CN111027484B - Tunnel steel arch identification method based on three-dimensional imaging - Google Patents

Tunnel steel arch identification method based on three-dimensional imaging Download PDF

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CN111027484B
CN111027484B CN201911262862.0A CN201911262862A CN111027484B CN 111027484 B CN111027484 B CN 111027484B CN 201911262862 A CN201911262862 A CN 201911262862A CN 111027484 B CN111027484 B CN 111027484B
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谢斌
丘文杰
张文婷
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Central South University
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Abstract

The invention discloses a tunnel steel arch identification method based on three-dimensional imaging, which comprises the following steps: the method comprises the steps of data preprocessing, point cloud coordinate system correction, radial filtering, steel arch characteristic point extraction, steel arch extraction and the like, and steel arches in a tunnel under construction can be accurately identified through processing three-dimensional point cloud data, so that the method has strong practical engineering significance for detecting the installation position of the steel arches and improving the mechanical automation of tunnel engineering.

Description

Tunnel steel arch identification method based on three-dimensional imaging
Technical Field
The embodiment of the invention relates to the technical field of three-dimensional reconstruction of tunnels and internal feature recognition thereof, in particular to a tunnel steel arch recognition method based on three-dimensional imaging.
Background
Tunnels are important building forms for people to overcome complex terrains and make full use of geographic spaces to build highways and railways, and have great significance in infrastructure construction of all parts of the world. Thus, the construction of tunnels is also more and more frequent. Meanwhile, we also face the severe environment brought by tunnel construction, such as limited light source, humidity, thin air, falling rocks and even collapse, especially when the tunnel face is subjected to guniting treatment, dust and noise are further aggravated, the harm to the body of construction workers is further aggravated, although the tunnel guniting technology is more and more emphasized at present, tunnel guniting also gradually develops towards the direction of mechanization and intelligence, and a plurality of novel tunnel guniting machines are developed and put into use, but the situation cannot be fundamentally changed because the tunnel guniting machines also need a certain number of operators and accompanying personnel, so that the full-automatic unmanned tunnel guniting is increasingly important.
In recent years, as rapid development of laser scanning technology and three-dimensional image processing are increasingly emphasized, many people begin to apply three-dimensional reconstruction to tunnel construction, and because laser scanning and three-dimensional image processing can obtain high-precision data and positioning even in adverse environments, unlike the method of photographing and two-dimensional image processing which are greatly affected by tunnel environments, the three-dimensional reconstruction technology will gradually become the mainstream technology of tunnel data processing.
To realize unmanned spraying, firstly, a spraying area is identified, and the spraying area is generally positioned between every two steel arches, so that the identification of the steel arches is particularly important, and no existing technology is available at present for identifying the steel arches on a three-dimensional point cloud.
Disclosure of Invention
The invention provides a tunnel steel arch identification method based on three-dimensional imaging, which aims to solve the technical problem that the identification of a steel arch in a tunnel through machine vision is not available at present.
In order to achieve the above object, the present invention provides the following technical solutions:
a tunnel steel arch identification method based on three-dimensional imaging comprises the following steps:
step one, carrying out integral scanning on the inside of a tunnel to obtain original point cloud data, and carrying out data preprocessing;
step two, correcting a point cloud coordinate system of the preprocessed data;
step three, radial filtering is carried out on the corrected data to filter out point cloud data outside the tunnel wall;
extracting feature points of the steel arch through a normal alignment radial feature key point algorithm;
and fifthly, performing three-dimensional circle fitting on the extracted characteristic points to realize extraction of the steel arch and complete identification.
In the tunnel steel arch identification method based on three-dimensional imaging, in the first step, the data preprocessing is to sequentially perform voxel filtering and direct filtering on original point cloud data.
In the tunnel steel arch identification method based on three-dimensional imaging, in the second step, the point cloud coordinate system correction comprises the following steps:
step 1, performing cylindrical fitting on a tunnel point cloud through a random sampling consistency algorithm to obtain the axial direction and the axis of the tunnel point cloud;
and 2, axially rotating the tunnel point cloud to be overlapped with the x-axis of the point cloud coordinate system through the rotation matrix, and overlapping the axis of the tunnel point cloud with the origin of the point cloud coordinate system through translation.
