A subway shield tunnel point cloud unfolding method

Abstract

The application discloses a subway shield tunnel point cloud unfolding method and belongs to the technical field of tunnel unfolding. The method comprises the following steps: acquiring point cloud data of a tunnel inner surface, cutting the point cloud data into a plurality of section point clouds according to a preset section width, projecting the section point clouds to a tunnel cross section plane to acquire two-dimensional point clouds, performing elliptical fitting on the two-dimensional point clouds to acquire optimal elliptical fitting parameters and a corresponding optimal fitting ellipse, constructing an arc length integral formula of the optimal fitting ellipse according to the optimal elliptical fitting parameters, calculating arc lengths from each data point on the optimal fitting ellipse to a vault vertex according to the arc length integral formula of the optimal fitting ellipse, and unfolding the optimal fitting ellipse along the vault vertex according to the arc lengths from each data point on the optimal fitting ellipse to the vault vertex. The method can solve the projection deformation problem existing in the cylindrical projection unfolding process.

Description

TECHNICAL FIELD

[0001] The present application relates to a subway shield tunnel point cloud unfolding method, belonging to the technical field of tunnel unfolding. BACKGROUND

[0002] The subway has become an important part of urban rail transit. Considering the important role and position of underground tunnels, the structural safety of subway tunnels is increasingly valued. With the increase of subway operation time, due to the influence of time, surrounding infrastructure and other factors, tunnel deformation, diseases and other problems continue to occur.

[0003] The traditional subway shield tunnel monitoring method usually uses single-point measurement methods such as total station and level, and reflects the tunnel deformation by measuring specific points. Although this method has the advantage of high single-point measurement accuracy, the spatial resolution is too low to fully reflect the health status of the subway shield tunnel, especially for disease detection. This method cannot accurately and efficiently obtain relevant information.

[0004] In recent years, the rapid development of laser radar (Light Detection and Ranging, LiDAR) technology provides a new way. The existing subway shield tunnel detection method based on laser radar generally projects the dense point cloud obtained by scanning into a two-dimensional plane through a cylindrical model, and then uses two-dimensional data processing methods and algorithms to identify or detect deformation or diseases. Due to the influence of the change or deformation of the structure itself, the commonly used cylindrical model is usually not consistent with the actual state of the subway shield tunnel, which directly leads to errors in the projection process, which further affects the accuracy of subsequent deformation and disease identification and detection. SUMMARY

[0005] The purpose of the present application is to provide a subway shield tunnel point cloud unfolding method, which can solve the projection deformation problem existing in the cylindrical projection unfolding process.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] A subway shield tunnel point cloud unfolding method, comprising:

[0008] Obtain point cloud data of the inner surface of the tunnel, and cut the point cloud data into several section point clouds according to a preset section width;

[0009] Project the section point cloud to the tunnel transverse plane to obtain a two-dimensional point cloud, and perform elliptical fitting on the two-dimensional point cloud to obtain optimal elliptical fitting parameters and the corresponding optimal fitting ellipse;

[0010] According to the optimal elliptical fitting parameters, an arc length integral formula of the optimal fitting ellipse is constructed;

[0011] According to an arc length integral formula of the optimal fitting ellipse, arc lengths of each data point on the optimal fitting ellipse to the vault vertex are calculated, and the optimal fitting ellipse is unfolded along the vault vertex according to the arc lengths of each data point on the optimal fitting ellipse to the vault vertex.

[0012] Further, the expression of the point cloud data is:

[0013] T(x i ,y i ,z i ) i＝1，2，…，n

[0014] where i is the i-th data point in the point cloud data, n is the total number of data points in the point cloud data, x i is the X-axis coordinate of the i-th data point in the point cloud data, y i is the Y-axis coordinate of the i-th data point in the point cloud data, z i is the Z-axis coordinate of the i-th data point in the point cloud data, XOZ plane is the tunnel transverse plane, and YOZ plane is the tunnel longitudinal plane.

