CN104732544A - Method for rapidly searching for shape target points - Google Patents

Abstract

The invention relates to a method for rapidly searching for shape target points. The method can be effectively used for rapidly and accurately searching for the shape target points. The method includes the following steps that coordinates of a plurality of three-dimensional points of the surface of a detected object are obtained firstly, a mathematical model of the detected object is constructed, a minimum of the initial points are determined, initial parameters of the detected object are worked out according to three-dimensional coordinates of the initial points and the mathematical model of the detected object so as to obtain a root mean square error value of fitting calculation, and then a root mean square value is obtained through statistics according to a set of distances; a triple of the root mean square error value serves as a threshold value, the distances from all the points to the detected object described through the initial parameters are worked out, meanwhile, a root mean square error value of the distances from the initial points to the detected object described through initial values is worked out, the process is repeated then, namely all the points meeting the range of the threshold value are found out, and final parameters of the detected object are worked out. The method is simple, operation is easy, the degree of automation is high, the speed is high, consumed time is short, positioning is accurate, the error rate is low, and practicality is high.

Description

A kind of method of fast finding shape objects point

Technical field

The present invention relates to commercial measurement, particularly a kind of method of fast finding shape objects point.

Background technology

In field of industrial measurement, obtain a large amount of three-dimensional point cloud coordinate in testee surface by high-precision measuring equipment, then calculate the Geometrical Parameter of testee according to the mathematical model and measurement pointcloud coordinate that describe testee.And by build the Geometrical Parameter of measured object and the original mathematical model of measured object compare, obtain all deflections participating in the measured object superficial objects point calculated, thus obtain the loss of measured object in process or production and application process, be convenient to be described the distortion of measured object accurately, improve measured object serviceable life and service efficiency.In this process, there is a committed step, from body surface three-dimensional point cloud, find authentic and valid impact point exactly, namely to the point of measured object accurate description, calculate measured object Geometrical Parameter originally.

Existing method of searching body form impact point is all manually choose.Operating personnel, according to the shape facility of object, from a large amount of cloud data, manually go Search and Orientation to belong to the impact point of body form.Such method both expended time in, and there will be again because human eye erroneous judgement causes the impact point mistake chosen, thus affected measured object Geometrical Parameter calculating really and accurately.

Summary of the invention

For above-mentioned situation, for overcoming the defect of prior art, the object of the present invention is just to provide a kind of method of fast finding shape objects point, effectively can solve fast, accurately search the problem of shape objects point.

The technical scheme that the present invention solves is, first multiple three-dimensional point coordinates on testee surface are obtained, form the mathematical model of testee, by the mathematical model of tested physics, determine minimum initial point, the mathematical model of foundation initial point three-dimensional coordinate and measured object, calculate the initial parameter of testee, while calculating initial parameter, obtain the root-mean-square error value of the Fitting Calculation, root-mean-square error value represents a statistic of one group of distance value of the three-dimensional point participating in the Fitting Calculation, represent that the three-dimensional point participating in the Fitting Calculation is to the distance of the measured object described by Geometrical Parameter, then according to this group distance, statistics obtains a root-mean-square value, represent a statistical value of the distance of the measured object of this group described by three-dimensional point to initial parameter, with the root-mean-square error value of three times for threshold value, calculate a little to the distance of the measured object described by initial parameter, when distance is in threshold range, the point in threshold range is joined initial point and concentrates, recalculate initial parameter, calculate the root-mean-square value of the measured object distance described by initial point to initial value simultaneously, then repeat this process, find by all points meeting threshold range, calculate the parameter of final measured object, realize the object of quick and precisely searching shape objects point.

The inventive method is simple, and easy to operate, automaticity is high, and speed is fast, and consuming time short, accurate positioning, error rate is low, has very strong practicality, is that on fast finding shape objects point innovates greatly.

Accompanying drawing explanation

Fig. 1 is process chart of the present invention.

