CN111145227A - Iterative integral registration method for multi-view point cloud in underground tunnel space - Google Patents

Iterative integral registration method for multi-view point cloud in underground tunnel space Download PDF

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CN111145227A
CN111145227A CN201911304642.XA CN201911304642A CN111145227A CN 111145227 A CN111145227 A CN 111145227A CN 201911304642 A CN201911304642 A CN 201911304642A CN 111145227 A CN111145227 A CN 111145227A
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CN111145227B (en
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郭明
闫冰男
王国利
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Beijing University of Civil Engineering and Architecture
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    • G06T7/33—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
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Abstract

The invention discloses an iterative integral registration method of underground tunnel space multi-view point clouds, which is based on registration of feature points, firstly, the feature points are utilized to carry out station-by-station registration according to a Reed-Solomon matrix, initial parameters of space transformation are solved, then integral adjustment is carried out on all station clouds, a weight iteration method is selected according to a posterior square difference to endow different weights for feature constraint, and the optimal value of registration is obtained through a process of not judging weight iteration. The method adopts the target ball as the mark, and has the advantages that the point cloud is not limited by the scanning angle, and the coordinate extraction is simple and convenient. When the accumulated error of the station-by-station registration is too large, the overall adjustment calculation is influenced, local station clouds of the tunnel are regarded as a whole, the local station clouds are subjected to overall adjustment and are registered into a reference coordinate system section by section, the calculation speed is improved, and the accuracy of the registration result is high.

Description

Iterative integral registration method for multi-view point cloud in underground tunnel space
Technical Field
The invention relates to the technical field of radar measurement, in particular to an iterative integral registration method for multi-view point clouds in an underground tunnel space.
Background
The laser radar measurement technology can quickly acquire high-precision tunnel point cloud data, has the advantages of high efficiency, safety, low cost and the like, and is widely applied to the aspects of line and slope adjustment measurement, tunnel monitoring, design inspection and the like. The tunnel space is usually a large-span linear structure, scanning needs to be performed from different angles and positions, point cloud registration is an essential step for acquiring complete tunnel space data, and a registration result is also a basis for subsequent point cloud processing and analysis. The seven-parameter model is a common model for space coordinate transformation, and because the scale of point cloud is not changed, coordinate transformation can be completed only by solving 3 rotation parameters and 3 translation parameters, and domestic and foreign scholars propose various space transformation methods suitable for large angles, including algorithms such as a quaternion method, a direction cosine method, a rodlike matrix method, a singular value decomposition method and the like, wherein the rodlike matrix has a simple structure and is convenient to calculate.
The current multi-view point cloud registration method can be essentially divided into point set-based registration and geometric feature-based registration. The ICP algorithm is a classic point set-based registration method, and spatial transformation parameters of point clouds are calculated through nearest neighbor points in adjacent point clouds, and searching and iterative computation are continuously carried out until convergence conditions are met. But the ICP algorithm is low in calculation speed, high in requirement on the initial position and easy to fall into local optimization.
To address these drawbacks, the prior art also proposes a number of optimization algorithms, such as: the algorithms such as point-to-plane and point-to-project of the k-d tree are successively applied to quicken searching of the nearest point, the simplified point set is used for matching the target point set, the data volume participating in calculation is reduced, noise points are eliminated by using relevant characteristics such as the included angle and the curvature of a point cloud normal vector as conditions, and the accuracy of point pair matching is improved. The geometric feature registration is to perform rigid body transformation on the above homonymous points, lines, surfaces and other features through 3. the registration method based on the feature points is the most common method at present, and is to extract the geometric features such as normal direction, curvature and the like and image features or directly extract artificial marks in point clouds. The characteristic registration is usually used as a coarse registration process, a point cloud position initial value is obtained, and then ICP and an improved algorithm thereof are adopted for accurate registration to obtain an accurate conversion relation. For example, in the prior art, a SIFT algorithm is used for extracting feature points of a common part of two point clouds, and the feature points are purified based on a feature point method vector to complete a coarse registration process. And calculating rigid body transformation of the three-dimensional point cloud based on the azimuth image characteristics, and then further performing fine registration on the point cloud by adopting an ICP algorithm based on SVD.