[0015] Further, the point cloud data is cut into a plurality of section point clouds according to a preset section width, including:

[0016] The maximum and minimum values of the point cloud data on the Y-axis are calculated, and the Y-axis coordinates of the point cloud data are centralized;

[0017] According to the maximum and minimum values of the point cloud data on the Y-axis, the point cloud data is cut into a plurality of section point clouds according to a preset section width;

[0018] wherein the expression of the section point cloud is:

[0019]

[0020] where t is the t-th section point cloud, t = 1, 2, …, snum, snum is the total number of section point clouds, y max , y min is the maximum and minimum values of the point cloud data on the Y-axis, w is the preset section width, ceil(·) is the upward rounding, n t is the total number of data points in the t-th section point cloud, x j is the X-axis coordinate of the j-th data point in the t-th section point cloud, y j is the Y-axis coordinate of the j-th data point in the t-th section point cloud, z j is the Z-axis coordinate of the j-th data point in the t-th section point cloud.

[0021] Further, the expression of the two-dimensional point cloud is:

[0022]

[0023] wherein x j′ is the X-axis coordinate of the jth data point in the two-dimensional point cloud obtained by projecting the tth cross-section point cloud to the tunnel cross-section, and z j′ is the Z-axis coordinate of the jth data point in the two-dimensional point cloud obtained by projecting the tth cross-section point cloud to the tunnel cross-section.

[0024] Further, the ellipse fitting of the two-dimensional point cloud is performed to obtain the optimal ellipse fitting parameters and the corresponding optimal fitting ellipse, which includes:

[0025] Five data points are randomly selected from the two-dimensional point cloud for least square ellipse equation fitting to obtain the ellipse fitting parameters and the corresponding fitting ellipse, and the number of iterations is initialized;

[0026] All data points in the two-dimensional point cloud are traversed, and if the distance from a data point to the fitting ellipse is less than a preset distance threshold, the data point is determined as an inlier, otherwise, the data point is determined as an outlier;

[0027] If the total number of inliers in the current iteration is greater than the total number of inliers in the last iteration, the total number of inliers in the current iteration and the ellipse fitting parameters are updated as the optimal total number of inliers and the optimal ellipse fitting parameters, otherwise, the optimal total number of inliers and the optimal ellipse fitting parameters remain unchanged;

[0028] If the optimal total number of inliers reaches a preset total number of inliers or the number of iterations reaches a preset upper limit of the number of iterations, the iteration is exited, and the optimal ellipse fitting parameters and the corresponding optimal fitting ellipse are output, otherwise, the iteration is repeated until the optimal total number of inliers reaches the preset total number of inliers or the number of iterations reaches the preset upper limit of the number of iterations.

[0029] Further, the expression of the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameters is:

[0030]

[0031] wherein x and z are the X-axis coordinate and Z-axis coordinate of the data point on the optimal fitting ellipse, a is the first ellipse fitting parameter, b is the second ellipse fitting parameter, x0 is the third ellipse fitting parameter, z0 is the fourth ellipse fitting parameter, and XOZ plane is the tunnel cross-section plane.

[0032] Further, the arc length integral formula of the optimal fitting ellipse is constructed according to the optimal ellipse fitting parameters, which includes:

[0033] The optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameters is converted into a parameter form;

[0034] constructing an arc length integral formula of the optimal fitting ellipse according to a parameter form of an optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameters;

[0035] wherein the parameter form of the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameters is:

[0036]

[0037] wherein x and z are X-axis coordinate and Z-axis coordinate of a data point on the optimal fitting ellipse, θ is a corresponding angle value of the data point on the optimal fitting ellipse in an ellipse parameter coordinate system, θ ∈ [0, 2π), a is the first ellipse fitting parameter, b is the second ellipse fitting parameter, x0 is the third ellipse fitting parameter, z0 is the fourth ellipse fitting parameter, and XOZ plane is a tunnel transverse plane;

[0038] the arc length integral formula of the optimal fitting ellipse is:

[0039]

[0040] wherein l is an arc length from a first data point to a second data point on the optimal fitting ellipse, θ1 is a corresponding angle value of the first data point in the ellipse parameter coordinate system, θ2 is a corresponding angle value of the second data point in the ellipse parameter coordinate system, θ1, θ1 ∈ [0, 2π), and e is an eccentricity of the optimal fitting ellipse,

[0041] Further, according to the arc length integral formula of the optimal fitting ellipse, the arc length from each data point on the optimal fitting ellipse to the vault vertex is calculated and acquired, and the optimal fitting ellipse is unfolded along the vault vertex based on the arc length from each data point on the optimal fitting ellipse to the vault vertex, including:

[0042] judging a quadrant in which each data point on the optimal fitting ellipse is located;

[0043] based on the quadrant in which each data point on the optimal fitting ellipse is located, the arc length from each data point on the optimal fitting ellipse to the vault vertex is calculated and acquired according to the arc length integral formula of the optimal fitting ellipse;

[0044] based on the quadrant in which each data point on the optimal fitting ellipse is located, a corresponding relationship between the arc length from each data point on the optimal fitting ellipse to the vault vertex and an X-axis coordinate after the optimal fitting ellipse is unfolded along the vault vertex is acquired;

[0045] the optimal fitting ellipse is unfolded along the vault vertex according to the corresponding relationship between the arc length from each data point on the optimal fitting ellipse to the vault vertex and the X-axis coordinate after the optimal fitting ellipse is unfolded along the vault vertex;

[0046] The Y-axis coordinate of each data point on the optimal fitting ellipse after being spread along the vault vertex is the Y-axis coordinate corresponding to each data point in the point cloud data, and the XOY plane is a tunnel spread plane.

[0047] Further, judging the quadrant in which each data point on the optimal fitting ellipse is located comprises:

[0048] If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is judged that the data point is located in the first quadrant.

[0049] If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is judged that the data point is located in the second quadrant.

[0050] If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is less than 0, it is judged that the data point is located in the third quadrant.

[0051] If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is less than 0, it is judged that the data point is located in the fourth quadrant.

[0052] The XOZ plane is a tunnel cross-sectional plane.

[0053] Further, for the data point located in the first quadrant on the optimal fitting ellipse, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being spread along the vault vertex is:

[0054]

[0055] For the data point located in the second quadrant on the optimal fitting ellipse, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being spread along the vault vertex is:

[0056]

[0057] For the data point located in the third quadrant on the optimal fitting ellipse, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being spread along the vault vertex is:

[0058]

[0059] For the data point located in the fourth quadrant on the optimal fitting ellipse, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being spread along the vault vertex is:

[0060]

[0061] wherein x fθ is the angle value of the data point on the optimal fitting ellipse corresponding to the optimal fitting ellipse parameter coordinate system, θ is the parameter form of the optimal fitting ellipse equation corresponding to the optimal fitting ellipse parameter, a is the first ellipse fitting parameter, and e is the eccentricity of the optimal fitting ellipse. i θ is the angle value of the data point on the optimal fitting ellipse corresponding to the optimal fitting ellipse parameter coordinate system, θ is the parameter form of the optimal fitting ellipse equation corresponding to the optimal fitting ellipse parameter, a is the first ellipse fitting parameter, and e is the eccentricity of the optimal fitting ellipse.

[0062] Compared with the prior art, the beneficial effects of the present application are:

[0063] The subway shield tunnel point cloud unfolding method provided by the present application cuts the obtained point cloud data into a plurality of cross section point clouds and projects them onto a tunnel cross section plane to obtain two-dimensional point clouds, performs ellipse fitting on the two-dimensional point clouds, obtains optimal ellipse fitting parameters and the corresponding optimal fitting ellipse, builds an arc length integral formula of the optimal fitting ellipse, calculates the arc length of each data point on the optimal fitting ellipse to the vault vertex, and then unfolds the optimal fitting ellipse along the vault vertex according to the arc length, so that the point cloud data of the inner surface of the subway shield tunnel can be accurately unfolded to a two-dimensional plane. Compared with the traditional cylindrical projection unfolding method, the deformation caused by projection is reduced, which is conducive to tunnel deformation analysis and detection based on point cloud data in the later stage. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is a subway shield tunnel point cloud unfolding method flowchart provided by an embodiment of the present application;

[0065] Figure 2 is a point cloud data cross section cutting schematic diagram provided by an embodiment of the present application;

[0066] Figure 3 is an ellipse fitting schematic diagram of two-dimensional point clouds provided by an embodiment of the present application;

[0067] Figure 4 is an integral principle schematic diagram provided by an embodiment of the present application;

[0068] Figure 5 is a subway shield tunnel unfolding schematic diagram provided by an embodiment of the present application. DETAILED DESCRIPTION

[0069] The technical solutions of the present application will be further described in detail below in combination with specific embodiments.

[0070] The embodiments of the present application will be described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference signs represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation on the present application. The technical features in the embodiments and the embodiments can be combined with each other without conflict.

