roads and residential areas. In the first stage, the road is simplified after constructing a displacement safety zone based on adjacent residential areas. In the second stage, a displacement safety zone for the residential area outline is constructed based on the simplified road, and the outlines of adjacent residential areas are simplified. To ensure visual quality, the four-point proximity method is used to simplify the outlines of non-adjacent residential areas. The simplification results are as follows: Figure 13 As shown.

[0102] The first stage of ODP simplification targets roads, significantly reducing their shape details. While the consistency with residential area outlines in terms of detail is poor, the overall shape is well preserved, and no topological errors are found. The second stage of ODP simplification targets residential area outlines. Although no topological errors exist, severe shape conflicts exist between roads and residential areas, as well as between residential areas themselves. In the original data, the convex and concave structures of residential areas on both sides of the roads corresponded, but after simplification, a large number of convex structures were eliminated, while concave structures were retained due to road constraints. The simplification styles for roads and residential areas are inconsistent, resulting in a cluttered visual effect. The distances between them are uneven, with some too close and others too far apart, easily leading to overlapping during symbolization. The root cause of these problems is that the ODP algorithm does not consider the shape similarity between features; it only uses one feature as a topological constraint for another, simplifying one feature before simplifying the other, failing to process both types of features simultaneously. While this algorithm effectively avoids topological conflicts, shape conflicts are inevitable.

[0103] This invention uses roads as a link to simultaneously process the roads and the residential areas on both sides of the roads, achieving synchronous simplification of all three. The simplified roads and residential areas have good shape and structure matching, with balanced distances between them, resulting in a harmonious visual effect. However, in principle, this method has unresolved systemic topological conflicts, mainly including displacement conflicts and symbolization conflicts. For example, in region B under collaborative simplification, some small, simple-shaped residential areas are not processed collaboratively. The positional changes caused by road simplification lead to topological conflicts, requiring displacement processing of these residential areas. Furthermore, some residential area outlines maintain an approximately parallel relationship with adjacent roads after simplification, but the spatial distance is too small and there is insufficient displacement space, resulting in overlapping after symbolization, requiring appropriate scaling of the residential areas.

[0104] Therefore, this invention can simultaneously simplify the target road and its adjacent residential areas on both sides. The simplified road and residential areas maintain a high degree of consistency in overall shape and local details, with relatively balanced spatial distances and good shape and structure matching between the residential areas on both sides of the road. The visual experience of the collaborative simplification result is more harmonious, effectively maintaining the shape similarity and topological consistency between the road and residential areas in adjacent regions. In addition, in non-adjacent areas, algorithms can be flexibly selected for the outline of residential areas, presenting different simplification styles according to the actual situation.

Claims

1. A method of road and residential area co-simplification, characterized by, The simplification method comprises the following steps: 1) extracting adjacent residential area contour segments by using a Delaunay triangulation network, inserting constraint points in the corresponding roads according to the positions of the head and tail nodes of the segments, and extracting road segments corresponding to the residential area contour segments; 2) performing node matching on the extracted residential area contour segments and their corresponding road segments, taking the roads as the reference and the residential areas as the target, and obtaining a preliminary matching result of the nodes in the roads and the residential areas by using a DTW algorithm; 3) simplifying the roads by using the constraint points, synchronously selecting and discarding the nodes of the roads according to the node matching result, and performing collaborative simplification on the corresponding residential area contours; The step 2) further comprises the step of optimizing the preliminary matching result according to the node angles, connection line lengths and connection line directions; The collaborative simplification process in the step 3) comprises: segmenting and simplifying all roads by taking the nodes inserted in the roads when extracting the residential area adjacent segments and the road end points as the breakpoints; arranging the road simplification result, extracting the deleted nodes in the segment simplification, and deleting the residential area nodes corresponding to the deleted road nodes according to the matching result; The segment simplification is performed by using a node selection-based simplification algorithm.

2. The road and residential co-simplification method according to claim 1, characterized by, The process of inserting the constraint points in the step 1) is as follows: the constraint points on the roads are the projections of the residential area segment end points, and the constraint points on the residential area contours are the projections of the road intersections, if there is a corresponding node with a distance from the residential area segment end point or the road intersection less than the adjacent distance, the node is set as the constraint point.

3. The road and residential coalescence simplification method according to claim 2, characterized by, When the residential area is completely adjacent to the road, the adjacent roads of the target residential area are connected into a ring road, the start and end points of the residential area contour and the start and end points of the ring road are reset to the adjacent positions, and the clockwise and counterclockwise adjustment of the residential area contour and the ring road coordinates is consistent.

4. The road and residential coalescence simplification method according to claim 1, characterized by, When the preliminary matching result is 1:1, the road nodes of the preliminary matching are merged q i with the residential node c j The following optimization is performed: A. Calculate Road Nodes q i Node Angle at α Node Opening Direction β Residential Node c j Node Angle at α′ Node Angle Bisector Direction β′ Road Node q i Connection Line Direction between c j Residential Node When the preliminary matching result is one-to-many or many-to-one, the matching node pair comprises a matching node and a corresponding matching point group, and the optimization process of the matching node pair is as follows: , α , a. calculating the lengths of all connection lines in the matching node pair, removing the nodes in the matching point group corresponding to the connection lines with abnormal lengths, if there is only one node in the matching point group, performing optimization in the one-to-one optimization mode, otherwise, executing b; ∈ [0, 180°], β ∈ [0, 180°]; B. Calculate road nodes q i With residential nodes c j The angle difference Δ between α Road nodes q i With residential nodes c j The difference in direction Δ between the angle bisectors β Δ is the directional deviation of the angle bisector of the node between the connecting line and the road or residential area. b. searching for a node set in the screened matching point group with the smallest angle difference from the matching node and satisfying the set requirements of the angle bisector direction difference and the direction deviation of the angle bisector according to the node angles of the nodes in the screened matching point group; If either of the differences is greater than the corresponding set threshold, then the two nodes cannot be matched.

5. The road and residential coalescence simplification method according to claim 1, characterized by, c. comparing the similarities of the node set and the matching point group with the matching node, if the similarity of the node set with the matching node is greater, only the matching relationship of the node set is reserved, otherwise, the matching relationship of the entire screened matching point group is reserved. The step 3) further comprises arranging the road simplification result, extracting the retained road nodes in the simplification, retaining the residential area contour nodes corresponding to the retained road nodes, and segmentally simplifying the still unprocessed parts in the residential area contour. ​ ​ 6. The road and residential coalescence simplification method according to claim 1, characterized by, ​

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