The above registration methods are all limited to the registration between two viewpoint clouds, and it is considered that the registration of adjacent point clouds in sequence can cause error accumulation, even cause the model not to be closed.
In addition, the underground tunnel point cloud features are few, the feature space distribution is single, the data volume is large, and the existing commercial software is high in registration difficulty and low in precision.
Based on the above analysis, how to provide an iterative integral registration method for multi-view point clouds in an underground tunnel space is a problem to be solved urgently by practitioners of the same industry.
Disclosure of Invention
In view of the above problems, the present invention provides an iterative integral registration method for multi-view point clouds in an underground tunnel space, which solves at least some of the above technical problems, and has the advantages of high calculation speed and high registration result accuracy.
The embodiment of the invention provides an iterative integral registration method of underground tunnel space multi-view point cloud, which comprises the following steps:
s1, collecting original point cloud data of an underground tunnel space, extracting available feature points from the original point cloud data, fitting feature constraints, and selecting a base station;
s2, performing station-to-station registration according to the Rodrigue matrix by using the available feature points, and settling space transformation initial parameters;
and S3, performing integral adjustment on all station clouds, giving different weights of feature constraints according to the posterior square difference selection weight iteration method, and acquiring the optimal value of registration through the process of undetermined weight iteration.
In one embodiment, the step S2 includes:
and reading the characteristic constraints of each station, registering the cloud of each station to the base station through the Reed-Solomon matrix, gradually expanding the base station outwards, and calculating the rotation matrix of each station and the coordinate of the same-name point as initial value parameters of the overall adjustment.
In an embodiment, the step S2 specifically includes:
the rodrieger matrix is constructed from an antisymmetric matrix S of 3 independent parameters as follows:
R＝(I-S)-1(I+S)
(1)；
(1) in the formula: i represents an identity matrix, and S represents an antisymmetric matrix formed by parameters a, b and c;
Figure BDA0002322754090000031
using target centre as characteristic, listing point error equation to make calculation, and using homonymous characteristic point X in two stations0＝(x0,y0,z0) And X ═ X, y, z, the following relationship exists:
X0-(λRX+ΔX)＝0
(2)
(2) in the formula, λ is a scale parameter, λ which is a scale invariant in point cloud conversion is 1, Δ X is an offset, and a barycentric coordinate is Xm and XnOrder:
Figure BDA0002322754090000032
after the coordinates are barycenter, the coordinate transformation between the points with the same name is shown as the following formula (3):
Figure BDA0002322754090000033
and (3) linearizing the equation to obtain an error equation of the rotation parameter as the equation (4):
V＝At-L
(4)
wherein ,
Figure BDA0002322754090000034
solving the solution of the equation, i.e., the values of the rodgerge parameters, a rotation matrix is constructed as follows:
Figure BDA0002322754090000041
in one embodiment, the step S3 includes:
s31, taking the initial value parameters of the feature constraint as an error equation of an observation value column, carrying out integral adjustment, and settling space transformation parameters and unknown point adjustment values through a light beam adjustment model;
s32, checking the error of each constraint;
s33, when the error is smaller than a preset threshold value, calculating and outputting a point cloud after registration;
and S34, when the error is larger than the preset threshold, recalculating the weight of each constraint through a weight function, executing S31-S34, and continuously correcting the weight of the observed value in the iteration process until the error is smaller than the preset threshold, stopping iteration and outputting the registration point cloud.
