CN102589437A - Calibration method for measuring head center position in light pen-type portable three-coordinate measuring system - Google Patents

Abstract

The invention discloses a calibration method for a measuring head center position in a light pen-type portable three-coordinate measuring system. In the method, a light pen measuring head is put into a standard cone; a light pen is rotated slowly; after images are captured by a charge coupled device (CCD) camera and are transmitted to a computer for processing, a rotation translation matrix of a light pen coordinate system and a camera coordinate system is obtained; and because the standard cone and the CCD camera are fixed relatively, and moreover, the light pen per se is a rigid object, the coordinates of the measuring head center in the light pen coordinate system are solved by an algorithm according to the position invariance of the measuring head center in the light pen coordinate system and the camera coordinate system. By the method, the calibration of the measuring head center position in the light pen-type portable three-coordinate measuring system can be realized rapidly and accurately on the measurement scene.

Description

The scaling method of gauge head center in the portable three-dimensional coordinates measurement of the light pen system

Technical field

The present invention relates to contact vision three-dimensional coordinates measurement field, more particularly, relate to the scaling method of gauge head center in the portable three-dimensional coordinates measurement of the light pen system.

Background technology

The three-dimensional coordinates measurement technology has important effect in commercial production, mainly be divided into contact and contactless two kinds.Contact type measurement is through gauge head contact testee surface, obtains the measured surface shape information, and more representational survey instrument is a three coordinate measuring machine, and this measuring method precision is high, but efficient is relatively low, and measurement range is also less relatively.Non-contact measurement mainly utilizes laser equipment or CCD phase machine testing measured object surface, and the combining image treatment technology obtains the shape information of measured surface, and wherein the vision three-dimensional coordinates measurement is typical case's representative of non-cpntact measurement.This measuring method precision is generally than low one to two one magnitude of contact type measurement; But it is fast to adopt spot speed; Measurement range is big, is that the common contact-type measuring machine is too far behind to catch up, and a lot of non-contact measurement machines also obtain the favor in each big commercial measurement field gradually on the market.

The portable three coordinate measuring machine of light pen mainly is made up of CCD camera, computing machine and light pen, can realize on-site rapid measurement.It with light pen as the contact measurement instrument; With the CCD camera as the vision-based detection means; Realized that vision non-contact type is measured and the perfect adaptation of contact type measurement, had advantages such as in light weight, simple to operate, that precision is higher, measurement range is big, received the great attention of various countries gradually.The light pen three coordinate measuring machine of releasing on the international market at present has the two/single CCD camera measuring system of Norway Metronor company and the V-STAR/M system of U.S. Geodetic company etc.; Domestic light pen measuring system research is started late, and also still is in conceptual phase at present.Infrarede emitting diode is adopted at the light pen reference mark in the Metronor system; Measuring accuracy is higher, yet cost is also higher, has light echo reflection reference mark in the V-STAR/M system on the light pen; Require camera must have flash unit, and system receive ambient light effects bigger.As the different patterns of the replaceable one-tenth of gauge head of the light pen of contact measurement instrument, to adapt to complicated measurement target, like deep hole, hidden place etc.Usually, dynamics is different during owing to the installation of the different perhaps gauge head of pattern, and also often there is deviation the gauge head center of at every turn installing, so must carry out the gauge head staking-out work before the measurement.

Though ripe product has abroad been arranged, and the data that relevant gauge head is demarcated is very limited, because the systematic research of light pen three-dimensional coordinates measurement also is in the starting stage at home, does not almost also have the valuable reference data.Therefore accomplish the demarcation of gauge head center fast and accurately in measure field, just become one of gordian technique in the portable three-coordinate measuring system.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art; Provide a kind of and realize the demarcation of gauge head center in the portable three-dimensional coordinates measurement of the light pen system, in order to realize the demarcation of gauge head center in the portable three-dimensional coordinates measurement of the light pen system in the measure field quick and accurate in the measure field quick and accurate.

It is different with the gauge head correction principle of the three coordinate measuring machine used always in the industry that the gauge head of light pen is demarcated; It is the diameter and the deflection deformation of proofreading and correct gauge head that the gauge head of three coordinate measuring machine is proofreaied and correct; The main standard ball of using is carried out, with manually, operating rod and automatic mode survey equally distributed point more than 5 in the maximum magnitude of standard ball, computer software is received the match computing of just carrying out ball behind the coordinate of these points; Obtain the sphere centre coordinate of match ball; Diameter and shape error deduct the diameter of standard ball with the diameter of match ball, just obtain proofreading and correct the diameter of back gauge head.It then is to find the solution the coordinate figure of gauge head center under the light pen coordinate system that the gauge head of light pen is demarcated.

