CN102609940A - Method for processing errors generated by point cloud registration in process of surface reconstruction of measuring object by using ground laser scanning technique - Google Patents

Abstract

The invention discloses a point cloud registration error processing method, namely, a method for processing errors generated by point cloud registration in the process of surface reconstruction of an object by using a ground laser scanning technique. The method comprises the following steps: carrying out image matching according to a photogrammetric image matching principle, and determining a mathematical model of error propagation of multistation point cloud registrations; obtaining a coefficient matrix according to error equations; calculating the variance of six parameters, the variance of model points and the variance of unit weight in a rotation matrix; according to a co-factor matrix of the six parameters, obtaining an observed-value co-factor matrix and a variance matrix of estimated observed values, and obtaining a diagonal variance matrix consisting of the six parameters and the model points; according to a law of covariance propagation and a coefficient matrix of error equations, obtaining error propagation models of point cloud registrations under two different scanning coordinate systems; and determining the number of sequential registrations, calculating a parameter error equation coefficient matrix of each registration, and multiplying the coefficient matrixes by a variance obtained after the previous registration is completed, so that an error propagation model of multistation registrations can be obtained.

Description

Utilize the territorial laser scanning technology to carry out measuring object resurfacing time point cloud registration error disposal route

Technical field

The present invention relates to Surveying Science and Technology, reverse-engineering, ancient architecture numerical protection field, when being specifically related to utilize the territorial laser scanning technology to carry out the subject surface reconstruction, to a cloud registration error disposal route.

Background technology

At present, the ground three-dimensional laser scanning technique is day by day ripe, and the ground three-dimensional laser scanner (its application and scope are along with going up deeply and both in depth and in breadth of research developed for terrestrial laser scanner, TLS) also commercialization gradually.Its value that all has a wide range of applications in scientific and engineering fields such as digital historical relic and historical building, digital museum, digital archaeology, topographic(al) reconnaissance, virtual reality, digital city, city planning, digital entertainment, the making of video display stunt, reverse-engineerings.The ground three-dimensional laser scanning technique is as a brand-new measuring technique; Its measurement result also must satisfy the concrete accuracy requirement of special engineering; If measurement result can not satisfy the accuracy requirement of concrete engineering, the surveying work that is carried out so is invalid, also is incredible.This just requires TLS is carried out accuracy assessment, theory of errors and the error propagation Study of model of accuracy of instrument evaluation, measurement achievement].Up to the present, both at home and abroad the achievement accuracy assessment is proofreaied and correct and measured in the check of ground laser 3 d scanner device, also form ripe, method in common and appraisement system, comprise that a research of cloud registration error all also is among the exploration.

The purpose of some cloud registration is to arrive the some cloud coordinate conversion under the different coordinates under the unified coordinate system.In photogrammetric, the method for coupling is to find the same place of adjacent image in picture side, is mapped to space side again, calculates the space similarity transformation parameter of adjacent model, splices with this.Carry out a cloud registration in this way, need to guarantee to have the enough good public target point cloud coordinate of precision.But because the accuracy limitations of ground spatial digitizer own; If the difference of station location; Personnel operation instrument improper; The various influences of external environment, the factors such as error that the power of public target target center reflectivity, the material of target and stickup, target center extract bring influence all can for the accuracy of the target target center coordinate of gathering.The same place that application contains error must bring error to the result of registration to carrying out a cloud registration.Object of multistation scanning need carry out multi-site cloud registration.For the first time there has been error in the some cloud behind the registration in twos, carries out registration next time again, and can causing next time, registration produces bigger error.

Therefore, there is error in some cloud registration, and the multistation registration must cause propagation of error.The accumulation of this error can make the error in point measurement at model end points place bigger, brings error even mistake for point accurate registration of cloud and even follow-up three-dimensional modeling.This carries out deep research with regard to pressing for the rule that a cloud matching error is propagated, and provides the quantitative relationship of a cloud registration accuracy and point cloud model cumulative errors, thereby a precision of cloud registration is made assessment.

Summary of the invention

The object of the invention is to be difficult to confirm and an assessment difficult problem to the error that some cloud registration exists, proposes a kind of principle based on photogrammetric image coupling, the method that the rule of utilizing least square method that a cloud matching error is propagated is handled.