In one embodiment, the step S31 includes:
the integral adjustment is resolved by a beam adjustment model, the result of station-by-station registration is used as an initial value, and an integral error equation is established;
characteristic point Xt0＝(xt0,yt0,zt0) And its observed value Xt＝(xt,yt,zt) There is the following relationship between:
Xt0-(λRXt+ΔX)＝0
(5)
(5) in the formula, the scale parameter λ is 1, Δ X is an offset, and an error equation is obtained after linear expansion:
V1＝A1t+BX-L1
(6)
(6) wherein, t is [ d Δ x d Δ y d Δ z d Δ a d Δ b d Δ c [ ]]TRepresenting the number of spatial transformation parameter corrections, A1Representing a matrix of transform parameter coefficients, X ═ dx0dy0dz0]TRepresenting the correction number of the undetermined point, B representing the coefficient matrix of the undetermined point, L1And (3) representing observed value residuals, wherein a matrix equation of the observed value residuals is shown as the following formula (7):
Figure BDA0002322754090000042
the abbreviation is as follows:
Figure BDA0002322754090000051
solving a law equation to obtain a space transformation parameter and a correction value of the undetermined point;
t＝(N11-N12N22 -1N21)-1(L1-N12N22 -1L2)
X＝N22 -1(L2-N21t)。
in one embodiment, in step S34, the recalculating the weight value of each constraint by a weight function includes:
selecting a weight function (8) of the weight iteration method according to the posterior variance, and re-weighting the observed value which is greater than a preset threshold value;
Figure BDA0002322754090000052
wherein, the amount of examination
Figure BDA0002322754090000053
Test quantity Fa，1，riTaking 4.13 corresponds to significant level α -0.1% and test efficacy β -80%.
The embodiment of the invention provides an iterative integral registration method of multi-view point cloud in underground tunnel space, which comprises the following steps:
the method is based on registration of feature points, and provides an iterative integral registration method for registration of tunnel point clouds. Firstly, performing station-by-station registration by using feature points according to a Rodrigue matrix, resolving a space transformation initial parameter, then performing overall adjustment on all station clouds, giving different weight values to feature constraints according to a post-test square difference selection weight iteration method, and obtaining an optimal value of registration through a process of undetermined weight iteration. The method adopts the target ball as the mark, and has the advantages that the point cloud is not limited by the scanning angle, and the coordinate extraction is simple and convenient. When the accumulated error of the station-by-station registration is too large, the overall adjustment calculation is influenced, local station clouds of the tunnel are regarded as a whole, the local station clouds are subjected to overall adjustment and are registered into a reference coordinate system section by section, the calculation speed is improved, and the accuracy of the registration result is high.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of an iterative integral registration method for a multi-view point cloud in a space of an underground tunnel according to an embodiment of the present invention;
fig. 2 is a simplified flowchart of an iterative global registration method according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating results before and after denoising of a portion of point clouds in an embodiment;
FIG. 4 is a schematic diagram of a portion of a fitted sphere center coordinate of an embodiment;
FIG. 5 is a schematic diagram of a portion of a program main interface in accordance with an exemplary embodiment;
FIG. 6 is a diagram of an example registration of a portion of a 3-station point cloud in accordance with an embodiment;
FIG. 7 is a partial registration error line graph of an exemplary embodiment;
fig. 8 is a partial registration error line graph of an exemplary embodiment.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
Referring to fig. 1-2, an iterative integral registration method for a multi-view point cloud in a subsurface tunnel space provided by an embodiment of the present invention includes:
s1, collecting original point cloud data of an underground tunnel space, extracting available feature points from the original point cloud data, fitting feature constraints, and selecting a base station;
s2, performing station-to-station registration according to the Rodrigue matrix by using the available feature points, and settling space transformation initial parameters;
and S3, performing integral adjustment on all station clouds, giving different weights of feature constraints according to the posterior square difference selection weight iteration method, and acquiring the optimal value of registration through the process of undetermined weight iteration.
