Method for reconstructing shape of planar point set, terminal device and computer readable storage medium

Abstract

This invention discloses a method, terminal device, and computer-readable storage medium for reconstructing the shape of a planar point set. The method includes constructing a minimum spanning tree for the planar point set; obtaining the proportion of mesh-structured points in the minimum spanning tree to the total number of points in the planar point set; determining the type of the planar point set based on the proportion, including linear point sets and planar point sets; mesh-structured points are points with three or more adjacent points; and determining the reconstruction method for the planar point set based on the type. The planar point set shape reconstruction method, terminal device, and computer-readable storage medium provided by this invention can effectively extract the inner and outer boundaries of complex linear and planar point sets without manually setting prior parameters. It can effectively extract the inner and outer boundaries of linear and planar point sets with different distributions (random and uniform) and densities, improving the accuracy of planar point set shape reconstruction and offering fast reconstruction speed.

Description

Technical Field

[0001] This invention belongs to the field of planar point set shape reconstruction technology, specifically relating to planar point set shape reconstruction methods, terminal devices, and computer-readable storage media. Background Technology

[0002] Planar point set shape reconstruction aims to extract the geometric shape representing a sample point set from a finite point set S with given coordinate information. It has been widely used in fields such as building outline extraction, image retrieval, molecular shape description, and geographic information retrieval.

[0003] Current research on shape reconstruction of planar point sets can be divided into three categories: convex hull-based methods, curve reconstruction methods, and Delaunay triangulation methods. Delaunay triangulation-based methods, conforming to Gestalt's proximity principle in visual psychology, have gained wider application. Existing methods for shape reconstruction of planar point sets include α-shape methods, χ-shape methods, and side-length ratio constraint methods. However, α-shape is easily affected by the initialization parameter α. While χ-shape achieves shape reconstruction of planar point sets with different distributions and densities, it also requires initialization parameters and cannot extract holes. Shape reconstruction algorithms constrained by side-length ratio require the user to provide four initialization parameters. Furthermore, existing technologies include planar point set shape reconstruction methods that consider multiple constraints, but their final shape reconstruction results still depend on the setting of one angle parameter; there are also shape reconstruction algorithms that can effectively identify noisy points within planar point sets and can identify holes relatively well, but these also require the user to specify some initialization parameters. To reduce the influence of subjective factors on point set shape reconstruction, parameter-free shape reconstruction algorithms have been proposed. However, they are not ideal for extracting narrow, elongated holes. None of the above algorithms adequately consider the shape reconstruction of linear point sets, resulting in poor performance in reconstructing linear point sets. Summary of the Invention

[0004] This invention provides a planar point set shape reconstruction method, terminal device, and computer-readable storage medium, which solves the technical problem of low reconstruction accuracy of planar point sets caused by neglecting the shape reconstruction of linear point sets in the prior art.

[0005] The first aspect of this invention discloses a method for reconstructing the shape of a planar point set, comprising: Construct the minimum spanning tree of a set of points in a plane; Obtain the proportion of the network structure points in the minimum spanning tree to the total number of points in the planar point set, and determine the type of the planar point set based on the proportion. The type includes linear point sets and planar point sets. The network structure points are points with 3 or more adjacent points. The reconstruction method for the planar point set is determined based on the type.

[0006] Preferably, determining the type of the planar point set according to the ratio specifically includes: The ratio is compared with a preset threshold. When the ratio is less than the preset threshold, the planar point set is a linear point set; when the ratio is greater than or equal to the threshold, the planar point set is a planar point set.

[0007] Preferably, when the planar point set is a linear point set, the reconstruction method for the planar point set is determined according to the type, specifically including: Construct the Delaunay triangulation of the linear point set, and obtain the initial outer boundary of the linear point set from the Delaunay triangulation; Obtain the new side length sequence; Based on the box plot method, determine the longest edge in the new edge length sequence; The triangle containing the longest edge is deleted from the initial outer boundary inwards until the outer boundary triangle no longer contains the longest edge, thus obtaining the reconstructed linear point set.

