CN104392476B - The method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm - Google Patents
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Abstract
The invention discloses a kind of method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm, this method extracts the point cloud slicing of Lining Ring by the tunnel minimum bounding box algorithm of varied angle step-length, then the point cloud slicing of extraction is solved into centre coordinate by oval or circle models fitting, method again through horizontal curve Second Order Continuous and vertical curve Second Order Continuous is smoothed to tunnel axis, finally obtains the three-dimensional axis in high-precision tunnel.It is an advantage of the invention that automatically extracting the three-dimensional axis of single targe structure using 3 D laser scanning original point cloud data and based on minimum bounding box algorithm, precision is high, and speed is fast, is available for tunnel axis detection, diameter convergence extraction, generation orthography etc. to use；In addition, the drawbacks of traditional treatment method needs to pre-enter Tunnel Design axis or actual measurement axis can be avoided, so as to greatly improve the automaticity of data processing.
Description
Technical field
The invention belongs to Tunnel Engineering field of measuring technique, and in particular to one kind extracts tunnel based on minimum bounding box algorithm
The method of three-dimensional axis.
Background technology
The axis in tunnel is an imaginary line parallel with its bearing of trend at tunnel internal space center position,
The spatial attitude and tendency in tunnel are reflected, is the premise that tunnel profile is extracted.
Using total station survey shield tunnel three-dimensional axis when, conventional method is typically real at regular intervals using total powerstation
The multiple characteristic points of Lining Ring piece section are surveyed, tunnel axis is used as to justify model of fit solution ring plate centre coordinate.During actual job,
Need manually to carry out measuring point aiming observation, measured profile limited amount at the scene.When measurement is repeated several times in this method, because Lining Ring is special
The arbitrariness of point coordinates collection is levied, Measurement results are easily influenceed by human factor.
The method for extracting tunnel axis using laser scanning data includes：Curve-fitting method, for scattered point set
Curve matching can use least square method (generalized least squares, GLS), Moving Least
(Moving Least-Squares, MLS), stochastical sampling consistency algorithm (Random Sample Consensus,
RANSAC), spline surface fitting process etc..The axis approximating method based on MLS has been discussed in detail in In-Kwon Lee；Toure leads to
Cross RANSAC algorithms and GLS algorithms complete the extraction of tunnel axis.In addition, Soohee Han are by the way that tunnel cloud data is thrown
Shadow obtains the axis in tunnel on two dimensional surface, recycling the framework extraction method of computer vision field.Above-mentioned algorithm is not
Consider that tunnel undercutting becomes (sedimentation) or the caused tunnel three-dimensional axis of splicing is reversed, therefore have one for the diameter for extracting tunnel
Fixed influence.
The content of the invention
According to the deficiencies of the prior art described above, It is an object of the present invention to provide one kind is carried based on minimum bounding box algorithm
The method for taking tunnel three-dimensional axis, this method extracts the point cloud of Lining Ring using the tunnel minimum bounding box algorithm of varied angle step-length
Section, so as to obtain the three-dimensional axis in high-precision tunnel.
The object of the invention is realized and completed by following technical scheme：
A kind of method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm, it is characterised in that methods described is included such as
Lower step：
(1) tunnel point cloud is obtained by single station 3 D laser scanning, by described tunnel point cloud with initial angle step-length α1
=(2k)jΔ α carries out 0 °~360 ° of rotation around vertical direction axle, wherein, k=1,2,3 ..., j are iterations, round numbers,
△ α are the minimum anglec of rotation of fixed step size；Bounding box is generated according to the coordinate range of each postrotational tunnel point cloud
AABB, and calculate its corresponding volume Vi, the volume V of minimum is therefrom found out afterwardsmin；The tunnel point cloud is recorded from initial bit
The angle [alpha] rotated when at bounding box AABB position of minimum volume around vertical direction axle is put, and according to bounding box AABB long side
The axis direction in tunnel described in direction discernment；
(2) (in the angular range of-α/2, α/2), with angle step α=(2k)j-1Δ α repeat steps (1), to update
VminWith α value；
(3) repeat step (2), reduction angle step is α=(2k)j-2Δ α, until reducing angle step to α=(2k
)j-nΔ α, wherein n=j, calculate now the tunnel point cloud from initial position to bounding box AABB position of minimum volume at when
The final angle α rotated through around vertical direction axle, minimum bounding box AABB when obtaining the tunnel point cloud at the position；
(4) the minimum bounding box AABB based on the tunnel point cloud generates the point cloud slicing of some tunnel-liner rings；
(5) some point cloud slicings extracted in step (4) are carried out with overall oval or circle respectively to be fitted, and asked respectively
Solution obtains described oval or circle three-dimensional centre coordinate, and each three-dimensional centre coordinate is linked in sequence as space curve by mileage
And smoothing processing is done, to constitute the axis in the tunnel.