In the three-dimensional imaging-based tunnel steel arch identification method, in the step 1 of correcting the point cloud coordinate system, the specific steps of carrying out cylindrical fitting on the tunnel point cloud by a random sampling consistency algorithm are as follows:
(1) Taking the tunnel point cloud data subjected to the data preprocessing in the first step as data to be detected;
(2) Establishing a cylindrical model, wherein parameters included in the establishment of the model are a cylindrical axis parameter and a cylindrical base circle radius, and the parameters form a cylindrical equation;
(3) Other custom parameters in the model are input, including minimum point number of subsets, maximum iteration times, maximum threshold value of distance from the inner point to the model and radius range of the model;
(4) The random sampling consistency algorithm achieves the goal by repeatedly selecting a set of random subsets in the data to be tested, the selected subsets are assumed to be local points, the model is evaluated by estimating the error rate of the local points and the input model after the algorithm is verified, and finally the model parameters are obtained.
The tunnel steel arch identification method based on three-dimensional imaging, wherein the step 2 of correcting the point cloud coordinate system comprises the following steps:
1) Taking the tunnel axial direction obtained after cylindrical fitting as P n (a, b, c), wherein a, b, c are each vector P n Corresponding components in x, y and z directions in a coordinate system, and the axis is P c (x 0 ,y 0 ,z 0 );
2) Will P n (a, b, c) rotating around the z-axis in the point cloud coordinate system to a plane xoz, wherein the rotation angle is-alpha, and alpha is P n The projection onto the plane xoy is at an angle to the x-axis,obtaining vectors
Figure BDA0002312038010000031
The rotation matrix is:
Figure BDA0002312038010000032
wherein the method comprises the steps of
Figure BDA0002312038010000033
3) Will be
Figure BDA0002312038010000034
Rotated about the y-axis to the xoy plane, where the angle of rotation is beta, beta is Q n Included angle with x axis, original tunnel point cloud axial direction P after rotation n Then the rotation matrix is coincident with the x-axis:
Figure BDA0002312038010000035
wherein the method comprises the steps of
Figure BDA0002312038010000036
4) And then shift P c (x 0 ,y 0 ,z 0 ) Coinciding with the origin of the point cloud coordinate system, wherein the translation matrix is:
Figure BDA0002312038010000037
the tunnel steel arch identification method based on three-dimensional imaging comprises the following steps:
and taking a point on the axial direction of the tunnel as the axial center of the radial section of the tunnel, and filtering all points, which are not more than a radial threshold, in the point cloud data on the radial section of the tunnel, wherein the radial threshold is a value obtained by subtracting a preset steel arch thickness value from a radius value obtained when cylindrical fitting is carried out on the point cloud of the tunnel.
The tunnel steel arch identification method based on three-dimensional imaging comprises the following steps:
step (1), extracting object edges of point clouds to obtain edge points;
and (2) extracting key points from the edge points, wherein the key points are required to be positioned on the actual boundary and surface structure of the tunnel steel arch and are not blocked by other object point clouds, and meanwhile, the points are positioned at positions capable of providing stable areas for conventional estimation or descriptor calculation, and the extracted key points are taken as characteristic points.
In the tunnel steel arch identification method based on three-dimensional imaging, in the step (1) of extracting the steel arch characteristic points, the step of extracting the edges is as follows:
step I, projecting the three-dimensional point cloud into a depth image;
step II, traversing each depth image point, taking the currently traversed point as p i Then p is i Taking a square frame with a side length s as a center, and taking the middle point of the square frame as an edge point searching point set;
step III, calculating p i Distance from all points in the box, d 0 Representation and p i The nearest point, p i Itself to
Figure BDA0002312038010000042
Representation and p i The furthest point is then taken as d 0 And->
Figure BDA0002312038010000041
Represented and p i Average value of distance, selecting point d corresponding to the average value m
Step IV, according to the selected d m The edge point search point is concentrated to a distance greater than d m The point of (2) is set as an edge point set;
step V, performing non-maximum suppression on the edge point set, and taking out the maximum value as an edge point;
and step VI, returning to the step II until all points are traversed.
The tunnel steel arch identification method based on three-dimensional imaging comprises the following steps:
step one, inputting point cloud data and characteristic point data of only the remaining tunnel surface after the treatment in the step three;
step two, carrying out three-dimensional circular model parameter estimation on the characteristic point data by using a random sampling consistency algorithm, and deleting the characteristic points used for estimation;
thirdly, fitting the parameters estimated in the second step into a three-dimensional circular formula, substituting the three-dimensional circular formula into the point cloud data of the tunnel face, extracting and independently storing points on the circle, wherein the extracted points are steel arch points;
and step four, repeating the steps two and three by using the rest data until the rest data cannot meet the requirement of continuing to estimate the parameters of the three-dimensional circular model.