Technical scheme of the present invention is following:

A kind of territorial laser scanning technology of utilizing is carried out measuring object resurfacing time point cloud registration error disposal route, and it is characterized in that: it specifically may further comprise the steps:

(1), utilize the least square adjustment method to resolve 6 space similarity transformation parameters

ω, κ, Δ X, Δ Y, Δ Z; I.e. three angle rotation parameters:

ω, κ and three translation parameterss: Δ X, Δ Y, Δ Z, and confirm that the mathematical model that some cloud registration error propagates is following:

Wherein, (X, Y is Z) with (x, y z) are respectively same coordinate under different scanner coordinate systems, and R is a rotation matrix;

(2), formula (1) is utilized Taylor series expansion, get once, then have

Wherein:

Can obtain error equation thus:

Make that K is V in the formula (2) ^(k)Factor arrays, L=F-F ₀, then have

According to registration principle and formula (1), (2), can get the error equation of n same place under two scan coordinate system:

Make

then formula (4) can be expressed as:

V ^k＝KX _d-L (5)

(3), order

For

ω, κ, Δ X, Δ Y, the registration variance of the variance of Δ Z and target central point x, y, z according to the indirect adjustment principle, makes 6 space similarity transformation parameters

ω, κ, Δ X, Δ Y, the weight matrix of Δ Z are P,

The variance of target central point x, V, z does

X so _dCorresponding variance does

At V ^TPV is for obtaining separating of unknown number under the minimum condition, and P is a unit matrix here, and V is the correction of finding the solution 6 space similarity transformation parameter estimator values, and B is the coefficient of finding the solution the error equation of 6 space similarity transformation parameters foundation, then has:

X＝(B ^TB) ^-1B ^TL (6)

Can know that according to the measurement adjustment principle variance of unit weight

is:

${\mathrm{\σ}}_0^2=\frac{V^T\mathrm{PV}}{3n-6}---\left(7\right)$

In the formula (1), n is the same place logarithm;

(4), making association's factor of 6 space similarity transformation parameters in the indirect adjustment is Q _Xx, Q then _Xx=(B ^TB) ^-1Use association's factor and propagate law, the variance of 6 space similarity transformation parameters can be found the solution by following formula:

$\mathrm{Dx}={\mathrm{\σ}}_0^2{Q}_{\mathrm{xx}}---\left(8\right)$

Association's factor battle array of target central point scan values is:

$Q_{\hat{X}\hat{X}}=Q-B{Q}_{\mathrm{XX}}{B}^T---\left(9\right)$

In the formula (9), Q is a unit matrix,

The variance that (5), can get the estimated value of target central point scan values by formula (8) is:

$D={\mathrm{\σ}}_0^2{Q}_{\hat{X}\hat{X}}={\mathrm{\σ}}_0^2-B{D}_X{B}^T---\left(10\right)$

Therefore, X _dThe diagonal angle square formation of the variance of 9 parameters formation 9*9 is D among the corresponding variance Dn _N, order

$D_M={\left[\begin{array}{ccccccc}{\mathrm{\σ}}_X^2& & & & & & \\ & {\mathrm{\σ}}_Y^2& & & & & \\ & & {\mathrm{\σ}}_Z^2& & & & \\ & & & O& & & \\ & & & & {\mathrm{\σ}}_{\mathrm{Xn}}^2& & \\ & & & & & {\mathrm{\σ}}_{\mathrm{Yn}}^2& \\ & & & & & & {\mathrm{\σ}}_{\mathrm{Zn}}^2\end{array}\right]}_{3n\×3n}.$

(6), propagate law, can get by formula (4) according to covariance:

D _M＝KD _NK ^T (11)

Formula (11) is exactly the error propagation model of following some cloud registration of two different scanning coordinate systems, can resolve the error in point measurement behind the registration thus, as an index of weighing some position registration quality;

(7), for the multistation registration; Confirm the number of times of registration successively; Calculate each registration parameter error equation factor arrays; The error propagation model that again variance behind these error equation factor arrays and the preceding registration is multiplied each other and can draw the multistation registration, be about to positional accuracy behind the registration each time will given value substitution propagation model as registration next time in; Concrete computing method are following:

The propagation model of multistation registration error is:

$D_n=K_n\mathrm{\Λ}{K}_1\left(K_0{D}_0{K}_0^T\right)K_1^T\mathrm{\Λ}{K}_n^T---\left(12\right)$

K wherein _i(i=0,1,2 ..., n) be the determined matrix of registration parameter that obtains of registration each time, but through type (3) is found the solution;

Be the positional accuracy behind the first time registration, after this positional accuracy behind the registration each time In will given value substitution propagation model as registration next time.