Embodiment

Below in conjunction with concrete condition, the specific embodiment of the present invention is elaborated.

Provided by Fig. 1, the present invention is realized by following steps in concrete enforcement, first select initial point, calculate initial parameter, realize initial value and select, after selecting initial value, carry out threshold value setting, search impact point according to threshold value, recalculate initial parameter, fast finding goes out shape objects point, and concrete steps are as follows:

The first step: coordinate X, Y, Z of being obtained multiple three-dimensional point on testee surface by commercial measurement equipment, described testee is the heteroid body of straight line body, plane body or right cylinder;

Second step: choose some initial points from multiple three-dimensional point coordinate, by initial point three-dimensional coordinate, calculate the initial parameter of testee, described initial parameter comprises the three-dimensional point coordinate (Xs, Ys, Zs) of testee, the direction vector of testee coordinate (i, j, k), after the three-dimensional point coordinate obtaining testee, selects the minimum number of initial point: straight line body at least 2, plane body at least 3, at least 5, right cylinder; Then according to the point that these are selected, utilize binding characteristic method to obtain body initial parameter in body the Fitting Calculation, method is:

Choosing of enantiomorph matching initial value is equivalent to choose a model, and is placed in an orientation by this model, makes measurement pointcloud be distributed on the both sides of this model, and first, being placed on by this model in an orientation in space: for sphere, is namely the position determining the centre of sphere; For the face of cylinder, it is namely the orientation of deterministic type over glaze line; For circular conical surface, it is namely the orientation of deterministic type over glaze line and conical point; After scope is determined, then the size of Confirming model: for sphere and the face of cylinder, be namely determine corresponding radius; For circular conical surface, be namely determine cone angle; Binding characteristic method refers to that utilization is treated that the surrounding features of fit characteristic retrains step by step and treated the degree of freedom of fit characteristic in space, until spatial degrees of freedom is zero, locates complete; Behind location, by following formula, calculate error (residual error) v of initial parameter _i;

When measured object is straight line body, the error equation formula calculating initial parameter is:

$v_i=\sqrt{{(X_i-\mathrm{xp})}^2+{(Y_i-\mathrm{yp})}^2+{(Z_i-\mathrm{zp})}^2}$

$\left\{\begin{array}{c}\mathrm{xp}=\mathrm{Xs}+i\×i\×X_i+i\×j\×Y_i+i\×k\×Z_i-i\×i\×\mathrm{XS}-i\×j\×\mathrm{YS}-i\×k\×\mathrm{ZS}\\ \mathrm{yp}=\mathrm{Ys}+i\×j\×X_i+j\×j\×Y_i+j\×k\×Z_i-i\×j\×\mathrm{XS}-j\×j\×\mathrm{YS}-j\×k\×\mathrm{ZS}\\ \mathrm{zp}=\mathrm{Zs}+i\×k\×X_i+j\×k\×Y_i+k\×k\×Z_i-i\×k\×\mathrm{XS}-j\×k\×\mathrm{YS}-k\×k\×\mathrm{ZS}\end{array}\right.$

Wherein:

V _icomposition matrix form V;

According to least square fitting principle, V ^tpV is minimum, can obtain the best initial parameter of measured object;

^tthe transposition of representing matrix, P representation unit matrix;

Xs, Ys, Zs are the three-dimensional coordinates of testee position, and i, j, k are the direction vector of testee coordinate Xs, Ys, Zs respectively;

X _i, Y _i, Z _iit is the coordinate of multiple three-dimensional point on testee surface;

In formula, subscript i represents from 0 to the sequence number (as follows) of actual three-dimensional point number;

When measured object is plane body, the error equation formula calculating initial parameter is:

v _i＝-aX _i-bY _i-cZ _i-d

According to least square fitting principle, V ^tpV is minimum, can obtain the transposition of best initial parameter a, b, c, d, the T representing matrix of measured object, P representation unit matrix;