In this embodiment, referring to fig. 2, the iterative global registration can be divided into three processes: and preprocessing data, resolving initial value parameters and integral adjustment. Firstly, extracting available features in the point cloud to prepare for registration. And determining a registration base station, wherein the initial value parameters are provided by local station-by-station coarse registration. Searching adjacent homonymous feature points outwards from a base station, registering each station cloud to the base station through a Reed-Solomon matrix, gradually expanding the base station outwards, and calculating a rotation matrix of each station and a homonymous point coordinate as initial value parameters of the integral adjustment. The accuracy of the station-by-station registration is getting lower and lower because the registration stations are prone to error accumulation. And taking the initial value of the characteristic constraint as an error equation of an observation value column, carrying out integral adjustment, and resolving a space transformation parameter and an unknown point adjustment value through a light beam method adjustment model. And (3) checking the error of each constraint, outputting a registration result when the error is smaller than a specified threshold, recalculating the weight of each constraint through a weight function if the error is overlarge, continuously correcting the weight of the observed value in an iteration process until the precision requirement is met, stopping iteration and outputting a registration point cloud. Compared with the prior art, the method can be used for iterating the integral registration method, the calculation speed is improved, and the registration result is high in accuracy.
In one embodiment, the initial parameters are provided by local station-by-station coarse registration, which is described as follows:
local coarse registration utilizes feature constraints between the base stations and the registration stations to perform station-to-station registration through a Reed-Solomon matrix. The coordinate transformation model is established by using 3 antisymmetric elements to replace Euler angles in the Rodrigue matrix idea, parameters are respectively solved, a scale parameter is calculated firstly, a rotation parameter is calculated secondly, a translation parameter is calculated finally, the translation parameter and the rotation parameter are separately solved by centrobaring coordinates, and the severity of the ill-conditioned state of the normal equation can be reduced. The rodrieger matrix is constructed from an antisymmetric matrix S of 3 independent parameters as follows:
R＝(I-S)-1(I+S)
(1)；
(1) in the formula: i represents an identity matrix, and S represents an antisymmetric matrix formed by parameters a, b and c;
Figure BDA0002322754090000081
the characteristic constraints can be points, lines, surfaces and the like, and the point error equation is listed for calculation by using the target sphere center as the characteristic. According to the coordinate conversion principle, three pairs of homonymous points which are not on a straight line in the space can be solved to obtain space conversion parameters. Homonymous feature point X in two stations0＝(x0,y0,z0) And X ═ X, y, z, the following relationship exists:
X0-(λRX+ΔX)＝0
(2)
(2) in the formula, λ is a scale parameter, λ which is a scale invariant in point cloud conversion is 1, Δ X is an offset, and a barycentric coordinate is Xm and XnOrder:
Figure BDA0002322754090000082
after the coordinates are barycenter, the coordinate transformation between the points with the same name is shown as the following formula (3):
Figure BDA0002322754090000083
and (3) linearizing the equation to obtain an error equation of the rotation parameter as the equation (4):
V＝At-L
(4)
wherein ,
Figure BDA0002322754090000084
solving the solution of the equation, i.e., the values of the rodgerge parameters, a rotation matrix is constructed as follows:
Figure BDA0002322754090000085
the error equation for the translation parameters is expressed as follows:
V＝ΔX-(X0-RX)。
in one embodiment, the integral adjustment is solved by a bundle adjustment model, and an integral error equation is established by taking a station-by-station registration result as an initial value;
characteristic point Xt0＝(xt0,yt0,zt0) And its observed value Xt＝(xt,yt,zt) There is the following relationship between:
Xt0-(λRXt+ΔX)＝0
(5)
(5) in the formula, the scale parameter λ is 1, Δ X is an offset, and an error equation is obtained after linear expansion:
V1＝A1t+BX-L1
(6)