It is the step of the generation point cloud slicing in the step (4)：The tunnel point cloud of single station 3 D laser scanning
Original point set be P={ P1,P2,...,Pn, Pi={ xi,yi,zi}∈R3(i=1,2 ..., m), point set P coordinate range is
(xmin,ymin,zmin)~(xmax,ymax,zmax), wherein n is the segmentation hop count of the tunnel point cloud, and m is each section of tunnel point
Points in cloud；Planar set T is expressed as Y=(Y1,Y2,····,Yn), its method arrow points to the tunnel axis direction, wherein
Y1=ymin, Yn=ymax, Yi=Y1+ i* ε (i=1,2 ..., n-1)；The centre position for defining each section of tunnel point cloud afterwards is
The reference projection face of correspondence section, the reference projection face can pass through(i=1,2 ..., n-1) is calculated, its
Middle ε is the thickness of each section of tunnel point cloud；By the projection of all spot projections in each section of tunnel point cloud to this section
The plane of reference, to generate the point cloud slicing of each section of tunnel point cloud.
The method that the smoothing processing is utilized is horizontal curve Second Order Continuous and vertical curve Second Order Continuous computational methods.
It is an advantage of the invention that being carried automatically using 3 D laser scanning original point cloud data and based on minimum bounding box algorithm
The three-dimensional axis of single targe structure is taken, precision is high, and speed is fast, be available for tunnel axis detection, diameter convergence extraction, generation orthography
Etc. using；In addition, the drawbacks of traditional treatment method needs to pre-enter Tunnel Design axis or actual measurement axis can be avoided, so that greatly
The big automaticity for improving data processing.
Brief description of the drawings
Fig. 1 is the method flow diagram in the present invention；
Fig. 2 is tunnel minimum bounding box schematic diagram in the present invention；
Fig. 3 is the point cloud slicing schematic diagram of extraction Lining Ring in the present invention；
The schematic diagram that Fig. 4 is smoothed for tunnel axis in the present invention；
Fig. 5 for tunnel axis in the present invention about the z axis different rotation angle when fitting major axis and short axle changing trend diagram；
Fig. 6 for tunnel axis in the present invention around horizontal plane different rotation angle when fitting major axis and short axle variation tendency
Figure.
Embodiment
The feature and other correlated characteristics of the present invention are described in further detail by embodiment below in conjunction with accompanying drawing, with
It is easy to the understanding of technical staff of the same trade：
Mark 1-2 is respectively in such as Fig. 1-6, figure：Tunnel 1, minimum bounding box 2.
Embodiment：As shown in figure 1, the present embodiment, which is specifically related to a kind of minimum bounding box algorithm that is based on, extracts tunnel three-dimensional shaft
The method of line, this method utilizes 3 D laser scanning tunnel cloud data, is surrounded by a kind of tunnel minimum of varied angle step-length
Box algorithm extracts the point cloud slicing of Lining Ring, and then the point cloud slicing of extraction is solved center and sat by circle (or oval) models fitting
Mark, then the method through horizontal curve Second Order Continuous and vertical curve Second Order Continuous are smoothed to tunnel axis, final to obtain high
The tunnel three-dimensional axis of precision.The arbitrariness of traditional work method human factor can be avoided, contributes to unified tunnel three-dimensional axis
Detection method and precision.
As shown in figure 3, X-Y-Z coordinate systems in the present embodiment, its X-direction is tunnel radial direction, Y direction is tunnel
Axially, Z-direction is perpendicular to X-Y plane.