[0008] Preferably, obtaining a new side length sequence specifically includes: Obtain the longest edge in the minimum spanning tree constructed by the Delaunay triangulation; Construct an ordered sequence Q in ascending order using the edges in the Delaunay triangulation whose length is less than or equal to the longest edge; Perform a difference operation between the ordered sequence Q and the Delaunay triangulation to obtain the set W; The new side length sequence is obtained based on the set W.

[0009] Preferably, obtaining a new side length sequence based on the set W specifically includes: The new side length sequence is determined using the first formula, which is:

[0010] In the formula, Let Q be the new side length sequence, Q be the ordered sequence, and Count be the counting function. Let c be the minimum spanning tree corresponding to the plane point set S, where the value of c ranges from 0.2 to 0.4. Let W be the set of edges determined from set W.

[0011] Preferably, the longest side of the new side length sequence is determined according to the box plot method, specifically including: Combining the box plot method, the side length threshold is determined using the second formula, which is: Threshold = Q3 + 1.5 * (Q3 - Q1) In the formula, Threshold is the side length threshold, and Q1 and Q3 are the quarter and third quartiles of the side length sequence, respectively. The edges in the Delaunay triangulation are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold, it is considered to be the longest edge in the new edge length sequence.

[0012] Preferably, when the planar point set is a surface point set, the reconstruction method for the planar point set is determined according to the type, specifically including: Construct the Delaunay triangulation of the areal point set, and obtain the initial outer boundary of the areal point set from the Delaunay triangulation; Obtain the side lengths within the initial outer boundary and sort them in ascending order to obtain a sorted sequence; The longest edge in the sorted sequence is determined using the box plot method; The triangle containing the longest edge is deleted from the initial outer boundary inward until the outer boundary triangle no longer contains the longest edge, thus obtaining the reconstructed surface point set.

[0013] Preferably, the method of determining the longest edge in the sorted sequence using a box plot method specifically includes: Combining the box plot method, the side length threshold is determined using the third formula, which is: Threshold = Q3 + 1.5 * (Q3 - Q1) In the formula, Threshold is the side length threshold, and Q1 and Q3 are the quarter and third quarter digits of the sorted sequence, respectively. The edges in the Delaunay triangulation are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold, it is considered to be an extremely long edge.

[0014] A second aspect of this invention discloses a terminal device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0015] A third aspect of this invention discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0016] Compared with the prior art, the present invention has the following advantages: The planar point set shape reconstruction method, terminal device, and computer-readable storage medium provided by this invention can effectively extract the inner and outer boundaries of complex line and surface planar point sets without the need for manual setting of prior parameters. It can better realize the extraction of the inner and outer boundaries of line and surface planar point sets with different distributions (random and uniform) and different densities, which can improve the accuracy of planar point set shape reconstruction and has a fast reconstruction speed. Attached Figure Description