The ultimate principle of technical scheme of the present invention is: utilize a standard cone; The light pen gauge head is placed in the taper hole; Slowly rotate light pen, after the CCD camera absorbs image and passes to Computer Processing, obtain the rotation translation matrix of light pen coordinate system and camera coordinates system; Because standard cone and CCD camera are relatively-stationary; And light pen this as rigid objects, according to the location invariance of gauge head center under being with camera coordinates the light pen coordinate system under, find the solution the coordinate of gauge head center under the light pen coordinate system through algorithm.

If the gauge head center camera coordinates system down and the coordinate of light pen coordinate system be respectively (u, v, w) ^T, (x, y, z) ^TBe tied to the rotation translation relation that camera coordinates is based on spatial point from the light pen coordinate, can know:

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{cc}R& T\end{array}\right]\·\left[\begin{array}{c}u\\ v\\ w\\ 1\end{array}\right]---\left(1\right)$

Rotation translation matrix R and T can and combine document (Yuan J S-C through the camera Perspective transformation model; A general photogrammetric method for determining object position and orientation; IEEE Trans on Robotics and Automation; 1989,5 (2): the newton-Gaussian processes 129-142) is found the solution and is obtained.

When if light pen turns to i position, the actual coordinate of gauge head center under camera coordinates system is (u _i, v _i, w _i) ^T, ideal value be (u, v, w) ^T, then can get optimization objective function:

$g\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(f_i\right)}^2---\left(2\right)$

Wherein, $f_i(x,y,z,u,v,w)=\sqrt{{(u_i-u)}^2+{(v_i-v)}^2+{(w_i-w)}^2},$ Optimization variable X=(x, y, z, u, v, w), i.e. the coordinate of gauge head center under light pen coordinate system and camera coordinates system.

The Nonlinear System of Equations of system is:

f _i(x，y，z，u，v，w)＝0 i＝1，2，L，n (3)

Can use the generalized inverse method of least square solution to find the solution this system of equations, can obtain corresponding coordinate (u, v, w) ^T, (x, y, z) ^T

The basic performing step of scheme is following:

(1) utilize the CCD camera to take the light pen image; And be transferred to computer and carry out image and handle the centre coordinate obtain light target mark control point (being the gauge head center), and calculate every width of cloth image corresponding rotation translation matrix R and T respectively based on camera Perspective transformation model and newton-Gaussian processes;

(2) utilize the above image of 2 width of cloth to find the solution initial value, and make iterations k=0;

(3) utilize the generalized inverse method iterative computation Nonlinear System of Equations f of least square solution _i(x, y, z, u, v, w)=0 i=1,2, L, the optimum solution of n;

(4) convergence is judged, when the absolute difference of adjacent twice optimum solution | and α _kΔ X ^(k)| enough hour, stop iteration, otherwise make k=k+1, change step 4;

(5) satisfy the condition of convergence after, with step 5 resulting (x, y, z) ^TAs the coordinate figure of gauge head center under the light pen coordinate system.

Further specify this programme in conjunction with above-mentioned steps.

The first step: CCD camera and standard cone all are fixed on the vibration isolators, and the adjustment relative position makes light pen be imaged on the CCD camera as the centre position, plane, and rocks down in certain amplitude, and the image at all light target mark reference mark still can guarantee on as the plane, to appear; Hand-held light pen is placed on gauge head in the taper hole of standard cone; Slowly rotate light pen; The CCD camera absorbs the light pen image of different poses; And pass to computing machine through the gigabit netting twine and handle in real time, follow the tracks of and the least square ellipse fitting through image filtering, Threshold Segmentation, black and white upset, profile, obtain all reference mark centre coordinates;

Second step: the CCD camera was demarcated in advance, and the perspective projection as the plane concerns from the coordinate under the camera coordinates system to ideal to utilize the center, reference mark, and the orthogonality of rotation matrix, can solve rotation translation matrix R and T through newton-Gauss's process of iteration.