In the tunnel steel arch identification method based on three-dimensional imaging, in the step three of steel arch extraction, the parameter equation of the three-dimensional circle is as follows:
estimating 7 three-dimensional circular model parameters by using a random sampling consistency algorithm, wherein the parameters are three-dimensional circular center coordinates (x c ,y c ,z c ) Radius r, normal vector n (n) x ,n y ,n z );
First, a vector u (u x ,u y ,u z ) Wherein u is x ,u y ,n z The components of the vector u on the coordinate axes x, y and z are respectively:
Figure BDA0002312038010000051
because of
Figure BDA0002312038010000052
Wherein T is the matrix transpose symbol;
then, a vector v=n×u orthogonal to both n and u is obtained, and the vector v is also on the plane of the circle:
Figure BDA0002312038010000053
then u and v are all converted into corresponding unit vectors
Figure BDA0002312038010000054
Figure BDA0002312038010000055
Figure BDA0002312038010000056
The parametric equation for a circle is expressed as
Figure BDA0002312038010000057
The method has the technical effects that 1, the method realizes the identification and extraction of the steel arch in the surface to be sprayed in the three-dimensional point cloud of the tunnel through the steps of data preprocessing, point cloud coordinate system correction, radial filtering, steel arch characteristic point extraction, steel arch extraction and the like, which is a direction not yet involved in the prior art, provides environmental perception support for the later tunnel guniting automation, and has stronger practical significance for the tunnel engineering mechanical automation. 2. As a steel arch recognition technology, the method can provide technical support for steel arch installation position detection later, and has strong practical significance for tunnel safety detection.
Drawings
FIG. 1 is a system flow diagram of steel arch identification of the present invention;
FIG. 2 shows the corresponding position and orientation of the tunnel point cloud on the coordinate system during three-dimensional reconstruction according to the present invention;
FIG. 3 is a graph showing the results of radial filtering according to the present invention, wherein (a) is a graph showing the results of the point cloud from the side view of the tunnel after radial filtering, (b) is a graph showing the results of the point cloud from the front view of the tunnel after radial filtering, (c) is a graph showing the results of the point cloud from the side view of the point cloud in the tunnel after radial filtering, (d) is a graph showing the results of the point cloud from the front view of the point cloud in the tunnel after radial filtering, the point cloud in the tunnel is a retention point cloud, and the point cloud in the tunnel is a filtered point cloud;
FIG. 4 is a graph showing the result of extraction of feature points of a steel arch according to the present invention;
fig. 5 is a graph of the result of extraction of the steel arch of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the attached drawings so that the advantages and features of the present invention will be more readily understood by those skilled in the art, and thus the scope of the present invention will be more clearly defined.
As shown in fig. 1 to 5, the invention provides a tunnel steel arch identification method based on three-dimensional imaging, which comprises the following steps:
the invention sequentially executes data preprocessing, point cloud coordinate system correction, radial filtering, steel arch characteristic point extraction and steel arch extraction to complete the identification process. The data preprocessing part firstly carries out voxel filtering on original point cloud data, reduces the data quantity of the point cloud on the basis of not damaging the characteristics of each part so as to improve the operation efficiency in the subsequent processing process, and then carries out direct filtering on the point cloud after voxel filtering so as to filter noise points outside a target main body. The point cloud coordinate system correction section corrects the coordinate system by the rotation matrix after obtaining the point cloud rotation angle. The radial filtering part filters out points within the radius of the tunnel axial direction at a certain radius to remove the influence of the tunnel face, the ground and noise points in the air and on the ground (including reconstructed people, vehicles and other interferents in the scanning range). The steel arch feature point extraction part extracts feature points in the tunnel point cloud through NARF, and points on the steel arch are judged as feature points due to the shape characteristics of the steel arch and the installation position characteristics of the steel arch. The steel arch extracting part extracts the characteristic points of the steel arch belonging to the same steel arch into the same point cloud through three-dimensional circular fitting by RANSAC, and finally, the steel arch is extracted.
The data preprocessing is to sequentially perform voxel filtering and direct filtering on original point cloud data, wherein parameters are set as follows:
(1) The size of each voxel grid in the voxel filtering is set to be 50mm and 50mm;
(2) Points between-20000 mm and 20000mm are reserved in the x, y and z directions in the straight-through filtering.