[0017] Figure 1 This is a simplified flowchart of the planar point set shape reconstruction method according to an embodiment of the present invention; Figure 2 This is a detailed flowchart of the planar point set shape reconstruction method according to an embodiment of the present invention; Figure 3 (a) in the figure represents the linear point set of an embodiment of the present invention; Figure 3 (b) in the figure represents the minimum spanning tree corresponding to the linear point set in this embodiment of the invention; Figure 4 (a) in the figure represents the planar point set of an embodiment of the present invention; Figure 4 (b) in the figure represents the minimum spanning tree corresponding to the planar point set in this embodiment of the invention; Figure 5 The proportion of the mesh structure points in this embodiment of the invention; Figure 6 This is a diagram illustrating the shape reconstruction process of a linear point set according to an embodiment of the present invention, where (a) is the original point set; (b) is a Delaunay triangulation; (c) is the initial outer boundary; and (d) is the final boundary. Figure 7 This is a histogram of all edges in the Delaunay triangulation of this invention embodiment; Figure 8 This is a histogram of some edges in the Delaunay triangulation of this invention embodiment; Figure 9 This is the extraction result of the longest edge in the linear point set according to an embodiment of the present invention; Figure 10 This is the extraction result of the longest edge in the planar point set according to an embodiment of the present invention; Figure 11 The linear point set and the area point set are the simulation data of the embodiments of the present invention, wherein (a) to (c) are linear point sets; and (d) to (i) are area point sets; Figure 12 In the simulation data of this embodiment of the invention, the qualitative analysis results of four methods for linear point sets are shown, where (a) is the χ-shape result; (b) is the side length ratio constraint result; (c) is the SRGT result; and (d) is the USRG result. Figure 13The quantitative analysis results of four methods for linear point sets are presented in the simulation data of this embodiment of the invention. Figure 14 In the simulation data of this embodiment of the invention, the qualitative analysis results of four methods for the areal point set are shown, where (a) is the χ-shape result; (b) is the side length ratio constraint result; and (c) is the SRGT or USRG result. Figure 15 The simulation data of this invention includes the quantitative analysis results of four methods for a set of areal points, where (a) is the result of a uniform distribution and (b) is the result of a random distribution. Figure 16 Here is a shape reconstruction diagram of the floating car trajectory according to an embodiment of the present invention; wherein (a) is a floating car GPS trajectory data diagram; and (b) is a shape reconstruction diagram of the USRG algorithm. Figure 17 The images show roof point clouds and building roof outlines extracted by two algorithms in this embodiment of the invention, where (a) is the original roof point cloud data; (b) is the comparison data between USRG and SRGT; and (c) is the USRG extraction result. Detailed Implementation

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are merely illustrative and explanatory of the present invention and should not be construed as limiting the scope of protection of the present invention. All technologies implemented based on the above content of the present invention are covered within the scope of protection intended by the present invention.

[0019] According to the cognitive rules of Gestalt visual psychology, people always perceive things as a whole first, and then as parts. Based on this cognitive idea, this invention proposes a planar point set shape reconstruction method based on Gestalt visual psychology—USRG (Unified Shape Reconstruction based on Gestalt). First, at the macro level, planar point sets are classified into linear and planar point sets based on whether the minimum spanning tree constructed from the planar point sets has "network" characteristics. Then, based on the proximity and simplification principles of Gestalt visual psychology, shape extraction methods for linear and planar point sets are constructed respectively, ultimately achieving the integrated reconstruction of the shapes of linear and planar point sets.

[0020] For ease of subsequent description, the present invention provides the following definition: Let S = {P1, P2, ..., P...} n Let} be a set of points in a plane, P1, P2, ..., P. nLet S be N discrete points in a planar point set S, and assume that S does not contain any noise points. Delau(S) represents the Delaunay triangulation constructed from S, and MST(S) represents the minimum spanning tree constructed from Delau(S).

[0021] The first aspect of this invention discloses a method for reconstructing the shape of a planar point set, such as... Figure 1 and Figure 2 As shown, it includes: Step 1: Construct the minimum spanning tree of the planar point set.

[0022] Experiments on shape reconstruction from a large number of planar point sets (linear point sets and planar point sets) have revealed that: Figure 3 (a) The linear point set generated as follows Figure 3 (b) The minimum spanning tree usually does not have the characteristics of a network structure (i.e., the proportion of "network" structure points is relatively small), while... Figure 4 (a) is constructed from a set of points in an area as shown in the figure. Figure 4 (b) The minimum spanning tree typically exhibits a distinct mesh structure (i.e., a high proportion of "mesh" structure points). Inspired by the visual differences between linear and planar point sets, this invention classifies planar point sets into linear point sets or planar point sets based on whether the minimum spanning tree generated from the planar point set possesses a mesh structure. The specific classification method is described in step 2.