The 3rd step: because every width of cloth image can obtain 3 nonlinear equations, optimization variable X has 6 unknown numbers, so the initial value of X can obtain through the image calculation more than two width of cloth.

The 4th step: after gathering n width of cloth image, promptly can obtain containing the Nonlinear System of Equations f of n equation _i(x, y, z, u, v, w)=0 i=1,2, L, n utilizes the generalized inverse method of least square solution to find the solution this system of equations, and is specific as follows:

(a) Jacobian matrix of the above-mentioned Nonlinear System of Equations of calculating:

$A=\left(\begin{array}{cccccc}\frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;x}& \frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;y}& \frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;z}& \frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;u}& \frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;v}& \frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000142204070000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;w}\\ \frac{{\&PartialD;f}_2}{\&PartialD;x}& \frac{{\&PartialD;f}_2}{\&PartialD;y}& \frac{{\&PartialD;f}_2}{\&PartialD;z}& \frac{{\&PartialD;f}_2}{\&PartialD;u}& \frac{{\&PartialD;f}_2}{\&PartialD;v}& \frac{{\&PartialD;f}_2}{\&PartialD;w}\\ M& M& M& M& M& M\\ \frac{{\&PartialD;f}_n}{\&PartialD;x}& \frac{{\&PartialD;f}_n}{\&PartialD;y}& \frac{{\&PartialD;f}_n}{\&PartialD;z}& \frac{{\&PartialD;f}_n}{\&PartialD;u}& \frac{{\&PartialD;f}_n}{\&PartialD;v}& \frac{{\&PartialD;f}_n}{\&PartialD;w}\end{array}\right)---\left(4\right)$

(b) calculate the iterative formula that it is separated:

X ^(k+1)＝X ^(k)-α _kΔX ^(k) (5)

Wherein, α _kBe to make the function of a single variable of iteration step length α Reach minimizing point, can adopt reasonable extremum method search to obtain.Δ X ^(k)Be system of linear equations A ^(k)Δ X ^(k)=F ^(k)Least square solution.A ^(k)Be k iterative value X ^(k)Jacobian matrix, F ^(k)Be the left end functional value of k iteration, that is:

$F^{\left(k\right)}={(f_1^{\left(k\right)},f_2^{\left(k\right)},L,f_n^{\left(k\right)})}^T$

f _i ^(k)＝f _i(x ^(k)，y ^(k)，z ^(k)，u ^(k)，v ^(k)，w ^(k))?i＝1，2，L，n

Through above-mentioned iterative computation, make X=X ^(k+1)It is refreshable optimization variable.

The 5th step: restrain judgement, the absolute difference of adjacent twice optimum solution | α _kΔ X ^(k)|＜0.01 o'clock, stop iterative computation, with among the optimization variable X that obtains for the last time (x, y, z) ^TAs the coordinate figure of gauge head center under the light pen coordinate system.

Convergence judges it is the constraints that whole algorithm stops, and can manually stop algorithm based on the variation of last coordinate data simultaneously.

The present invention utilizes the characteristics of system itself to realize the demarcation certainly of light pen gauge head; Use CCD camera picked-up light pen image; And be transferred to computing machine and handle in real time; Utilize camera transmission projection relation to obtain the rotation translation matrix that the light pen coordinate is tied to camera coordinates system, and set up Nonlinear System of Equations, the Nonlinear System of Equations of asking through the generalized inverse method of least square separate the coordinate of center under the light pen coordinate system that is gauge head.This algorithm is ageing strong, simple to operate, realizes easily, and is fast stable, can realize high-precision three-dimensional coordinates measurement in the measure field help system.

Description of drawings

The portable three-dimensional coordinates measurement of Fig. 1 light pen system forms sketch, mainly is made up of light pen, CCD camera and computing machine.

Fig. 2 IMAQ synoptic diagram, the slowly rotation light pen of left-right and front-back during collection.

Fig. 3 perspective projection schematic diagram is a basis of asking for image rotational transform matrix.

4 kinds of different light pen poses during Fig. 4 IMAQ are respectively to the right, rotate left, backward and forward.

Fig. 5 camera image that collect and after treatment, wherein (a) image effect of collecting for camera (b) is the image effect after threshold value 80 is cut apart, and (c) is the image effect after the black and white upset, (d) for obtaining the image effect of circle after the profile tracking.

The actual gauge head of Fig. 6 is demarcated and is implemented figure.