As Figure 1-4, the specific steps of tunnel three-dimensional axis are extracted such as based on minimum bounding box algorithm in this implementation
Under：
【Step one】Set up tunnel minimum bounding box
(I) obtains one section of tunnel point cloud by single station 3 D laser scanning, by this section of tunnel point cloud of acquisition with initial angle
Spend step-length α1=(2k)jΔ α carries out 0 °~360 ° of rotation, the tunnel point cloud that wherein K is obtained with 3 D laser scanning about the z axis
Density is relevant, and point cloud density is bigger, and K values are bigger, and it is iterations that K, which takes 2, j, in the present embodiment, and j=4, △ α are taken in the present embodiment
For the minimum anglec of rotation of fixed step size, therefore initial angle step-length is α1=4j·Δα；According to each postrotational tunnel point
The coordinate range of cloud generates corresponding bounding box AABB (Axis-Aligned Bounding Boxes), and calculates corresponding bag
Enclose box AABB volumes Vi, the volume V of minimum is found out from each bounding box AABB afterwardsmin；Record tunnel point cloud from initial position to
The angle [alpha] rotated about the z axis when at bounding box AABB position of minimum volume, and tunnel is recognized according to bounding box AABB long side direction
1 axis direction；
(II) is (in the angular range of-α/2, α/2), with angle step α2=4j-1Δ α repeat steps (I), to update
VminWith α value, i.e.,：(in the angular range of-α/2, α/2), with angle step α2=4j-1Δ α rotates about the z axis, according to each
The coordinate range of postrotational tunnel point cloud generates corresponding bounding box AABB, and calculates corresponding bounding box AABB volumes Vi,
The volume V of minimum is found out from each bounding box AABB afterwardsmin；And record tunnel point cloud from initial position to bounding box AABB most
The angle [alpha] rotated about the z axis when at small size position；
(III) repeat step (II), reduction angle step is α=4j-2Δ α, until reducing angle step to α=4j-4·
Δ α, calculate now tunnel point cloud from initial position to bounding box AABB position of minimum volume at when the final angle that rotates through about the z axis
α is spent, the minimum bounding box 2 when obtaining tunnel point cloud at the position, as shown in Figure 2；
Minimum bounding box algorithm in this step first passes through larger angle step-length and carries out " coarse search ", then again by smaller
Angle step carries out " essence search ", can effectively improve efficiency of algorithm；After calculating obtains minimum bounding box, it can guarantee that and extracted
Point cloud slicing be each perpendicular to tunnel three-dimensional axis, three-dimensional axis can be independently built from point cloud slicing.
【Step 2】Point cloud slicing is generated
The original point set of the tunnel point cloud of single station 3 D laser scanning is P={ P1,P2,...,Pn, Pi={ xi,yi,zi}
∈R3(i=1,2 ..., m), point set P coordinate range is (xmin,ymin,zmin)~(xmax,ymax,zmax), wherein n is tunnel
The segmentation hop count of point cloud, m is the points in each section of tunnel point cloud；
As shown in figure 3, make planar set T for one perpendicular to tunnel direction parallel plane, planar set T method arrow point to tunnel
Axis (mileage) direction, then planar set T can be expressed as Y=(Y1,Y2,····,Yn), wherein Y1=ymin, Yn=ymax, Yi
=Y1+ i* ε (i=1,2 ..., n-1)；The centre position for defining each section of tunnel point cloud afterwards is the reference projection face of correspondence section, is thrown
The shadow plane of reference can pass through(i=1,2 ..., n-1) is calculated, and wherein ε is the thickness of each section of tunnel point cloud；Will
The reference projection face in all spot projections to correspondent section in each section of tunnel point cloud, is cut with the point cloud for generating each section of tunnel point cloud
Piece.
【Step 3】Solution point cloud centre of slice
Carry out overall oval (or circle) fitting respectively to each point cloud slicing extracted in step 2, solve obtain ellipse respectively
The three-dimensional centre coordinate of (or circle), and using central point O as tunnel axis on point.
【Step 4】Tunnel axis carries out smooth
The each point cloud centre of slice point O extracted in step 3 is linked in sequence as space curve by mileage, respectively by flat
The method of curve Second Order Continuous and vertical curve Second Order Continuous is smoothed to tunnel axis, the effect before and after tunnel axis is smooth
Fruit is as shown in Figure 4.
In order to verify the precision of the tunnel three-dimensional axis extracted in the present embodiment based on minimum bounding box algorithm, carry out with
Lower comparative analysis：
For judge section whether the actual axis of Vertical tunnel, by the axis of extraction in the range of -3 ° to+3 ° press 0.2 °
Angle step continuously rotated about the z axis with horizontal plane respectively, often rotate 0.2 ° of extraction, one section, and section point cloud entered
Row ellipse fitting, solves the major axis and short axle of ellipse, and records the angle accordingly rotated.In theory, when axis is revolved about the z axis
Turn, only major axis changes, when axis rotates and (rotated around X-axis or Z axis) around horizontal plane, only short axle changes.
But it is due to that data are unstable, is not exclusively in addition standard ellipse after the deformation of tunnel actual profile, is rotated about the z axis with horizontal plane
When, all there are small variations in short axle and major axis, as shown in Figure 5,6.
Wherein, Fig. 5 be axis about the z axis different rotation angle when fitting major axis and short axle changing trend diagram, Cong Zhongke
Find out, when axis rotates about the z axis, transverse change is more apparent, when axis rotates 0.2 °, transverse is minimum,
Illustrate that the axis extracted only differs 0.2 ° or so in the horizontal plane with actual axis.