[0023] Step 2: Obtain the proportion of network structure points to the total number of points in the planar point set in the minimum spanning tree. Determine the type of planar point set based on the proportion, which includes linear point sets and planar point sets. Network structure points are points with 3 or more adjacent points, specifically: Obtain the proportion of network structure points in the minimum spanning tree to the total number of points in the planar point set, and compare the proportion with a preset threshold. When the proportion is less than the preset threshold, the planar point set is a linear point set; when the proportion is greater than or equal to the threshold, the planar point set is a planar point set.

[0024] In this embodiment of the invention, 50 representative simulated data sets are used to obtain the threshold for classifying line and planar point sets. Each set comprises 25 line and 25 planar point sets, derived from objects of different shapes, such as birds, cat faces, dogs, seahorses, and administrative divisions. To enhance the universality of the threshold, the simulated data includes planar point sets with different distributions (random, uniform), different densities (low, medium, high), and those containing holes. Experimental analysis is performed on the 50 simulated data sets, and the proportion of "network" structure points in each set is statistically analyzed to obtain the following results: Figure 5 The results are shown. (By...) Figure 5It can be observed that: ① The maximum proportion of "network" structure points in the linear point set is less than 4%, while the minimum proportion of "network" structure points in the area point set is greater than 13%; ② The classification of linear and area point sets is not sensitive to the selection of thresholds, therefore the classification thresholds for linear and area point sets are 4%-13%. In this embodiment of the invention, 9% is used as the benchmark value for distinguishing between linear and area point sets.

[0025] Step 3: Determine the reconstruction method for the planar point set based on its type, specifically as follows: When the planar point set is a linear point set, the shape of the linear point set is reconstructed using the box plot gross error detection method; When the planar point set is a surface point set, the shape of the surface point set is reconstructed using the box plot gross error detection method.

[0026] In this invention, when the planar point set is a linear point set, the shape of the linear point set is reconstructed using a box plot gross error detection method. The operation process of this step is as follows: Figure 6 As shown, it specifically includes: Step 31, Construction Figure 6 (a) The Delaunay triangulation of the linear point set is constructed as follows: Figure 6 As shown in (b), the initial outer boundary of the linear point set is obtained from the Delaunay triangulation. The obtained initial outer boundary is as follows: Figure 6 As shown in (c).

[0027] In this embodiment of the invention, before constructing the Delaunay triangulation of the linear point set, the planar point set is first preprocessed, that is, data cleaning techniques are used to retain only one point from the overlapping planar points. Then, the Delaunay triangulation of the preprocessed linear point set is constructed. Finally, the edge in the Delaunay triangulation shared by only one triangle is identified as the initial outer boundary of the linear point set.

[0028] Step 32: Obtain the new side length sequence.

[0029] This invention employs a gross error detection method to identify extremely long sides in a linear point set Delau(S). Bipolar or 3σ gross error detection methods require the side lengths in Delau(S) to follow a normal distribution to obtain good results, but the side lengths in the linear point set Delau(S) do not possess this characteristic at all. Figure 7 As shown. Therefore, the bipolar or 3σ gross error detection method cannot effectively identify the longest edges in a Delaunay triangulation.

[0030] Since most edges in the Delau(S) of a linear point set are extremely long edges (e.g., Figure 6 (b) shows that only a minority of edges are ultimately retained (as shown in the image). Figure 6(d) shows that (below 50%), directly using gross error detection cannot effectively detect extremely long edges perceived by the human eye. Numerous experiments on the extraction of line point set boundaries have revealed that the number of outer boundaries in the shape reconstruction results of line point sets is no greater than N, and the final retained boundaries are similar to the minimum spanning tree height constructed from the line point set, such as... Figure 3 (b) and Figure 6 As shown in (d). Based on this finding, the present invention defines the longest edge in Delau(S) as the edge in Delau(S) whose length is statistically significantly greater than that of MST(S).