Embodiment

Further specify technical scheme of the present invention below in conjunction with specific embodiment.

This programme can be realized the demarcation of light pen gauge head center in the portable three-dimensional coordinates measurement of the light pen system; The portable three-dimensional coordinates measurement of light pen wherein as shown in Figure 1 system is made up of light pen shown in the figure, CCD camera and computing machine; Camera is a Basler industry black and white camera, and camera is in advance through demarcating before gauge head is demarcated.

The practical implementation process is:

(1) according to shown in Figure 1, put up the relative position of system and fixed camera and standard cone, the light pen gauge head places in the vertebral foramen of standard cone, lights LED light target mark reference mark, prepares the beginning staking-out work.

(2) as shown in Figure 2 CCD camera pickup image is transferred to computing machine through the gigabit netting twine and handles in real time by the rotation slowly of manually-operated light pen left-right and front-back, obtains all reference mark as the coordinate on the plane and calculate every width of cloth image corresponding R, T.Through the 6 coordinate initial values of width of cloth image calculation gauge head center under the light pen coordinate system is (77.163 ,-21.935 ,-117.855).

(3) continue to gather piece image and be transferred to computing machine; According to the camera coordinates system as shown in Figure 3 and the projection projection relation of desirable photo coordinate system; And light pen gauge head center unchangeability under camera coordinates system and light pen coordinate system; Ask for the coordinate of gauge head center under the light pen coordinate system and be (76.410 ,-20.918 ,-118.402).This coordinate figure and initial value are deducted absolute value mutually for (0.753,1.017,0.547), discovery can not satisfy convergent requirement (absolute difference of adjacent twice optimum solution | α _kΔ X ^(k)|＜0.01), then continue images acquired.Every increase piece image, just carry out iterative computation optimization variable X=(x, y, z, u, v w), and does once convergence and judges.

(4) through after 211 width of cloth image calculation, must arrive last twice coordinate figure and be respectively: (75.103 ,-24.258;-120.121) and (75.104 ,-24.260 ,-120.123); Restrain judgement and meet the demands, termination of iterations calculates, and accomplishes the staking-out work of light pen gauge head; With (75.104 ,-24.260 ,-120.123) as the coordinate of gauge head center at the light pen coordinate system.

More than the present invention has been done exemplary description; Should be noted that; Under the situation that does not break away from core of the present invention, the replacement that is equal to that any simple distortion, modification or other those skilled in the art can not spend creative work all falls into protection scope of the present invention.

Claims (2)

1. the scaling method of gauge head center in the portable three-dimensional coordinates measurement of the light pen system is characterized in that, carries out according to following step: utilize a standard cone; The light pen gauge head is placed in the taper hole, slowly rotates light pen, after the CCD camera absorbs image and passes to Computer Processing; Obtain the rotation translation matrix of light pen coordinate system and camera coordinates system; Because standard cone and CCD camera are relatively-stationary, and light pen this as rigid objects, according to the gauge head center the light pen coordinate system under and the location invariance of camera coordinates under being; Find the solution the coordinate of gauge head center under the light pen coordinate system through algorithm, said algorithm basic principle is:

The gauge head center camera coordinates system down and the coordinate of light pen coordinate system be respectively (u, v, w) ^T, (x, y, z) ^TBe tied to the rotation translation relation that camera coordinates is based on spatial point from the light pen coordinate, can know:

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{cc}R& T\end{array}\right]\&CenterDot;\left[\begin{array}{c}u\\ v\\ w\\ 1\end{array}\right]$

Rotation translation matrix R and T can and combine newton-Gaussian processes to find the solution through the camera Perspective transformation model to obtain.

When if light pen turns to i position, the actual coordinate of gauge head center under camera coordinates system is (u _i, v _i, w _i) ^T, ideal value be (u, v, w) ^T, then can get optimization objective function:

$g\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(f_i\right)}^2$

Wherein, $f_i(x,y,z,u,v,w)=\sqrt{{(u_i-u)}^2+{(v_i-v)}^2+{(w_i-w)}^2},$ Optimization variable X=(x, y, z, u, v, w), i.e. the coordinate of gauge head center under light pen coordinate system and camera coordinates system

The Nonlinear System of Equations of system is:

f _i(x，y，z，u，v，w)＝0?i＝1，2，L，n

Can use the generalized inverse method of least square solution to find the solution this system of equations, can obtain corresponding coordinate (u, v, w) ^T, (x, y, z) ^T