The specific steps of the point cloud coordinate system correction are as follows:
(1) Performing cylindrical fitting on the tunnel point cloud through RANSAC, and obtaining the axial direction and the axis of the tunnel point cloud after fitting;
(2) Axially rotating the tunnel point cloud to be overlapped with the x-axis of the point cloud coordinate system through the rotation matrix, and overlapping the axis of the tunnel point cloud with the origin of the point cloud coordinate system through translation;
in the step (1) of correcting the point cloud coordinate system, the specific step of performing cylindrical fitting on the tunnel point cloud through the RANSAC is as follows:
(1) And taking the tunnel point cloud data subjected to the data preprocessing in the step one as data to be detected.
(2) Establishing a cylindrical model, wherein parameters included in establishing the model are a cylindrical axis parameter and a cylindrical base circle radius, the cylindrical model is adapted to data to be measured, the cylindrical axis parameter comprises a cylindrical axis vector (a, b, c), and coordinates (x c ,y c ,z c ) The radius of the bottom circle of the cylinder is r 0 These parameters constitute the cylindrical equation:
(x-x c ) 2 +(y-y c ) 2 +(z-z c ) 2 -[a(x-x c )+b(y-y c )+c(z-z c )] 2 =r 0 2
(3) Other custom parameters in the model are input, including minimum point number of subsets, maximum iteration number, maximum threshold value of distance from inner point to the model, and radius range of the model. The specific values adopted in this embodiment are:
subset minimum points: 100000.
subset maximum points: 1000000.
maximum number of iterations: 50.
the maximum threshold of distance of the interior point to the model: 200.
model radius: 5000 mm-9000 mm.
(4) The random sampling consistency algorithm achieves the goal by repeatedly selecting a set of random subsets in the data to be tested, the selected subsets are assumed to be local points, the model is evaluated by estimating the error rate of the local points and the input model after the algorithm is verified, and finally model parameters are obtained: tunnel axial direction P n (a, b, c), an axis P c (x 0 ,y 0 ,z 0 ) Radius r of cylinder base circle 0
In the step (2) of correcting the point cloud coordinate system, the step of correcting the tunnel point cloud through the rotation matrix is as follows:
(1) Let the tunnel axis obtained by cylindrical fitting be P n (a, b, c), wherein a, b, c are each vector P n Corresponding components in x, y and z directions in a coordinate system, and the axis is P c (x 0 ,y 0 ,z 0 )。
(2) Will P n (a, b, c) rotates about the z-axis to a plane xoz, wherein the angle of rotation is-alpha (alpha is P n The projection on the plane xoy forms an included angle with the x-axis), and the vector is obtained after rotation
Figure BDA0002312038010000081
The rotation matrix is:
Figure BDA0002312038010000082
wherein the method comprises the steps of
Figure BDA0002312038010000083
(3) Will be
Figure BDA0002312038010000084
Rotated about the y-axis to the xoy-plane, wherein the angle of rotation is beta (beta is Q n Included angle with x-axis), the original tunnel point cloud axial direction P after rotation n Then coincides with the x-axis. The rotation matrix is:
Figure BDA0002312038010000085
wherein the method comprises the steps of
Figure BDA0002312038010000091
(4) And then shift P c (x 0 ,y 0 ,z 0 ) Coinciding with the origin of the point cloud coordinate system, the translation matrix is as follows:
Figure BDA0002312038010000092
the calibration of the coordinate system is completed, the scanning device is generally placed on the ground, so that the scanning device does not need to rotate around the x-axis any more, and meanwhile, no matter where the axis is located on the x-axis of the coordinate system, the axis does not affect the subsequent processing, so that the x-axis is not translated during translation.
The specific method corresponding to the radial filtering is as follows:
when cylindrical fitting is carried out on the tunnel point cloud, the radius parameter of the tunnel point cloud can be obtained, the radius threshold value which is used for filtering is subtracted by 500mm on the basis of the radius of the tunnel point cloud, an x-axis (namely the axial direction of the tunnel) is taken as an axis, if the Euclidean distance from the x-axis is larger than the radius threshold value, the point of the tunnel face is judged, meanwhile, the point is reserved, otherwise, the point in the tunnel is filtered, so that interference objects on the tunnel face, the ground and the ground are filtered, and the accuracy of steel arch identification is improved.
The extraction of the steel arch characteristic points comprises the following steps:
(1) Edge extraction is performed on the point cloud because points on the edge are more likely to be key points relative to other points. In the NARF algorithm, the edges of the point cloud are divided into three types: object edges, shadow edges, veil point sets. Since the present invention is to identify steel arches, only the object edges need to be extracted.