[0031] Step 32 of this embodiment of the invention is specifically as follows: Step 321: Sort the edge lengths of the Delaunay triangulation Delau(S) and the minimum spanning tree MST(S) constructed by the Delaunay triangulation in ascending order, and obtain the longest edge Max(S) in the minimum spanning tree MST(S) constructed by the Delaunay triangulation. Step 322: Construct an ordered sequence Q in ascending order using the edges in the Delaunay triangulation Delau(S) whose length is less than or equal to the longest edge Max(S); Step 323: Perform a difference operation between the ordered sequence Q and the Delaunay triangulation Delau(S) to obtain set W (most of the edges in W are extremely long edges). Step 324: Obtain a new sequence of side lengths based on set W, specifically as follows: Select [c*Count(MST(S))] edges from W and perform a union operation with the ordered sequence Q, as shown in formula (1). Here, c takes values ​​between (0, 0.5), and Count represents the counting function. This represents the new sequence of side lengths after merging.

[0032] (1) From formula (1), we can see that, The number of extremely long sides is mainly affected by the parameter c. A smaller value for c allows for more sensitive detection of extremely long sides using the coarse error detection method, but also carries a greater risk of false identification, such as preventing the final shape reconstruction from forming a closed shape. This invention has found that c values ​​between 0.2 and 0.4 yield good shape reconstruction results (i.e., the final reconstruction result is not sensitive to the value of c). Therefore, this invention sets c to 0.3.

[0033] Step 33: Determine the longest edge of the new edge length sequence using the box plot method.

[0034] By following the above steps, you can achieve the following: Figure 7 The histogram is transformed into Figure 8 As can be seen from Figure (8), although the conditions for determining the threshold of extremely long sides using the gross error detection method are met, the distribution is a long-tailed distribution, and the gross error detection method based on the normal distribution condition still cannot obtain a good reconstruction result. This invention uses a box plot method that does not make any assumptions about the data distribution to realize the identification of extremely long sides, as shown in Formula (2). Where Q1 and Q3 are the side length sequences, respectively. One-quarter and three-quarters of the divisor.

[0035] Threshold=Q3+1.5*(Q3-Q1)(2) In the formula, Threshold is the side length threshold.

[0036] The edges in the Delaunay triangulation Delau(S) are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold Threshold, it is considered to be the longest edge in the new edge length sequence.

[0037] Using the above methods to Figure 6 The longest side in (b) was probed, and the result is as follows: Figure 9 As shown, the results closely match the actual situation, demonstrating the rationality of the method.

[0038] Step 34: Delete the triangles containing the longest sides from the initial outer boundary inwards until the outer boundary triangles no longer contain the longest sides, and obtain the reconstructed linear point set.

[0039] In this embodiment of the invention, a peeling method is used to delete triangles containing extremely long sides from the outside in until the outer boundary triangle no longer contains extremely long sides. At this point, the refinement of the outer boundary is complete, resulting in a reconstructed linear point set, as shown below. Figure 6 As shown in (d).

[0040] In this invention, when the planar point set is a surface point set, the shape of the surface point set is reconstructed using the box plot method.

[0041] For the shape reconstruction of a planar point set, this invention adopts the Gestalt proximity and simplification principle to realize the shape reconstruction of the planar point set, which is mainly divided into four steps: extraction of the initial outer boundary, detection of the longest edge, refinement of the outer boundary, and extraction and optimization of the hole.

[0042] This invention uses a simple and quick box plot that does not make assumptions about the data distribution to identify extremely long sides.

[0043] The shape reconstruction of the facet point set specifically involves: Step 3-1: Construct the Delaunay triangulation Delau(S) of the areal point set, and obtain the initial outer boundary of the areal point set from the Delaunay triangulation.

[0044] The method for extracting the initial outer boundary is the same as the method for extracting the initial outer boundary of a linear point set, and will not be described again here.

[0045] Step 3-2: Obtain the side lengths within the initial outer boundary and sort them in ascending order to obtain the sorted sequence.

[0046] Step 3-3: Determine the longest edge in the sorted sequence using the box plot method. Specifically, combine the box plot method with formula (3) to determine the edge length threshold: Threshold=Q3+1.5*(Q3-Q1)(3) In the formula, Threshold is the side length threshold, and Q1 and Q3 are the quarter and third quartiles of the sorted sequence, respectively. The edges in the Delaunay triangulation are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold, it is considered to be an extremely long edge.