A, b, c, d are the parameters in the general expression of plane body equation:

aX _i+bY _i+cZ _i+d＝0

Formula is converted to the some French of plane body thus:

i×(X _i-XS)+j×(Y _i-YS)+k×(Z _i-ZS)＝0

When measured object is right cylinder, the error equation formula calculating initial parameter is:

$v_i=\sqrt{{(L_i-L)}^T\×R\×W\×R^T\×(L_i-L)}$

L _irepresenting matrix (X _iy _iz _i) ^t,

L representing matrix (Xs, Ys, Zs) ^t;

R representing matrix Ri × Rj × Rk

Ri represents $\left[\begin{array}{ccc}1& 0& 0\\ 0& i& -i\\ 0& i& i\end{array}\right],$ Rj represents $\left[\begin{array}{ccc}j& 0& -j\\ 0& 1& 0\\ j& 0& j\end{array}\right],$ Rk represents $\left[\begin{array}{ccc}k& -k& 0\\ k& k& 0\\ 0& 0& 1\end{array}\right]$

The direction vector of i, j, k in matrix and testee coordinate Xs, Ys, Zs;

While obtaining Geometrical Parameter, the root-mean-square error of matching body can be calculated according to formula below simultaneously:

RMS represents root-mean-square error, v _irepresent the residual error of the Fitting Calculation;

3rd step: according to initial parameter, dot system software is sought (as the shape objects on industrial measuring system computing machine seeks dot system software with computing machine shape objects, the computing machine shape objects of the industrial photogrammetry system of Zhengzhou Sunward Technology Co., Ltd. can be adopted to seek dot system software, prior art), search the three-dimensional point satisfied condition, and again calculate Geometrical Parameter according to least square fitting algorithm; Be benchmark according to the root-mean-square error obtained in body the Fitting Calculation, when with three of this root-mean-square error times of values for threshold value time, the three-dimensional point of more than 99% is found; Calculate the distance of all three-dimensional point to testee simultaneously, meet the three-dimensional point that distance value is less than threshold value all join in the calculating of matching body again by all, recalculate Geometrical Parameter and root-mean-square error, and repeat this step, until do not have three-dimensional point to join again in the calculating of matching body; Namely the three-dimensional point found is impact point.

Described least square fitting algorithm is based on LM method and Newton iteration method, and LM method solution calculating initial value is bad and iteration that is that cause does not restrain situation, makes Newton iteration method rapidly converge to optimum solution; Newton iteration method requires very strict to initial value, and belongs to local convergence; LM method is the improvement to Newton method, and by introducing non-negative iteration parameter, overcome Newton method to the strict problem of initial value requirement, when initial value is very poor, Newton method can produce does not restrain situation, and LM method can restrain; When LM method converges near true value, LM method now becomes Newton iteration, rapidly converges to the solution of Newton iteration;

LM method: the abbreviation being LEVENBERG – MARQUARDT method.

Below Binding experiment is described further the specific embodiment of the present invention again.

Experiment 1

The present invention is testee through a cube physical construction of certain military enterprise, need the linearity detecting its structure edge, but this perimeter also has a lot of three-dimensional point to detect other guide simultaneously, these points are easy to the matching interfering with edge line, so need to find the impact point on all edge lines, method is as follows:

1, use the SMN industrial measuring system of Zhengzhou Sunward Technology Co., Ltd. to coordinate transit survey equipment, measure the edge three-dimensional point 10 of physical construction, simultaneously because other need, measure the three-dimensional point 20 of perimeter, altogether 30 three-dimensional point;

2, computing machine shape objects is utilized to seek dot system software all 30 three-dimensional point obtained, three three-dimensional point at the head and the tail two ends and centre of choosing edge are in systems in which as initial point, ask the error equation formula of initial parameter to calculate the initial parameter of this straight line according to the straight line body in step 2: three-dimensional coordinate Xs, Ys, Zs position is 294.041mm, 95.014mm, 2179.355mm respectively, corresponding i, j, k direction vector is 0.029050,0.999528,0.009984;

3, the root-mean-square error 1.593mm of fitting a straight line is obtained in the calculation, be threshold value by three of this value times of 4.779mm, calculate the distance that other arrive a little this straight line simultaneously, what be less than threshold value 4.779mm is the three-dimensional point of searching and satisfying condition, in 30 three-dimensional point, have found 7 impact points satisfied condition, 3 three-dimensional point chosen before adding, 10 impact points are all correctly found altogether.