(2) And after the edge is extracted, extracting key points from the edge points to serve as characteristic points.
In the step (1) of extracting the steel arch characteristic points, the corresponding specific method of edge extraction is as follows:
and step I, projecting the three-dimensional point cloud into a depth image.
Step II, traversing each depth image point, taking the currently traversed point as p i Then p is i Taking a square frame with a side length s as the center, and taking the middle point of the square frame as an edge point search point set.
Step III, calculating p i Distance from all points in the box, d 0 Representation and p i The nearest point, p i Itself to
Figure BDA0002312038010000093
Representation and p i The furthest point is then taken as d 0 And->
Figure BDA0002312038010000094
Represented and p i Average value of distance, selecting point d corresponding to the average value m
Step IV, according to the selected d m The edge point search point is concentrated to a distance greater than d m Is set as the set of edge points.
And V, performing non-maximum suppression on the edge point set, and taking out the maximum value as an edge point.
And step VI, returning to the step II until all points are traversed.
Preferably, in the step 2 of extracting the feature points of the steel arch, the key point extraction needs to consider the following factors:
(1) Information of the boundary and surface structure must be considered, i.e. the key points need to be on the actual boundary and surface structure of the tunnel steel arch.
(2) The position that can be reliably detected must be selected even if the object is viewed from another angle. I.e. not occluded by other object point clouds.
(3) These points must be located where the stable region is typically provided for conventional estimation or descriptor computation. The stable region is characterized in that a sufficient number of points are arranged near the position of the key point to calculate the descriptor and perform unique normal vector estimation, wherein the sufficient number of points are particularly characterized in that more than three points are arranged in a range of 50mm radius by taking the key point as the center of a circle.
The steel arch extraction steps are as follows:
(1) Inputting point cloud data and characteristic point data of the tunnel face only left after the third step;
(2) Estimating the three-dimensional circular model parameters of the characteristic point data by using RANSAC, and deleting the characteristic points for estimation;
(3) Fitting the parameters estimated in the step (2) into a three-dimensional circle formula, substituting the formula into the point cloud data of the tunnel face, extracting and independently storing points on the circle, wherein the extracted points are steel arch points;
(4) Repeating the step (2) and the step (3) by using the rest characteristic point cloud data until the three-dimensional circular model parameters cannot be estimated.
In the step of extracting the steel arch, the parameter equation of the three-dimensional circle is as follows:
estimating 7 three-dimensional circular model parameters by using a random sampling consistency algorithm, wherein the parameters are three-dimensional circular center coordinates (x c ,y c ,z c ) Radius r, normal vector n (n) x ,n y ,n z );
First, a vector u (u x ,u y ,u z ) Wherein u is x ,u y ,u z The components of the vector u on the coordinate axes x, y and z are respectively:
Figure BDA0002312038010000111
because of
Figure BDA0002312038010000112
Wherein T is the matrix transpose symbol;
then, a vector v=n×u orthogonal to both n and u is obtained, and the vector v is also on the plane of the circle:
Figure BDA0002312038010000113
then u and v are all converted into corresponding unit vectors
Figure BDA0002312038010000114
Figure BDA0002312038010000115
Figure BDA0002312038010000116
The parametric equation for a circle is expressed as
Figure BDA0002312038010000117
/>

Claims (4)

1. The tunnel steel arch identification method based on three-dimensional imaging is characterized by comprising the following steps of:
step one, carrying out integral scanning on the inside of a tunnel to obtain original point cloud data, and carrying out data preprocessing;
step two, correcting a point cloud coordinate system of the preprocessed data;
step three, radial filtering is carried out on the corrected data to filter out point cloud data outside the tunnel wall;
extracting feature points of the steel arch through a normal alignment radial feature key point algorithm;
fifthly, performing three-dimensional circle fitting on the extracted characteristic points to realize extraction of the steel arch and complete identification;
the fifth step comprises the following steps:
step one, inputting point cloud data and characteristic point data of only the remaining tunnel surface after the treatment in the step three;
step two, carrying out three-dimensional circular model parameter estimation on the characteristic point data by using a random sampling consistency algorithm, and deleting the characteristic points used for estimation;