(6) wherein, t is [ d Δ x d Δ y d Δ z d Δ a d Δ b d Δ c [ ]]TRepresenting the number of spatial transformation parameter corrections, A1Representing a matrix of transform parameter coefficients, X ═ dx0dy0dz0]TRepresenting the correction number of the undetermined point, B representing the coefficient matrix of the undetermined point, L1And (3) representing observed value residuals, wherein a matrix equation of the observed value residuals is shown as the following formula (7):
Figure BDA0002322754090000091
the abbreviation is as follows:
Figure BDA0002322754090000092
solving a law equation to obtain a space transformation parameter and a correction value of the undetermined point;
t＝(N11-N12N22 -1N21)-1(L1-N12N22 -1L2)
X＝N22 -1(L2-N21t)。
in one embodiment, feature constraints in the registration station can result in poor accuracy of the overall adjustment once large observation errors occur. And (3) performing gross error detection by adopting a selective weight iteration method, and reducing or eliminating the influence of gross error by iterating to gradually reduce the weight of large error constraint. The iterative integral registration algorithm continuously restricts the weighting and resolving of the observed value, and controls the error of the correction number of the observed value within a certain threshold value range until the registration is completed. The iterative process is as follows:
1) solving initial parameter values through local station-by-station coarse registration, wherein the initial values are approximate values of all constraint observation values in a base station coordinate system, and the result of the station-by-station Rodrig registration is the initial parameter values;
2) carrying out integral adjustment;
3) modifying the weight matrix, checking the error of the observed value, selecting a weight function (8) of the weight iterative method according to the posterior variance, and re-weighting the observed value exceeding the threshold value.
Figure BDA0002322754090000101
Wherein, the amount of examination
Figure BDA0002322754090000102
Test quantity Fa,1,riTest 4.13 corresponding to a significance level of α ═ 0.1%Efficacy β -80%.
4) Repeating the above two steps until the maximum correction number of the observed value is less than the threshold value, namely | | Vmax | | < sigma,
where Vmax represents all V1Is a custom parameter value representing the accuracy (e.g., the accuracy may be selected according to the requirements of a particular underground tunnel project), and the iteration is stopped.
The technical solution of the present invention is further illustrated by a specific example below:
the tunnel length is about 1300 m, and the tunnel passes through a turn with the radius of 650 m, and is total 85 station cloud data. According to the principle of iterative integral registration, a related algorithm is realized on a VS 2012 platform through a C # programming language, and the target center coordinates of all stations are read by a program for registration, so that a large amount of point clouds are prevented from participating in calculation in an experiment, the calculation speed is increased, a better registration result is obtained, and the feasibility of the method is verified.
Data preprocessing:
firstly, preprocessing data, generating noise point clouds under the influence of field environment and system factors when a three-dimensional laser scanner collects the data, and denoising the data before registering to reduce data redundancy. Fig. 3 shows the result of (b) obtained after denoising a segment of point cloud (a). During collection, target balls are distributed as characteristic marks, at least three public targets which are not on the same straight line and four public targets which are not on the same plane are arranged on two different measuring stations, target point clouds in each station are found out, target balls are fitted, and the coordinates and the marks of the centers of the balls are recorded to prepare for registration. In fig. 4, (a) represents a target sphere, (b) represents a target sphere point cloud, and (c) represents a fitted target sphere. Five to seven target balls are arranged in each station, and the coordinates of part of the target control points are shown in the following table 1.
Table 1 part station control point coordinates
Figure BDA0002322754090000111
Firstly, the coordinates of the sphere centers of the stations are read through a program, then the station-by-station registration is carried out, the registration error and the space transformation parameter are output, and finally the integral adjustment is carried out, as shown in fig. 5, the space transformation matrix, the registration error and the coordinates of the control points of each station are output after the registration. FIG. 6 is an example of registration of a 3-station point cloud, (a) representing an unregistered single-station point cloud, and (b) representing the point cloud after global adjustment.