This searches impact point, and accuracy rate is 100%, and service time is 0.5s, if all manually go to search, accuracy rate can only reach 80%, and skilled operating personnel also at least need the 30s time.

Experiment 2

Another experimental example of the present invention is a planar structure of certain enterprise, need to detect its structural plan degree, but also have other three-dimensional subsidiary point around this plane simultaneously, these points are easy to the matching interfering with plane, so need to find the impact point in all planes, in an experiment, according to the method that the present invention provides, following steps are adopted to test:

1, use the SMN industrial measuring system of Zhengzhou Sunward Technology Co., Ltd. to coordinate API tracker measuring equipment, measure the plane three-dimensional point 63 of structure.Simultaneously because other need, measure the three-dimensional point 53 of perimeter, altogether 116 three-dimensional point;

2, all 116 three-dimensional point obtained are imported to computing machine shape objects and seek dot system software, choose four three-dimensional point of plane end points in systems in which as initial point, ask the error equation formula of initial parameter to calculate the initial parameter of this plane according to the plane body in step 2: three-dimensional coordinate Xs, Ys, Zs position 127.473mm, 508.311mm, 1007.016mm, corresponding i, j, k direction vector 0.988301 ,-0.027275 ,-0.150057;

3, the root-mean-square error 0.727mm of plane fitting is obtained in the calculation, be threshold value by three of this value times of 2.181mm, calculate the distance that other arrive a little this plane simultaneously, what be less than threshold value 2.181mm is the three-dimensional point of searching and satisfying condition, in 116 three-dimensional point, have found 59 impact points, 4 three-dimensional point chosen before adding, 63 impact points are all correctly found altogether.

This searches impact point, and accuracy rate is 100%, and service time is 0.8s.If all manually go to search, accuracy rate can only reach 70%, and skilled operating personnel also at least need the 60s time.

Experiment 3

Another experiment of the present invention is the physical construction of a column type of certain heavy industry enterprise, needs the deflection detecting its surface, and need all impact points satisfied condition of body surface all to participate in calculating, according to the technical scheme that the present invention provides, test method is as follows:

1, use the MPS/S one camera industrial photogrammetry system of Zhengzhou Sunward Technology Co., Ltd., obtain 181 three-dimensional coordinates on the surface of column type physical construction, have subsidiary point 823 around it, altogether 1004 three-dimensional point;

2, all 1004 three-dimensional point obtained are imported to computing machine shape objects and seek dot system software, choose arbitrarily 5 points in systems in which as initial coordinate calculation level, ask the error equation formula of initial parameter to calculate the initial parameter of this cylinder according to the right cylinder in step 2: three-dimensional coordinate Xs, Ys, Zs position 518.828mm, 190.183mm ,-2179.355mm, corresponding i, j, k direction vector-0.959885 ,-0.193118,0.203290;

3, the root-mean-square error 1.577mm of plane fitting is obtained in the calculation.Be threshold value by three of this value times of 2.181mm, calculate the distance that other arrive a little this plane simultaneously, what be less than threshold value 4.731mm is the three-dimensional point of searching and satisfying condition, in 1004 three-dimensional point, have found 176 impact points, 5 three-dimensional point chosen before adding, 181 impact points are all correctly found altogether.

This searches impact point, and accuracy rate is 100%, and service time is 1.5s.If all manually go to search, accuracy rate can only reach 60%, and skilled operating personnel at least need the 180s time.