[0071] Figure 1 is a subway shield tunnel point cloud unfolding method flowchart provided by an embodiment of the present application. The flowchart only shows the logical order of the method of the embodiment, and the steps shown or described can be completed in an order different from that shown in other possible embodiments of the present application on the premise that they do not conflict with each other. Figure 1

[0072] Referring to Figure 1 , the method of the embodiment specifically includes the following steps:

[0073] Step 1: Obtain point cloud data of the inner surface of the tunnel, and cut the point cloud data into a plurality of cross section point clouds according to a preset cross section width.

[0074] In the embodiment, a section of the Nanjing subway shield tunnel is scanned by using a mobile laser radar to obtain the point cloud data of the inner surface of the tunnel.

[0075] The expression of the point cloud data is:

[0076] T(x i ,y i ,z i ) i＝1,2,…,n

[0077] wherein i is the i-th data point in the point cloud data, n is the total number of data points in the point cloud data, x i is the X-axis coordinate of the i-th data point in the point cloud data, y i is the Y-axis coordinate of the i-th data point in the point cloud data, z i is the Z-axis coordinate of the i-th data point in the point cloud data, XOZ plane is the tunnel transverse plane, and YOZ plane is the tunnel longitudinal plane.

[0078] Cutting the point cloud data into a plurality of cross section point clouds according to a preset cross section width includes the following steps:

[0079] Step 1: Calculate the maximum and minimum values of the point cloud data on the Y-axis, and center the Y-axis coordinates of the point cloud data.

[0080] Step 2: According to the maximum and minimum values of the point cloud data on the Y-axis, cut the point cloud data into a plurality of cross section point clouds according to a preset cross section width.

[0081] The expression of the cross section point cloud is:

[0082]

[0083] wherein t is the t-th cross section point cloud, t = 1, 2, …, snum, snum is the total number of cross section point clouds, y​max y min Here, n represents the maximum and minimum values ​​of the point cloud data along the Y-axis, w is the preset cross-sectional width, ceil(·) rounds up, and n... t Let x be the total number of data points in the point cloud of the t-th cross section. j Let y be the X-axis coordinate of the j-th data point in the point cloud of the t-th cross section. j Let z be the Y-axis coordinate of the j-th data point in the point cloud of the t-th cross section. j Let be the Z-axis coordinate of the j-th data point in the point cloud of the t-th cross section.

[0084] In this embodiment, the maximum value y of the point cloud data on the Y-axis is... max =4263.1396, the minimum value of point cloud data on the Y-axis. min =4243.1440, the maximum value of the point cloud data on the Y-axis after centering the Y-axis coordinates is y = 4243.1440. max =9.9978, the minimum value of point cloud data on the Y-axis. min = -9.9978, preset cross-sectional width w = 1m, total number of cross-sectional point clouds snum = 20, such as Figure 2 As shown, the point cloud data is cut into 20 cross-sectional point clouds.

[0085] Step 2: Project the cross-sectional point cloud onto the tunnel cross-sectional plane to obtain a two-dimensional point cloud, and perform ellipse fitting on the two-dimensional point cloud to obtain the optimal ellipse fitting parameters and the corresponding optimal fitted ellipse.

[0086] In this embodiment, the cross-sectional point cloud is projected onto the tunnel cross-section to obtain a two-dimensional point cloud, as shown in the figure. Figure 3 As shown.

[0087] The expression for a two-dimensional point cloud is:

[0088]

[0089] Where, x j′ Let z be the X-axis coordinate of the j-th data point in the 2D point cloud obtained by projecting the point cloud of the t-th cross section onto the tunnel cross section. j′ Let be the Z-axis coordinate of the j-th data point in the two-dimensional point cloud obtained by projecting the point cloud of the t-th cross section onto the tunnel cross section.