[0047] Using the methods in steps 3-1 to 3-3 Figure 2 The longest edge in Delau(S) is probed, and the result is as follows: Figure 10 As shown, it closely matches the actual situation.

[0048] Steps 3-4: Delete the triangles containing the longest sides from the initial outer boundary inwards until the outer boundary triangles no longer contain the longest sides, thus obtaining the reconstructed surface point set.

[0049] To verify the effectiveness of the method of this invention, experimental analysis was conducted using three sets of simulated datasets and two sets of real data, and compared with classic χ-shape, side-length ratio constraints, and SRGT. L... 2 Error norm serves as a quantitative indicator for evaluating the accuracy of reconstruction results: (4) Where Area (O) and Area (S) represent the original and reconstructed shapes, respectively, and L 2 L reflects the degree of difference in area between the original and reconstructed graphics. 2 The smaller the value, the closer the actual shape is to the reconstructed shape.

[0050] 1. Simulated data Simulated datasets can accurately capture the true shape of simulated planar point sets (lines and surfaces), facilitating quantitative comparison between the reconstructed shapes and the real graphics. Figure 11 This is a set of line and area points generated for a certain administrative division. Figure 11 (d) to Figure 11(i) represents uniformly and randomly distributed planar point sets, respectively. The point density in the three sets of simulation datasets increases sequentially from left to right. This simulation dataset contains complex boundary types (convex, concave regions, and holes), which can effectively evaluate the shape reconstruction effects of different methods.

[0051] 1.1 Linear point set 1) Qualitative comparison like Figure 12 As shown in (a), from left to right, χ = 0.4, 0.2, 0.1. χ-shape can extract the outer boundary of the linear point set, and the smaller the χ, the more refined the extracted outer boundary. At the same time, it can be found that χ-shape cannot extract holes.

[0052] like Figure 12 As shown in (b), the outer boundary of the linear point set extracted by the side length ratio constraint (where red represents the outer boundary and blue represents the inner boundary) is more accurate. However, the inner boundary extracted by this algorithm has the problem of local discontinuity, as shown in T1 and T2 in the figure.

[0053] from Figure 12 (c) It can be found that the outer boundary extracted by the SRGT algorithm deviates significantly from the actual situation in some local areas, and the hole extraction is not thorough enough. This is because the side lengths in the Delaunay triangulation constructed from linear point sets do not satisfy a normal distribution, and the gross error detection method using bipolar difference cannot effectively identify extremely long sides.

[0054] like Figure 12 As shown in (d), the USRG algorithm of this invention performs well in boundary extraction for planar point sets of different densities. Furthermore, since USRG can determine in advance that the point set is a linear point set, it does not need to extract holes in the point set, thus saving time required for shape reconstruction.

[0055] 2) Quantitative comparison Since the χ-shape algorithm cannot extract the inner boundary, and the inner boundary extracted by the side length ratio constraint algorithm in this example is discontinuous, the main comparison is made of the outer boundary L of the four algorithms. 2 Error. From Figure 13 It can be observed that the shape reconstruction results of the four algorithms differ significantly. The USRG algorithm is only slightly better than χ-shape when the point density is 0.23%, but it is superior in all other cases. The edge length constraint ratio algorithm has higher accuracy in extracting the outer boundary, while the SRGT algorithm has the worst outer boundary extraction result. This is because the edge length in the Delaunay triangulation constructed from linear point sets does not meet the conditions for detecting gross errors in the bipolar range.

[0056] 1.2. Area-like point set 1) Qualitative comparison from Figure 14 As can be seen in (a), the χ-shape algorithm can extract a relatively fine outer boundary in a set of randomly and uniformly distributed planar points by adjusting the initialization parameter χ, as shown in T1 in the figure. From left to right in the figure, χ=0.4,0.2,0.1.

[0057] like Figure 14 As shown in (b), the side length ratio constraint method can extract the shape of the point set well in both uniform and random point sets, and the extraction becomes more accurate as the point density increases.