Shown by above-mentioned experimental data, the present invention is easy to operate, also technical solution of the present invention can be integrated into a shape objects and seek dot system software, integrated shape objects is directly utilized to seek dot system software, carry out fast finding shape objects point, seek rate is fast, accurately, work efficiency is improved greatly, 60-120 can be improved doubly, and effectively reduce the error rate of prior art appearance, accuracy is high, compared with prior art, there is manual intervention few, require low to initial value levels of precision, automatically a large amount of point is chosen, speed is fast, consuming time short, location, some position is accurate, error rate is low, search one on shape objects point methods to innovate greatly, there is very strong practical value.

Claims (2)

1. the method for a fast finding shape objects point, it is characterized in that, first multiple three-dimensional point coordinates on testee surface are obtained, form the mathematical model of testee, by the mathematical model of tested physics, determine minimum initial point, the mathematical model of foundation initial point three-dimensional coordinate and measured object, calculate the initial parameter of testee, while calculating initial parameter, obtain the root-mean-square error value of the Fitting Calculation, root-mean-square error value represents a statistic of one group of distance value of the three-dimensional point participating in the Fitting Calculation, represent that the three-dimensional point participating in the Fitting Calculation is to the distance of the measured object described by Geometrical Parameter, then according to this group distance, statistics obtains a root-mean-square value, represent a statistical value of the distance of the measured object of this group described by three-dimensional point to initial parameter, with the root-mean-square error value of three times for threshold value, calculate a little to the distance of the measured object described by initial parameter, when distance is in threshold range, the point in threshold range is joined initial point and concentrates, recalculate initial parameter, calculate the root-mean-square value of the measured object distance described by initial point to initial value simultaneously, then repeat this process, find by all points meeting threshold range, calculate the parameter of final measured object, realize the object of quick and precisely searching shape objects point.

2. the method for fast finding shape objects point according to claim 1, it is characterized in that, concrete steps are as follows:

The first step: coordinate X, Y, Z of being obtained multiple three-dimensional point on testee surface by commercial measurement equipment, described testee is the heteroid body of straight line body, plane body or right cylinder;

Second step: choose some initial points from multiple three-dimensional point coordinate, by initial point three-dimensional coordinate, calculate the initial parameter of testee, described initial parameter comprises the three-dimensional point coordinate (Xs, Ys, Zs) of testee, the direction vector of testee coordinate (i, j, k), after the three-dimensional point coordinate obtaining testee, selects the minimum number of initial point: straight line body at least 2, plane body at least 3, at least 5, right cylinder; Then according to the point that these are selected, utilize binding characteristic method to obtain body initial parameter in body the Fitting Calculation, method is:

Choosing of enantiomorph matching initial value is equivalent to choose a model, and is placed in an orientation by this model, makes measurement pointcloud be distributed on the both sides of this model, and first, being placed on by this model in an orientation in space: for sphere, is namely the position determining the centre of sphere; For the face of cylinder, it is namely the orientation of deterministic type over glaze line; For circular conical surface, it is namely the orientation of deterministic type over glaze line and conical point; After scope is determined, then the size of Confirming model: for sphere and the face of cylinder, be namely determine corresponding radius; For circular conical surface, be namely determine cone angle; Binding characteristic method refers to that utilization is treated that the surrounding features of fit characteristic retrains step by step and treated the degree of freedom of fit characteristic in space, until spatial degrees of freedom is zero, locates complete; Behind location, by following formula, calculate error (residual error) v of initial parameter _i;

When measured object is straight line body, the error equation formula calculating initial parameter is:

$v_i=\sqrt{{(X_i-\mathrm{xp})}^2+{(Y_i-\mathrm{yp})}^2+{(Z_i-\mathrm{zp})}^2}$

$\left\{\begin{array}{c}\mathrm{xp}=\mathrm{Xs}+i\×i\×X_i+i\×j\×Y_i+i\×k\×Z_i-i\×i\×\mathrm{XS}-i\×j\×\mathrm{YS}-i\×k\×\mathrm{ZS}\\ \mathrm{yp}=\mathrm{Ys}+i\×j\×X_i+j\×j\×Y_i+j\×k\×Z_i-i\×j\×\mathrm{XS}-i\×j\×\mathrm{YS}-j\×k\×\mathrm{ZS}\\ \mathrm{zp}=\mathrm{Zs}+i\×k\×X_i+j\×k\×Y_i+k\×k\×Z_i-i\×k\×\mathrm{XS}-j\×k\×\mathrm{YS}-k\×k\×\mathrm{ZS}\end{array}\right.$

Wherein:

V _icomposition matrix form V;

According to least square fitting principle, V ^tpV is minimum, can obtain the best initial parameter of measured object;

^tthe transposition of representing matrix, P representation unit matrix;

Xs, Ys, Zs are the three-dimensional coordinates of testee position, and i, j, k are the direction vector of testee coordinate Xs, Ys, Zs respectively;

X _i, Y _i, Z _iit is the coordinate of multiple three-dimensional point on testee surface;

Subscript in formula _irepresent from 0 to the sequence number (as follows) of actual three-dimensional point number;

When measured object is plane body, the error equation formula calculating initial parameter is:

v _i＝-aX _i-bY _i-cZ _i-d

According to least square fitting principle, V ^tpV is minimum, can obtain best initial parameter a, b, c, the d of measured object, ^tthe transposition of representing matrix, P representation unit matrix;

A, b, c, d are the parameters in the general expression of plane body equation:

aX _i+bY _i+cZ _i+d＝0

Formula is converted to the some French of plane body thus:

i×(X _i-XS)+j×(Y _i-YS)+k×(Z _i-ZS)＝0

When measured object is right cylinder, the error equation formula calculating initial parameter is:

$v_i=\sqrt{{(L_i-L)}^T\×R\×W\×R^T\×(L_i-L)}$

L _irepresenting matrix (X _iy _iz _i) ^t,

L representing matrix (Xs, Ys, Zs) ^t;

R representing matrix Ri × Rj × Rk

Ri represents $\left[\begin{array}{ccc}1& 0& 0\\ 0& i& -i\\ 0& i& i\end{array}\right],$ Rj represents $\left[\begin{array}{ccc}j& 0& -j\\ 0& 1& 0\\ j& 0& j\end{array}\right],$ Rk represents $\left[\begin{array}{ccc}k& -k& 0\\ k& k& 0\\ 0& 0& 1\end{array}\right],$

I, j, k in matrix are the direction vector of testee coordinate Xs, Ys, Zs;

While obtaining Geometrical Parameter, the root-mean-square error of matching body can be calculated according to formula below simultaneously:

$\mathrm{RMS}=\√\sqrt{[\mathrm{\Σ}{v}_i^2/n]}$

RMS represents root-mean-square error, v _irepresent the residual error of the Fitting Calculation;

3rd step: according to initial parameter, dot system software is sought (as the shape objects on industrial measuring system computing machine seeks dot system software with computing machine shape objects, the computing machine shape objects of the industrial photogrammetry system of Zhengzhou Sunward Technology Co., Ltd. can be adopted to seek dot system software, prior art), search the three-dimensional point satisfied condition, and again calculate Geometrical Parameter according to least square fitting algorithm; Be benchmark according to the root-mean-square error obtained in body the Fitting Calculation, when with three of this root-mean-square error times of values for threshold value time, the three-dimensional point of more than 99% is found; Calculate the distance of all three-dimensional point to testee simultaneously, meet the three-dimensional point that distance value is less than threshold value all join in the calculating of matching body again by all, recalculate Geometrical Parameter and root-mean-square error, and repeat this step, until do not have three-dimensional point to join again in the calculating of matching body; Namely the three-dimensional point found is impact point.