thirdly, fitting the parameters estimated in the second step into a three-dimensional circular formula, substituting the three-dimensional circular formula into the point cloud data of the tunnel face, extracting and independently storing points on the circle, wherein the extracted points are steel arch points;
repeating the steps two and three with the rest data until the rest data can not meet the requirement of continuing to estimate the parameters of the three-dimensional round model;
in the second step, the point cloud coordinate system correction includes the following steps:
step 1, performing cylindrical fitting on a tunnel point cloud through a random sampling consistency algorithm to obtain the axial direction and the axis of the tunnel point cloud;
step 2, axially rotating the tunnel point cloud to be overlapped with the x-axis of the point cloud coordinate system through a rotation matrix, and overlapping the axis of the tunnel point cloud with the origin of the point cloud coordinate system through translation;
in the step 1 of correcting the point cloud coordinate system, the specific steps of carrying out cylindrical fitting on the tunnel point cloud by a random sampling consistency algorithm are as follows:
(1) Taking the tunnel point cloud data subjected to the data preprocessing in the first step as data to be detected;
(2) Establishing a cylindrical model, wherein parameters included in the establishment of the model are a cylindrical axis parameter and a cylindrical base circle radius, and the parameters form a cylindrical equation;
(3) Other custom parameters in the model are input, including minimum point number of subsets, maximum iteration times, maximum threshold value of distance from the inner point to the model and radius range of the model;
(4) The random sampling consistency algorithm achieves the goal by repeatedly selecting a group of random subsets in the data to be tested, the selected subsets are assumed to be local points, the model is evaluated by estimating the error rate of the local points and the input model after the algorithm is verified, and finally model parameters are obtained;
the step 2 of correcting the point cloud coordinate system comprises the following steps:
1) Taking the tunnel axial direction obtained after cylindrical fitting as P n (a, b, c), wherein a, b, c are each vector P n Corresponding components in x, y and z directions in a coordinate system, and the axis is P c (x 0 ,y 0 ,z 0 );
2) Will P n (a, b, c) rotating around the z-axis in the point cloud coordinate system to a plane xoz, wherein the rotation angle is-alpha, and alpha is P n The projection on the plane xoy forms an included angle with the x-axis to obtain a vector
Figure FDA0004126802270000021
The rotation matrix is: />
Figure FDA0004126802270000022
Wherein the method comprises the steps of
Figure FDA0004126802270000023
3) Will be
Figure FDA0004126802270000024
Rotated about the y-axis to the xoy plane, where the angle of rotation is beta, beta is Q n Included angle with x axis, original tunnel point cloud axial direction P after rotation n Then the rotation matrix is coincident with the x-axis:
Figure FDA0004126802270000025
wherein the method comprises the steps of
Figure FDA0004126802270000031
4) And then shift P c (x 0 ,y 0 ,z 0 ) Coinciding with the origin of the point cloud coordinate system, wherein the translation matrix is:
Figure FDA0004126802270000032
2. the method for identifying a tunnel steel arch based on three-dimensional imaging according to claim 1, wherein in the first step, the data preprocessing is to sequentially perform voxel filtering and straight-through filtering on the original point cloud data.
3. The method for identifying the tunnel steel arch based on the three-dimensional imaging according to claim 1, wherein the third step is as follows:
and taking a point on the axial direction of the tunnel as the axial center of the radial section of the tunnel, and filtering all points, which are not more than a radial threshold, in the point cloud data on the radial section of the tunnel, wherein the radial threshold is a value obtained by subtracting a preset steel arch thickness value from a radius value obtained when cylindrical fitting is carried out on the point cloud of the tunnel.
4. The tunnel steel arch identification method based on three-dimensional imaging according to claim 1, wherein in the step three of steel arch extraction, a parameter equation of a three-dimensional circle is:
estimating 7 three-dimensional circular model parameters by using a random sampling consistency algorithm, wherein the parameters are three-dimensional circular center coordinates (x c ,y c ,z c ) Radius r, normal vector n (n) x ,n y ,n z );
First, a vector u (u x ,u y ,u z ) Wherein u is x ,u y ,u z The components of the vector u on the coordinate axes x, y and z are respectively:
Figure FDA0004126802270000033
because of
Figure FDA0004126802270000034
Wherein T is the matrix transpose symbol;
then a vector v orthogonal to both n and u is obtained, and the vector v is also on the plane of the circle:
Figure FDA0004126802270000041
then u and v are all converted into corresponding unit vectors
Figure FDA0004126802270000042
Figure FDA0004126802270000043
Figure FDA0004126802270000044
The parametric equation for a circle is expressed as
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