And (3) precision analysis of a registration result:
when the sphere center coordinates of all stations are read, the error of local station-by-station coarse registration is shown as (a) in fig. 7, the error of the coarse registration of the front part stations is small, but the error accumulation is obvious from the 45 th station, and the maximum error reaches 6.4 meters. The coarse registration error of the rear part of the measuring station is overlarge, and the integral adjustment result is not converged, so that the calculation is divided into a front part and a rear part. The cloud of the first 44 stations directly carries out integral adjustment, and the adjustment result is shown in (b) in fig. 7, so that the error of each station is effectively reduced. And (3) performing integral adjustment on the point cloud after the 44 th station, so that the cloud of the rear partial points is segmented and calculated, the tunnel is of a linear structure, the two segments are segmented according to the station serial number, the two segments are connected through one station of overlapped point cloud, the overlapped station is selected as a temporary base station, the coarse registration error of each segment is controlled to be in centimeter level, and the station-by-station registration error is shown in (c) of fig. 7. And then, carrying out integral adjustment on the local small-segment point clouds to obtain the optimal solution for registration of each segment of point cloud, registering the subsequent segment of point cloud into the previous segment of point cloud segment by segment according to the serial number of the survey station, and then converting the subsequent segment of point cloud into a base station coordinate system, wherein the registration error is shown in (d) of fig. 7. In fig. 7, the abscissa represents the station ID, the ordinate represents the registration error, the broken line represents the variation trend of the error, and the dots represent the registration error corresponding to each station point cloud.
Through the integral adjustment, the error of each measuring station is controlled to be less than 7mm, and the registration result is shown in figure 8. Fig. 8 (a) shows a tunnel entire point cloud. In order to detect the registration quality, section data of different positions are intercepted from the point cloud, and whether the registration is layered or not is checked. In fig. 8, (b) is the section of a rectangular tunnel, and (c) is the section of a circular tunnel, the registration result is not layered, the registration quality is good, and the accuracy of the method and the practicability in the tunnel point cloud registration are verified.
Aiming at the registration problem of tunnel point cloud, the embodiment of the invention provides an iterative integral registration method, registration is carried out through characteristic points without traversing the point cloud, approximate values constrained in a base station coordinate system are provided by station-by-station Rodrigue registration, then integral adjustment is carried out on all observation values, the observation values with larger errors are reweighed by a post-test square difference option iterative method, and iterative adjustment is carried out for multiple times until parameter correction number meets the requirement of a threshold value, the algorithm is simple, the calculation time is short, and the related algorithm is realized based on a VS 2013 platform and a C # programming language.
The experiment takes the tunnel point cloud with the length of about 1300 meters as a research object, the registration error is controlled to be below 7mm, the feasibility of the algorithm is verified, a new thought and method are provided for the registration of the underground space multi-view point cloud, and the method has practical application value. However, due to the spatial limitation of the tunnel, a large number of control points are distributed in a narrow and long space, the spatial distribution is single, whether a plurality of control points are collinear or coplanar cannot be guaranteed, the spatial distribution condition of the control points should be detected, the collinear or coplanar control points are screened out, the matrix calculation divergence during the integral adjustment is prevented, and the integral registration model is further optimized.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (6)

1. An iterative integral registration method for multi-view point clouds in an underground tunnel space is characterized by comprising the following steps:
s1, collecting original point cloud data of an underground tunnel space, extracting available feature points from the original point cloud data, fitting feature constraints, and selecting a base station;
s2, performing station-to-station registration according to the Rodrigue matrix by using the available feature points, and settling space transformation initial parameters;
and S3, performing integral adjustment on all station clouds, giving different weights of feature constraints according to the posterior square difference selection weight iteration method, and acquiring the optimal value of registration through the process of undetermined weight iteration.
2. The iterative global registration method for the multi-view point cloud in the space of the underground tunnel as claimed in claim 1, wherein the step S2 comprises:
and reading the characteristic constraints of each station, registering the cloud of each station to the base station through the Reed-Solomon matrix, gradually expanding the base station outwards, and calculating the rotation matrix of each station and the coordinate of the same-name point as initial value parameters of the overall adjustment.