Fig. 6 be axis around horizontal plane different rotation angle when fitting major axis and short axle changing trend diagram, can from figure
Find out, when axis rotates around horizontal plane, short axle is changed greatly, in axis rotation 0 ° (not rotating), transverse
Minimum, the axis that this explanation is extracted coincide substantially with actual axis on vertical plane.
It is the analysis result of single group section above, in order to more fully analyze shadow of the axis detection deviation to generation section
Ring.The present embodiment also have chosen 691 groups of other sections, during every group of section asks its minimum major axis and minimum short axle and its be corresponding
The axis anglec of rotation.Rotated about the z axis so as to analyze axis, the variation tendency of major axis；Axis rotates around horizontal plane, short axle
Variation tendency.Following table is the transverse extracted when the minimum major axis of 691 sections and minimum short axle do not rotate with axis respectively
With the statistical form of the difference of short axle.
It was found from from upper table, there is the major axis fitness bias of 92.6% section within 5mm, the short axle of 85.8% section
Fitness bias is within 5mm.Due to accidental error, the deviation for having a small number of sections is more than 10mm.Thus institute in the present embodiment is illustrated
The axis of extraction coincide substantially with actual axis, and precision is higher.
Claims (3)
1. a kind of method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm, it is characterised in that methods described includes as follows
Step：
(1) tunnel point cloud is obtained by single station 3 D laser scanning, by described tunnel point cloud with initial angle step-length α1=(2k
)jΔ α carries out 0 °~360 ° of rotation around vertical direction axle, wherein, k=1,2,3 ..., j are iterations, round numbers, △ α
For the minimum anglec of rotation of fixed step size；Bounding box is generated according to the coordinate range of each postrotational tunnel point cloud
AABB, and calculate its corresponding volume Vi, the volume V of minimum is therefrom found out afterwardsmin；The tunnel point cloud is recorded from initial bit
The angle [alpha] rotated when at bounding box AABB position of minimum volume around vertical direction axle is put, and according to bounding box AABB long side
The axis direction in tunnel described in direction discernment；
(2) (in the angular range of-α/2, α/2), with angle step α=(2k)j-1Δ α repeat steps (1), to update VminAnd α
Value；
(3) repeat step (2), reduction angle step is α=(2k)j-2Δ α, until reducing angle step to α=(2k)j-n·
Δ α, wherein n=j, calculate now the tunnel point cloud from initial position to bounding box AABB position of minimum volume at when around vertical
The final angle α that axis of orientation is rotated through, minimum bounding box AABB when obtaining the tunnel point cloud at the position；
(4) the minimum bounding box AABB based on the tunnel point cloud generates the point cloud slicing of some tunnel-liner rings；
(5) some point cloud slicings extracted in step (4) are carried out with overall oval or circle respectively to be fitted, and solved respectively
To described oval or circle three-dimensional centre coordinate, each three-dimensional centre coordinate is linked in sequence as space curve and done by mileage
Smoothing processing, to constitute the axis in the tunnel；
(6) axis for calculating acquisition is continuously revolved about the z axis in the range of -3 ° to+3 ° by 0.2 ° of angle step
Turn, choose a section perpendicular with the axis, often rotate 0.2 ° and extract the once section, on each section
Point cloud carry out ellipse fitting, and solve each oval major axis and short axle；Described on each anglec of rotation correspondence section
Transverse value is compared with the transverse value on 0 ° of section, and the residing anglec of rotation is when choosing difference minimum
The axis and the error angle of actual axis in the horizontal plane.
2. a kind of method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm according to claim 1, its feature
Be that the step (4) is middle is the step of generating the point cloud slicing：The original of the tunnel point cloud of single station 3 D laser scanning
Initial point integrates as P={ P1,P2,...,Pn, Pi={ xi,yi,zi}∈R3(i=1,2 ..., m), point set P coordinate range is
(xmin,ymin,zmin)~(xmax,ymax,zmax), wherein n is the segmentation hop count of the tunnel point cloud, and m is each section of tunnel point
Points in cloud；Planar set T is expressed as Y=(Y1,Y2,····,Yn), its method arrow points to the tunnel axis direction, wherein
Y1=ymin, Yn=ymax, Yi=Y1+ i* ε (i=1,2 ..., n-1)；The centre position for defining each section of tunnel point cloud afterwards is
The reference projection face of correspondence section, the reference projection face can pass throughCalculate, its
Middle ε is the thickness of each section of tunnel point cloud；By the projection of all spot projections in each section of tunnel point cloud to this section
The plane of reference, to generate the point cloud slicing of each section of tunnel point cloud.
3. a kind of method that tunnel three-dimensional axis is extracted based on minimum bounding box algorithm according to claim 1, its feature
It is that the method that the smoothing processing is utilized is horizontal curve Second Order Continuous and vertical curve Second Order Continuous computational methods.
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