[0090] To perform ellipse fitting on a two-dimensional point cloud and obtain the optimal ellipse fitting parameters and the corresponding optimal fitted ellipse, the following steps are involved:

[0091] Step i: Randomly select 5 data points from the 2D point cloud to fit the least squares ellipse equation, obtain the ellipse fitting parameters and the corresponding fitted ellipse, and initialize the number of iterations;

[0092] Step ii: traverse all data points in the two-dimensional point cloud, if the distance from a data point to the fitted ellipse is less than a preset distance threshold, then determine that the data point is an inner point, otherwise, determine that the data point is an outer point;

[0093] Step iii: if the total number of inner points in the current loop is greater than the total number of inner points in the last loop, then update the total number of inner points in the current loop and the ellipse fitting parameters as the optimal total number of inner points and the optimal ellipse fitting parameters, otherwise, keep the optimal total number of inner points and the optimal ellipse fitting parameters unchanged;

[0094] Step iv: if the optimal total number of inner points reaches a preset total number of inner points or the number of loops reaches a preset upper limit of loops, then exit the loop and output the optimal ellipse fitting parameters and the corresponding optimal fitted ellipse, otherwise, repeat the loop until the optimal total number of inner points reaches the preset total number of inner points or the number of loops reaches the preset upper limit of loops.

[0095] The expression of the optimal fitted ellipse equation corresponding to the optimal ellipse fitting parameters is:

[0096]

[0097] wherein x and z are the X-axis coordinate and Z-axis coordinate of a data point on the optimal fitted ellipse, a is the first ellipse fitting parameter, b is the second ellipse fitting parameter, x0 is the third ellipse fitting parameter, z0 is the fourth ellipse fitting parameter, and XOZ plane is the tunnel transverse plane.

[0098] In the embodiment, the two-dimensional point cloud is subjected to ellipse fitting, and in the obtained optimal ellipse fitting parameters, the first ellipse fitting parameter a = 2.7814, the second ellipse fitting parameter b = 2.7452, the third ellipse fitting parameter x0 = 0.0549, and the fourth ellipse fitting parameter z0 = 1.0841, and the optimal fitted ellipse corresponding to the optimal ellipse fitting parameters is as shown in FIG. 2. Figure 3

[0099] Step three: constructing an arc length integral formula of the optimal fitted ellipse according to the optimal ellipse fitting parameters;

[0100] Constructing the arc length integral formula of the optimal fitted ellipse according to the optimal ellipse fitting parameters includes the following steps:

[0101] Step i: converting the optimal fitted ellipse equation corresponding to the optimal ellipse fitting parameters into a parameter form;

[0102] The parameter form of the optimal fitted ellipse equation corresponding to the optimal ellipse fitting parameters is:

[0103]

[0104] ​Wherein, x, z are the X-axis coordinate, Z-axis coordinate of the data points on the optimal fitting ellipse, θ is the corresponding angle value of the data points on the optimal fitting ellipse in the ellipse parameter coordinate system, θ∈[0, 2π), a is the first ellipse fitting parameter, b is the second ellipse fitting parameter, x0 is the third ellipse fitting parameter, z0 is the fourth ellipse fitting parameter, XOZ plane is the tunnel transverse plane.

[0105] Step II: According to the parameter form of the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameter, the arc length integral formula of the optimal fitting ellipse is constructed;

[0106] The arc length integral formula of the optimal fitting ellipse is:

[0107]

[0108] Wherein, l is the arc length of the first data point to the second data point on the optimal fitting ellipse, θ1 is the corresponding angle value of the first data point in the ellipse parameter coordinate system, θ2 is the corresponding angle value of the second data point in the ellipse parameter coordinate system, θ1, θ1∈[0, 2π), e is the eccentricity of the optimal fitting ellipse,

[0109] Step four: According to the arc length integral formula of the optimal fitting ellipse, the arc length of each data point on the optimal fitting ellipse to the vault vertex is calculated and obtained, and the optimal fitting ellipse is unfolded along the vault vertex according to the arc length of each data point on the optimal fitting ellipse to the vault vertex.

[0110] According to the arc length integral formula of the optimal fitting ellipse, the arc length of each data point on the optimal fitting ellipse to the vault vertex is calculated and obtained, and the optimal fitting ellipse is unfolded along the vault vertex according to the arc length of each data point on the optimal fitting ellipse to the vault vertex, including the following steps:

[0111] Step 1: Determine the quadrant of each data point on the optimal fitting ellipse;

[0112] Determine the quadrant of each data point on the optimal fitting ellipse, including the following steps:

[0113] Step (1): If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is determined that the data point is located in the first quadrant;

[0114] Step (1): If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is determined that the data point is located in the second quadrant;

[0115] Step (1): If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is less than 0, it is determined that the data point is located in the third quadrant;

[0116] Step (1): If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is less than 0, it is determined that the data point is located in the fourth quadrant.