[0058] like Figure 14 As shown in (c), the results obtained by USRG and SRGT are consistent. Both algorithms have good extraction effects in areal point sets with different distributions and densities, and the extraction becomes more refined as the point density increases.

[0059] 2) Quantitative comparison from Figure 15 (a) It can be observed that the side length ratio constraint method, USRG, and SRGT all have good shape reconstruction results when the planar point set is uniformly distributed. Among them, the L of USRG and SRGT algorithms are the best. 2 The error values ​​were the same and the lowest among all algorithms. However, as the point set density increased, the extraction results of the four algorithms remained almost consistent. Figure 15 The random distribution results in (b) show almost the same conclusions as those for the uniform distribution.

[0060] 2. Real data experiment 2.1 Floating car trajectory data This data originates from open-source data from the Ministry of Transport of the People's Republic of China—a GPS dataset and map dataset of a floating car on an experimental road in Guangzhou (http: / / www.mot.gov.cn / sjkf / 201911 / t20191119_3333161.html), as shown by the black 'line' in Figure 16(a). The background map is Amap (Gaode Maps). Because Amap uses the GCJ02 coordinate system, while the floating car data in this invention uses the WGS-84 coordinate system, there is a certain offset between the two.

[0061] This data is a linear point set containing concave and convex regions, which can effectively verify the USRG's extraction performance on linear point sets. Experiments show that USRG can accurately determine the point set type without requiring manual definition, and can accurately extract the floating car's trajectory. Even the "micro" shapes within the floating car's trajectory can be identified relatively accurately, such as... Figure 16 (b) shows T1 and T2.

[0062] 2.2 Building Point Clouds This invention uses point cloud data of the rooftops of ancient buildings in Zhangguying Village, such as... Figure 17 As shown in (a), the USRG algorithm can automatically distinguish between line and planar point sets compared to SRGT, and it improves the gross error detection algorithm of SRGT for identifying extremely long edges, while maintaining the same performance elsewhere. Therefore, this section mainly compares the USRG and SRGT algorithms.

[0063] Experiments showed that the USGR algorithm can also accurately identify the data as a set of areal points. Figure 17 (b) shows that the outer boundaries extracted by the SRGT and USRG algorithms are completely consistent. However, the USRG algorithm is more sensitive than SRGT in the process of identifying holes, as shown in K1, K2, and K3 in the figure (the remaining holes are consistent). This also confirms that the box plot method has good anti-grossing effect. However, since the area of ​​the broken holes shown in K1-3 is small, they are all removed during the hole optimization process. The final shape reconstruction result of the USRG algorithm is as follows. Figure 17 As shown in (c). From Figure 17 (c) It can be observed that both the SRGT and USRG algorithms suffer from the problem of misidentifying a single courtyard, although this is relatively small compared to the entire roof area. Although the final reconstruction results of both are consistent, the USRG algorithm is more efficient than SRGT because it does not need to update the mean and mean error of the side lengths successively during the identification of extremely long sides. In this real-world case, the USRG algorithm took 34 seconds less time than SRGT (with consistent software and hardware environments). Therefore, even when the known point set is a planar point set, the USRG algorithm is still superior to the SRGT algorithm.

[0064] The shape reconstruction of planar point sets must conform to people's visual habits of spatial cognition, and the principles of Gestalt visual psychology are an important influencing factor that needs to be considered. This invention first, based on the Gestalt visual psychology principle of cognition from the whole to the part, classifies planar point sets into line-like and planar point sets by defining the concept of a mesh structure. Then, shape reconstruction methods for line-like and planar point sets are constructed separately. Based on the Gestalt proximity principle, robust estimation technology—box plots—is used to detect extremely long edges during the shape reconstruction of line-like point sets. Based on the Gestalt proximity and simplification principles, box plots and 3σ techniques are used to identify extremely long edges and optimize holes during the shape reconstruction of planar point sets. By comparing with χ-shape, edge ratio constraint method, and SRGT, it is found that the proposed USRG can effectively extract the inner and outer boundaries of line-like and planar point sets with different distributions (random, uniform), and densities. However, the USRG algorithm also has some areas for improvement, such as the presence of jagged shapes in the extraction results.