Beneficial effect of the present invention:

The present invention has not only provided the rule that some cloud matching error is propagated, and has confirmed the quantitative relationship of some cloud registration accuracy and point cloud model cumulative errors; Can also resolve the error in point measurement behind the registration,, thereby a precision of cloud registration made assessment as an index of weighing some position registration quality.

Description of drawings

Fig. 1 puts cloud registration error research experiment step for the present invention.

Fig. 2 is a fixed target target point cloud chart of the present invention.

Fig. 3 is the point cloud chart of moving target mark of the present invention.

Fig. 4 is the software design process flow diagram that calculates based on Matlab point cloud registration error propagation model.

Fig. 5 is the scanner distribution schematic diagram of certain buildings of scanning.

Fig. 6 (A), (B), (C), (D) be that each scanner collects among Fig. 5 the building sides point cloud chart.

Fig. 7 is the whole point cloud chart of the buildings among Fig. 5.

Embodiment

A kind of territorial laser scanning technology of utilizing is carried out measuring object resurfacing time point cloud registration error disposal route, specifically may further comprise the steps:

(1), utilize the least square adjustment method to resolve 6 space similarity transformation parameters

ω, κ, Δ X, Δ Y, Δ Z; I.e. three angle rotation parameters:

ω, κ and three translation parameterss: Δ X, Δ Y, Δ Z, and confirm that the mathematical model that some cloud registration error propagates is following:

Wherein, (X, Y is Z) with (x, y z) are respectively same coordinate under different scanner coordinate systems, and R is a rotation matrix;

(2), formula (1) is utilized Taylor series expansion, get once, then have

Wherein:

Can obtain error equation thus:

Make that K is V in the formula (2) ^(k)Factor arrays, L=F-F ₀, then have

According to registration principle and formula (1), (2), can get the error equation of n same place under two scan coordinate system:

Make

then formula (4) can be expressed as:

V ^k＝KX _d-L (5)

(3), order For ω, κ, Δ X, Δ Y, the registration variance of the variance of Δ Z and target central point x, y, z according to the indirect adjustment principle, makes 6 space similarity transformation parameters

ω, κ, Δ X, Δ Y, the weight matrix of Δ Z are P,

The variance of target central point x, y, z does

X so _dCorresponding variance does

At V ^TPV is for obtaining separating of unknown number under the minimum condition, and P is a unit matrix here, and V is the correction of finding the solution 6 space similarity transformation parameter estimator values, and B is the coefficient of finding the solution the error equation of 6 space similarity transformation parameters foundation, then has:

X＝(B ^TB) ^-1B ^TL (6)

Can know that according to the measurement adjustment principle variance of unit weight

is:

${\mathrm{\σ}}_0^2=\frac{V^T\mathrm{PV}}{3n-6}---\left(7\right)$

In the formula (1), n is the same place logarithm;

(4), making association's factor of 6 space similarity transformation parameters in the indirect adjustment is Q _Xx, Q then _Xx=(B ^TB) ^-1

Use association's factor and propagate law, the variance of 6 space similarity transformation parameters can be found the solution by following formula:

$\mathrm{Dx}={\mathrm{\σ}}_0^2{Q}_{\mathrm{xx}}---\left(8\right)$

Association's factor battle array of target central point scan values is:

$Q_{\hat{X}\hat{X}}=Q-B{Q}_{\mathrm{XX}}{B}^T---\left(9\right)$

In the formula (9), Q is a unit matrix,

The variance that (5), can get the estimated value of target central point scan values by formula (8) is:

$D={\mathrm{\σ}}_0^2{Q}_{\hat{X}\hat{X}}={\mathrm{\σ}}_0^2-B{D}_X{B}^T---\left(10\right)$

Therefore, X _dThe diagonal angle square formation of the variance of 9 parameters formation 9*9 is D among the corresponding variance Dn _N, order

$D_M={\left[\begin{array}{ccccccc}{\mathrm{\σ}}_X^2& & & & & & \\ & {\mathrm{\σ}}_Y^2& & & & & \\ & & {\mathrm{\σ}}_Z^2& & & & \\ & & & O& & & \\ & & & & {\mathrm{\σ}}_{\mathrm{Xn}}^2& & \\ & & & & & {\mathrm{\σ}}_{\mathrm{Yn}}^2& \\ & & & & & & {\mathrm{\σ}}_{\mathrm{Zn}}^2\end{array}\right]}_{3n\×3n}.$