[0117] In this embodiment, the XOZ plane is the tunnel transverse plane.

[0118] Step 2: Based on the quadrant in which each data point on the optimal fitting ellipse is located, the arc length from each data point on the optimal fitting ellipse to the vault vertex is calculated according to the arc length integral formula of the optimal fitting ellipse.

[0119] In this embodiment, for a data point on the optimal fitting ellipse located in the first quadrant, the arc length l1 from the data point to the vault vertex is:

[0120]

[0121] For a data point on the optimal fitting ellipse located in the second quadrant, the arc length l2 from the data point to the vault vertex is:

[0122]

[0123] For a data point on the optimal fitting ellipse located in the third quadrant, the arc length l3 from the data point to the vault vertex is:

[0124]

[0125] For a data point on the optimal fitting ellipse located in the fourth quadrant, the arc length l4 from the data point to the vault vertex is:

[0126]

[0127] Step 3: Based on the quadrant in which each data point on the optimal fitting ellipse is located, the corresponding relationship between the arc length from each data point on the optimal fitting ellipse to the vault vertex and the X-axis coordinate after the vault vertex is unfolded is obtained.

[0128] In this embodiment, for a data point on the optimal fitting ellipse located in the first quadrant, the corresponding relationship between the arc length from the data point to the vault vertex and the X-axis coordinate after the vault vertex is unfolded is:

[0129]

[0130] For a data point on the optimal fitting ellipse located in the second quadrant, the corresponding relationship between the arc length from the data point to the vault vertex and the X-axis coordinate after the vault vertex is unfolded is:

[0131]

[0132] For a data point on the optimal fitting ellipse located in the third quadrant, the corresponding relationship between the arc length from the data point to the vault vertex and the X-axis coordinate after the vault vertex is unfolded is:

[0133]

[0134] For a data point in the fourth quadrant of the best-fit ellipse, the relationship between its arc length to the apex and its X-axis coordinate after unfolding along the apex is as follows:

[0135]

[0136] Where, x f Let θ be the X-axis coordinate of the data points on the optimally fitted ellipse after unfolding along the apex of the arch. i Let θ be the angle value corresponding to the data point in the elliptical parametric coordinate system, θ be the angle value corresponding to the data point on the optimal fitted ellipse in the parametric form of the optimal fitted ellipse equation corresponding to the optimal ellipse fitting parameters, a be the first ellipse fitting parameter, and e be the eccentricity of the optimal fitted ellipse.

[0137] In this embodiment, the schematic diagram of the integration principle is as follows: Figure 4 As shown, Figure 4 In the diagram, G is the apex of the arch, P is a data point of the optimally fitted ellipse, and P' is the data point obtained by expanding the data point P along the apex G. For example... Figure 4 As shown, when data point P is located in the first quadrant, the X-axis coordinate of data point P' after it is expanded along the apex G is the arc length from the apex G. Similarly, when data point P is located in the fourth quadrant, the X-axis coordinate of data point P' after it is expanded along the apex G is also the arc length from the apex G. Correspondingly, when data point P is located in the second or third quadrant, the X-axis coordinate of data point P' after it is expanded along the apex G is the negative of the arc length from the apex G.

[0138] Step 4: Based on the correspondence between the arc length of each data point on the optimally fitted ellipse to the apex of the arch and its X-axis coordinate after being unfolded along the apex of the arch, unfold the optimally fitted ellipse along the apex of the arch.

[0139] In this embodiment, the Y-axis coordinates of each data point on the optimal fitting ellipse, after unfolding along the apex of the arch, are the corresponding Y-axis coordinates of each data point in the point cloud data, and the XOY plane is the tunnel unfolding plane. A schematic diagram of the subway shield tunnel unfolding is shown below. Figure 5 As shown.

[0140] The subway shield tunnel point cloud unfolding method provided in the embodiment cuts the obtained point cloud data into a plurality of cross section point clouds and projects the cross section point clouds to a tunnel cross section plane to obtain two-dimensional point clouds, performs elliptical fitting on the two-dimensional point clouds to obtain optimal elliptical fitting parameters and a corresponding optimal fitting ellipse, builds an arc length integral formula of the optimal fitting ellipse, calculates arc lengths of each data point on the optimal fitting ellipse to a vault point, and thus unfolds the optimal fitting ellipse along the vault point according to the arc lengths, so that the point cloud data of the inner surface of the subway shield tunnel can be accurately unfolded to a two-dimensional plane, compared with a traditional cylindrical projection unfolding method, the deformation caused by the projection is reduced, and this is beneficial to tunnel deformation analysis and detection based on the point cloud data in the later period.