[0065] The second aspect of this invention discloses a terminal device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0066] A third aspect of this invention discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0067] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for reconstructing the shape of a planar point set, characterized in that, include: Construct the minimum spanning tree of a set of points in a plane; Obtain the proportion of the network structure points in the minimum spanning tree to the total number of points in the planar point set, and determine the type of the planar point set based on the proportion. The type includes linear point sets and planar point sets. The network structure points are points with 3 or more adjacent points. The reconstruction method for the planar point set is determined based on the type; When the planar point set is a linear point set, the reconstruction method for the planar point set is determined according to the type, specifically including: Construct the Delaunay triangulation of the linear point set, and obtain the initial outer boundary of the linear point set from the Delaunay triangulation; Obtain the new side length sequence; Based on the box plot method, determine the longest edge of the new edge length sequence; The triangle containing the longest edge is deleted from the initial outer boundary inward until the outer boundary triangle no longer contains the longest edge, thus obtaining the reconstructed linear point set. Obtaining the new side length sequence specifically includes: Obtain the longest edge in the minimum spanning tree constructed by the Delaunay triangulation; Construct an ordered sequence Q in ascending order using the edges in the Delaunay triangulation whose length is less than or equal to the longest edge; Perform a difference operation between the ordered sequence Q and the Delaunay triangulation to obtain the set W; Obtain a new sequence of side lengths based on the set W.

2. The method as described in claim 1, characterized in that, The type of the planar point set is determined according to the ratio, specifically including: The ratio is compared with a preset threshold. When the ratio is less than the preset threshold, the planar point set is a linear point set; when the ratio is greater than or equal to the threshold, the planar point set is a planar point set.

3. The method as described in claim 1, characterized in that, Obtaining a new sequence of side lengths based on the set W specifically includes: The new side length sequence is determined using the first formula, which is: In the formula, Let Q be the new side length sequence, Q be the ordered sequence, and Count be the counting function. Let c be the minimum spanning tree corresponding to the plane point set S, where the value of c ranges from 0.2 to 0.

4. Let W be the set of edges determined from set W.

4. The method as described in claim 1, characterized in that, Based on the box plot method, the longest edge of the new edge length sequence is determined, specifically including: Combining the box plot method, the side length threshold is determined using the second formula, which is: Threshold = Q3 + 1.5 * (Q3 - Q1) In the formula, Threshold is the side length threshold, and Q1 and Q3 are the quarter and third quartiles of the side length sequence, respectively. The edges in the Delaunay triangulation are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold, it is considered to be the longest edge in the new edge length sequence.

5. The method as described in claim 1, characterized in that, When the planar point set is a surface point set, the reconstruction method for the planar point set is determined according to the type, specifically including: Construct the Delaunay triangulation of the areal point set, and obtain the initial outer boundary of the areal point set from the Delaunay triangulation; Obtain the side lengths within the initial outer boundary and sort them in ascending order to obtain a sorted sequence; The longest edge in the sorted sequence is determined using the box plot method; The triangle containing the longest edge is deleted from the initial outer boundary inward until the outer boundary triangle no longer contains the longest edge, thus obtaining the reconstructed surface point set.

6. The method as described in claim 5, characterized in that, Determining the longest edges in the sorted sequence using the box plot method specifically includes: Combining the box plot method, the side length threshold is determined using the third formula, which is: Threshold = Q3 + 1.5 * (Q3 - Q1) In the formula, Threshold is the side length threshold, and Q1 and Q3 are the quarter and third quarter digits of the sorted sequence, respectively. The edges in the Delaunay triangulation are compared with the edge length threshold. When an edge in the Delaunay triangulation is greater than the edge length threshold, it is considered to be an extremely long edge.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 6.

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