(6), propagate law, can get by formula (4) according to covariance:

D _M＝KD _NK ^T (11)

Formula (11) is exactly the error propagation model of following some cloud registration of two different scanning coordinate systems, can resolve the error in point measurement behind the registration thus, as an index of weighing some position registration quality;

(7), for the multistation registration; Confirm the number of times of registration successively; Calculate each registration parameter error equation factor arrays; The error propagation model that again variance behind these error equation factor arrays and the preceding registration is multiplied each other and can draw the multistation registration, be about to positional accuracy behind the registration each time will given value substitution propagation model as registration next time in; Concrete computing method are following:

The propagation model of multistation registration error is:

$D_n=K_n\mathrm{\Λ}{K}_1\left(K_0{D}_0{K}_0^T\right)K_1^T\mathrm{\Λ}{K}_n^T---\left(12\right)$

K wherein _i(i=0,1,2 ..., n) be the determined matrix of registration parameter that obtains of registration each time, but through type (3) is found the solution;

Be the positional accuracy behind the first time registration, after this positional accuracy behind the registration each time

In will given value substitution propagation model as registration next time.

It is following that the embodiment of the invention is carried out process:

(1), sees that Fig. 1, Fig. 2, Fig. 3, example laboratory are divided into the registration of Spherical Target standard configuration standard and some cloud unique point, take the multistation registration experimental program of closed hoop; From the off promptly, carry out the multistation registration, get back to starting point at last along closed hoop; Same group of spherical target of starting point or same group of some cloud characteristic point coordinates are compared; And calculate registration parameter and middle error, estimate the quality of multistation registration, thereby the error propagation model of multistation registration is verified.

(2), referring to Fig. 4, for the ease of the fast processing of data with raise the efficiency, according to the calculation procedure of the error propagation model of a cloud registration, utilization matlab 7.0 programmings realize the calculating of multi-site cloud registration error propagation models; Result of calculation is referring to table 1, table 2.

Each variable result of calculation of table 1 multistation registration error propagation model

Coordinate behind the closed registration of the coordinate of table 2 comparison point scanning and multistation relatively

(3), Fig. 5 be scanning certain buildings embodiment, point scanned successively from No. 1 o'clock to No. 4, guaranteed that adjacent two survey stations have public target.Shown the building sides point cloud chart that each survey station is gathered among Fig. 6.Can know according to above-mentioned (1), (2); Estimate the quality of cloud data registration, the error of analysis site cloud registration must calculate corresponding error earlier; Whether the error that just can know cloud data is in the scope of regulation and stipulation, and registration error situation about propagating continuously.If meet the requirements, carry out the later stage three-dimensional modeling so, thereby realize the reconstruction of buildings.This just need carry out following several steps:

1. according to the registration parameter of adjacent two survey stations of above-mentioned algorithm computation;

2. by above-mentioned some cloud registration error Model Calculation registration variance in twos, analyze this variance whether in Discrepancy Control Area, if meet the requirements, the cloud data collection is correct.

3. further calculate the multistation registration error and propagate variance, analyze the degree that this variance is understood the registration error accumulation, if do not transfinite, the cloud data of all collections can carry out the later stage three-dimensional modeling.

Table 3 has shown the result of aforementioned calculation, and Fig. 7 has shown buildings point cloud chart behind the various cloud data registrations.

Table 3 multistation registration transformation calculation of parameter result (unit: m)

Showing clearly during treatment effect of the present invention and necessity are stated in the above, is most important content in the whole Point Cloud Processing.Therefore; Some cloud registration error propagation model among application the present invention and computing method are calculation level cloud registration accuracy and the quantitative relation of point cloud model cumulative errors and the error in point measurement behind the registration effectively; Can be used as the index of weighing some position registration quality, thereby a precision of cloud registration is made reasonable assessment.Three-dimensional laser scanning technique has been successfully applied to the projects such as protection of digital the Forbidden City, the Dunhuang Caves and Yungang Grottoes; Some cloud registration data based on three-dimensional reconstruction is handled, and the present invention can be widely used in fields such as survey field, virtual reality, reverse-engineering, ancient architecture protection.