3. The iterative global registration method for the underground tunnel space multi-view point cloud as claimed in claim 2, wherein the step S2 specifically includes:
the rodrieger matrix is constructed from an antisymmetric matrix S of 3 independent parameters as follows:
R＝(I-S)-1(I+S)
(1)；
(1) in the formula: i represents an identity matrix, and S represents an antisymmetric matrix formed by parameters a, b and c;
Figure FDA0002322754080000011
using target centre as characteristic, listing point error equation to make calculation, and using homonymous characteristic point X in two stations0＝(x0,y0,z0) And X ═ X, y, z, the following relationship exists:
X0-(λRX+ΔX)＝0
(2)
(2) in the formula, λ is a scale parameter, λ which is a scale invariant in point cloud conversion is 1, Δ X is an offset, and a barycentric coordinate is Xm and XnOrder:
Figure FDA0002322754080000021
after the coordinates are barycenter, the coordinate transformation between the points with the same name is shown as the following formula (3):
Figure FDA0002322754080000022
and (3) linearizing the equation to obtain an error equation of the rotation parameter as the equation (4):
V＝At-L
(4)
wherein ,
Figure FDA0002322754080000023
solving the solution of the equation, i.e., the values of the rodgerge parameters, a rotation matrix is constructed as follows:
Figure FDA0002322754080000024
4. the iterative global registration method for the multi-view point cloud in the space of the underground tunnel as claimed in claim 2, wherein the step S3 comprises:
s31, taking the initial value parameters of the feature constraint as an error equation of an observation value column, carrying out integral adjustment, and settling space transformation parameters and unknown point adjustment values through a light beam adjustment model;
s32, checking the error of each constraint;
s33, when the error is smaller than a preset threshold value, calculating and outputting a point cloud after registration;
and S34, when the error is larger than the preset threshold, recalculating the weight of each constraint through a weight function, executing S31-S34, and continuously correcting the weight of the observed value in the iteration process until the error is smaller than the preset threshold, stopping iteration and outputting the registration point cloud.
5. The iterative global registration method for the multi-view point cloud of the underground tunnel space as claimed in claim 4, wherein the step S31 comprises:
the integral adjustment is resolved by a beam adjustment model, the result of station-by-station registration is used as an initial value, and an integral error equation is established;
characteristic point Xt0＝(xt0,yt0,zt0) And its observed value Xt＝(xt,yt,zt) There is the following relationship between:
Xt0-(λRXt+ΔX)＝0
(5)
(5) in the formula, the scale parameter λ is 1, Δ X is an offset, and an error equation is obtained after linear expansion:
V1＝A1t+BX-L1
(6)
(6) wherein, t is [ d Δ x d Δ y d Δ z d Δ a d Δ b d Δ c [ ]]TRepresenting the number of spatial transformation parameter corrections, A1Representing a matrix of transform parameter coefficients, X ═ dx0dy0dz0]TRepresenting the correction number of the undetermined point, B representing the coefficient matrix of the undetermined point, L1And (3) representing observed value residuals, wherein a matrix equation of the observed value residuals is shown as the following formula (7):
Figure FDA0002322754080000031
the abbreviation is as follows:
Figure FDA0002322754080000032
solving a law equation to obtain a space transformation parameter and a correction value of the undetermined point;
t＝(N11-N12N22 -1N21)-1(L1-N12N22 -1L2)
X＝N22 -1(L2-N21t)。
6. the iterative global registration method for the multi-view point cloud in the underground tunnel space of claim 4, wherein the step S34 of recalculating the weight of each constraint by a weight function includes:
selecting a weight function (8) of the weight iteration method according to the posterior variance, and re-weighting the observed value which is greater than a preset threshold value;
Figure FDA0002322754080000041
wherein, the amount of examination
Figure FDA0002322754080000042
Test quantity Fa,1,riTaking 4.13 corresponds to significant level α -0.1% and test efficacy β -80%.
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