[0141] The above is only the preferred embodiment of the present application, and it should be noted that those skilled in the art can make several improvements and modifications without departing from the technical principles of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A method for unrolling a metro shield tunnel point cloud, characterized in that, The method comprises the following steps: acquiring point cloud data of a tunnel inner surface, and cutting the point cloud data into a plurality of section point clouds according to a preset section width; projecting the section point clouds onto a tunnel cross section plane to acquire two-dimensional point clouds, and performing elliptical fitting on the two-dimensional point clouds to acquire optimal elliptical fitting parameters and a corresponding optimal fitting ellipse; constructing an arc length integral formula of the optimal fitting ellipse according to the optimal elliptical fitting parameters; calculating arc lengths from each data point on the optimal fitting ellipse to a vault vertex according to the arc length integral formula of the optimal fitting ellipse, and unfolding the optimal fitting ellipse along the vault vertex according to the arc lengths from each data point on the optimal fitting ellipse to the vault vertex. The expression of the point cloud data is: ； in, For the point cloud data Data points, The total number of data points in the point cloud data. For the point cloud data The X-axis coordinates of the data points For the point cloud data The Y-axis coordinates of the data points For the point cloud data The Z-axis coordinates of the data points; the XOZ plane is the tunnel cross section plane; and the YOZ plane is the tunnel longitudinal section plane. cutting the point cloud data into a plurality of section point clouds according to a preset section width comprises: calculating a maximum value and a minimum value of the point cloud data on a Y axis, and centralizing Y axis coordinates of the point cloud data; cutting the point cloud data into a plurality of section point clouds according to a preset section width according to the maximum value and the minimum value of the point cloud data on the Y axis; The expression of the section point cloud is: ； in, For the first A cross-sectional point cloud, , This represents the total number of point clouds across the cross-section. , , For the maximum and minimum values ​​of the point cloud data on the Y-axis, For the preset cross-sectional width, To round up, For the first The total number of data points in a cross-sectional point cloud. For the first In the point cloud of the cross section, the first The X-axis coordinates of the data points For the first The first cross-sectional point cloud The Y-axis coordinates of the data points For the first The first cross-sectional point cloud Z-axis coordinates of each data point; calculating arc lengths from each data point on the optimal fitting ellipse to a vault vertex according to the arc length integral formula of the optimal fitting ellipse, and unfolding the optimal fitting ellipse along the vault vertex according to the arc lengths from each data point on the optimal fitting ellipse to the vault vertex comprises: judging quadrants in which each data point on the optimal fitting ellipse is located; calculating arc lengths from each data point on the optimal fitting ellipse to a vault vertex according to the arc length integral formula of the optimal fitting ellipse based on the quadrants in which each data point on the optimal fitting ellipse is located; acquiring a corresponding relationship between the arc lengths from each data point on the optimal fitting ellipse to the vault vertex and X axis coordinates of each data point on the optimal fitting ellipse after being unfolded along the vault vertex based on the quadrants in which each data point on the optimal fitting ellipse is located; unfolding the optimal fitting ellipse along the vault vertex according to the corresponding relationship between the arc lengths from each data point on the optimal fitting ellipse to the vault vertex and the X axis coordinates of each data point on the optimal fitting ellipse after being unfolded along the vault vertex; wherein, Y axis coordinates of each data point on the optimal fitting ellipse after being unfolded along the vault vertex are Y axis coordinates corresponding to each data point in the point cloud data, and an XOY plane is a tunnel unfolding plane.