2. the scaling method of gauge head center in the portable three-dimensional coordinates measurement of the light pen according to claim 1 system is characterized in that the basic performing step of scaling method scheme is following:

The first step: CCD camera and standard cone all are fixed on the vibration isolators, and the adjustment relative position makes light pen be imaged on the CCD camera as the centre position, plane, and rocks down in certain amplitude, and the image at all light target mark reference mark still can guarantee on as the plane, to appear; Hand-held light pen is placed on gauge head in the taper hole of standard cone; Slowly rotate light pen; The CCD camera absorbs the light pen image of different poses; And pass to computing machine through the gigabit netting twine and handle in real time, follow the tracks of and the least square ellipse fitting through image filtering, Threshold Segmentation, black and white upset, profile, obtain all reference mark centre coordinates;

Second step: the CCD camera was demarcated in advance, and the perspective projection as the plane concerns from the coordinate under the camera coordinates system to ideal to utilize the center, reference mark, and the orthogonality of rotation matrix, can solve rotation translation matrix R and T through newton-Gauss's process of iteration;

The 3rd step: because every width of cloth image can obtain 3 nonlinear equations, optimization variable X has 6 unknown numbers, so the initial value of X can obtain through the image calculation more than two width of cloth;

The 4th step: after gathering n width of cloth image, promptly can obtain containing the Nonlinear System of Equations f of n equation _i(x, y, z, u, v, w)=0 i=1,2, L, n utilizes the generalized inverse method of least square solution to find the solution this system of equations, and is specific as follows:

(a) Jacobian matrix of the above-mentioned Nonlinear System of Equations of calculating:

$A=\left(\begin{array}{cccccc}\frac{{\&PartialD;f}_1}{\&PartialD;x}& \frac{{\&PartialD;f}_1}{\&PartialD;y}& \frac{{\&PartialD;f}_1}{\&PartialD;z}& \frac{{\&PartialD;f}_1}{\&PartialD;u}& \frac{{\&PartialD;f}_1}{\&PartialD;v}& \frac{{\&PartialD;f}_1}{\&PartialD;w}\\ \frac{{\&PartialD;f}_2}{\&PartialD;x}& \frac{{\&PartialD;f}_2}{\&PartialD;y}& \frac{{\&PartialD;f}_2}{\&PartialD;z}& \frac{{\&PartialD;f}_2}{\&PartialD;u}& \frac{{\&PartialD;f}_2}{\&PartialD;v}& \frac{{\&PartialD;f}_2}{\&PartialD;w}\\ M& M& M& M& M& M\\ \frac{{\&PartialD;f}_n}{\&PartialD;x}& \frac{{\&PartialD;f}_n}{\&PartialD;y}& \frac{{\&PartialD;f}_n}{\&PartialD;z}& \frac{{\&PartialD;f}_n}{\&PartialD;u}& \frac{{\&PartialD;f}_n}{\&PartialD;v}& \frac{{\&PartialD;f}_n}{\&PartialD;w}\end{array}\right)---\left(4\right)$

(b) calculate the iterative formula that it is separated:

X ^(k+1)＝X ^(k)-α _kΔX ^(k) (5)

Wherein, α _kBe to make the function of a single variable of iteration step length α Reach minimizing point, can adopt reasonable extremum method search to obtain; Δ X ^(k)Be system of linear equations A ^(k)Δ X ^(k)=F ^(k)Least square solution; A ^(k)Be k iterative value X ^(k)Jacobian matrix, F ^(k)Be the left end functional value of k iteration, that is:

$F^{\left(k\right)}={(f_1^{\left(k\right)},f_2^{\left(k\right)},L,f_n^{\left(k\right)})}^T$

f _i(k)＝f _i(x ^(k)，y ^(k)，z ^(k)，u ^(k)，v ^(k)，w ^(k))i＝1，2，L，n

Through above-mentioned iterative computation, make X=X ^(k+1)It is refreshable optimization variable;

The 5th step: restrain judgement, the absolute difference of adjacent twice optimum solution | α _kΔ X ^(k)|＜0.01 o'clock, stop iterative computation, with among the optimization variable X that obtains for the last time (x, y, z) ^TAs the coordinate figure of gauge head center under the light pen coordinate system.

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