Claims (1)

1. one kind is utilized the territorial laser scanning technology to carry out measuring object resurfacing time point cloud registration error disposal route, and it is characterized in that: it specifically may further comprise the steps:

(1), utilize the least square adjustment method to resolve measuring object surface same point 6 space similarity transformations parameter

ω, κ, Δ X, Δ Y, Δ Z; I.e. three angle rotation parameters:

ω, κ and three translation parameterss: Δ X, Δ Y, Δ Z, and confirm that the mathematical model that some cloud registration error propagates is following:

Wherein, (X, Y is Z) with (x, y z) are respectively the same coordinate under different scanner coordinate systems of subject surface, and R is a rotation matrix;

(2), formula (1) is utilized Taylor series expansion, get once, then have

Wherein:

Can obtain error equation thus:

Make that K is V in the formula (2) ^(k)Factor arrays, L=F-F ₀, then have

According to registration principle and formula (1), (2), can get the error equation of n same place under two scan coordinate system:

Make

then formula (4) can be expressed as:

V ^k＝KX _d-L (5)

(3), order For

ω, κ, Δ X, Δ Y, the registration variance of the variance of Δ Z and target central point x, y, z according to the indirect adjustment principle, makes 6 space similarity transformation parameters

ω, κ, Δ X, Δ Y, the weight matrix of Δ Z are P,

The variance of target central point x, y, z does X so _dCorresponding variance does

At V ^TPV is for obtaining separating of unknown number under the minimum condition, and P is a unit matrix here, and V is the correction of finding the solution 6 space similarity transformation parameter estimator values, and B is the coefficient of finding the solution the error equation of 6 space similarity transformation parameters foundation, then has:

X＝(B ^TB) ^-1B ^TL (6)

Can know that according to the measurement adjustment principle variance of unit weight is:

${\mathrm{\σ}}_0^2=\frac{V^T\mathrm{PV}}{3n-6}---\left(7\right)$

In the formula (1), n is the same place logarithm;

(4), making association's factor of 6 space similarity transformation parameters in the indirect adjustment is Q _Xx, Q then _Xx=(B ^TB) ^-1

Use association's factor and propagate law, the variance of 6 space similarity transformation parameters can be found the solution by following formula:

$\mathrm{Dx}={\mathrm{\σ}}_0^2{Q}_{\mathrm{xx}}---\left(8\right)$

Association's factor battle array of target central point scan values is:

$Q_{\hat{X}\hat{X}}=Q-B{Q}_{\mathrm{XX}}{B}^T---\left(9\right)$

In the formula (9), Q is a unit matrix,

The variance that (5), can get the estimated value of target central point scan values by formula (8) is:

$D={\mathrm{\σ}}_0^2{Q}_{\hat{X}\hat{X}}={\mathrm{\σ}}_0^2-B{D}_X{B}^T---\left(10\right)$

Therefore, X _dThe diagonal angle square formation of the variance of 9 parameters formation 9*9 is D among the corresponding variance Dn _N, order

$D_M={\left[\begin{array}{ccccccc}{\mathrm{\σ}}_X^2& & & & & & \\ & {\mathrm{\σ}}_Y^2& & & & & \\ & & {\mathrm{\σ}}_Z^2& & & & \\ & & & O& & & \\ & & & & {\mathrm{\σ}}_{\mathrm{Xn}}^2& & \\ & & & & & {\mathrm{\σ}}_{\mathrm{Yn}}^2& \\ & & & & & & {\mathrm{\σ}}_{\mathrm{Zn}}^2\end{array}\right]}_{3n\×3n}.$

(6), propagate law, can get by formula (4) according to covariance:

D _M＝KD _NK ^T (11)

Formula (11) is exactly the error propagation model of following some cloud registration of two different scanning coordinate systems, can resolve the error in point measurement behind the registration thus, as an index of weighing some position registration quality;

(7), for the multistation registration; Confirm the number of times of registration successively; Calculate each registration parameter error equation factor arrays; The error propagation model that again variance behind these error equation factor arrays and the preceding registration is multiplied each other and can draw the multistation registration, be about to positional accuracy behind the registration each time will given value substitution propagation model as registration next time in; Concrete computing method are following:

The propagation model of multistation registration error is:

$D_n=K_n\mathrm{\Λ}{K}_1\left(K_0{D}_0{K}_0^T\right)K_1^T\mathrm{\Λ}{K}_n^T---\left(12\right)$

K wherein _i(i=0,1,2 ..., n) be the determined matrix of registration parameter that obtains of registration each time, but through type (3) is found the solution;

Be the positional accuracy behind the first time registration, after this positional accuracy behind the registration each time In will given value substitution propagation model as registration next time.

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