2. The method of claim 1, wherein, The expression of the two-dimensional point cloud is: ； in, For the first The point cloud of the first cross section is projected onto the two-dimensional point cloud obtained from the tunnel cross section. The X-axis coordinates of the data points For the first The point cloud of the first cross section is projected onto the two-dimensional point cloud obtained from the tunnel cross section. The Z-axis coordinates of the data points. 3.The method of unrolling a metro shield tunnel point cloud according to claim 1, characterized in that, performing elliptical fitting on the two-dimensional point clouds to acquire optimal elliptical fitting parameters and a corresponding optimal fitting ellipse comprises: randomly selecting 5 data points from the two-dimensional point clouds to perform least square elliptical equation fitting to acquire elliptical fitting parameters and a corresponding fitting ellipse, and initializing a loop number; traversing all data points in the two-dimensional point clouds, if a distance from a data point to the fitting ellipse is less than a preset distance threshold, the data point is judged as an inner point, otherwise, the data point is judged as an outer point; if a total number of inner points in the current loop is greater than a total number of inner points in the last loop, the total number of inner points in the current loop and the elliptical fitting parameters are updated as an optimal total number of inner points and optimal elliptical fitting parameters, otherwise, the optimal total number of inner points and the optimal elliptical fitting parameters are kept unchanged; If the optimal inner point total reaches the preset inner point total or the loop number reaches the preset loop upper limit, the loop is exited, and the optimal ellipse fitting parameter and the corresponding optimal fitting ellipse are output, otherwise, the loop is repeated until the optimal inner point total reaches the preset inner point total or the loop number reaches the preset loop upper limit.

4. The method of claim 3, wherein, An expression of an optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameter is: ； wherein, , are the X-axis and Z-axis coordinates of the data points on the best-fit ellipse, are the first ellipse fitting parameters, are the second ellipse fitting parameters, are the third ellipse fitting parameters, are the fourth ellipse fitting parameters, and the XOZ plane is the tunnel transversal plane.

5. The method of claim 1, wherein, According to the optimal ellipse fitting parameter, constructing an arc length integral formula of the optimal fitting ellipse includes: Converting the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameter into a parameter form; According to the parameter form of the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameter, constructing an arc length integral formula of the optimal fitting ellipse; The parameter form of the optimal fitting ellipse equation corresponding to the optimal ellipse fitting parameter is: ； wherein, , is the X-axis coordinate, the Z-axis coordinate of the data point on the best-fitted ellipse, is the corresponding angle value of the data point on the best-fitted ellipse in the ellipse parameter coordinate system, , is the first ellipse fitting parameter, is the second ellipse fitting parameter, is the third ellipse fitting parameter, is the fourth ellipse fitting parameter, and the XOZ plane is the tunnel transverse plane. The arc length integral formula of the optimal fitting ellipse is: ； wherein, is the arc length of the first data point to the second data point on the best fit ellipse, is the corresponding angle value of the first data point in the parametric coordinate system of the ellipse, is the corresponding angle value of the second data point in the parametric coordinate system of the ellipse, , is the eccentricity of the best fit ellipse, .

6. The method of claim 1, wherein, Judging the quadrant where each data point on the optimal fitting ellipse is located includes: If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is judged that the data point is located in the first quadrant; If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is greater than 0 or equal to 0, it is judged that the data point is located in the second quadrant; If the X-axis coordinate of a data point on the optimal fitting ellipse is less than 0 or equal to 0 and the Z-axis coordinate is less than 0, it is judged that the data point is located in the third quadrant; If the X-axis coordinate of a data point on the optimal fitting ellipse is greater than 0 and the Z-axis coordinate is less than 0, it is judged that the data point is located in the fourth quadrant; The XOZ plane is a tunnel transverse plane.

7. The method of unrolling a metro shield tunnel point cloud according to claim 6, wherein, For a data point on the optimal fitting ellipse located in the first quadrant, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being developed along the vault vertex is: ； For a data point on the optimal fitting ellipse located in the second quadrant, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being developed along the vault vertex is: ； For a data point on the optimal fitting ellipse located in the third quadrant, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being developed along the vault vertex is: ； For a data point on the optimal fitting ellipse located in the fourth quadrant, the corresponding relationship between the arc length of the data point to the vault vertex and the X-axis coordinate of the data point after being developed along the vault vertex is: ； wherein, is the X-axis coordinate of the data point on the best-fit ellipse after being unwrapped along the dome vertex, is the corresponding angle value of the data point in the ellipse parameter coordinate system, is the corresponding angle value of the data point on the best-fit ellipse in the parameter form of the best-fit ellipse equation corresponding to the best-fit ellipse fitting parameters, is the first ellipse fitting parameter, is the eccentricity of the best-fit ellipse.

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