CN103489169A - Improved depth data splicing method based on least square method - Google Patents

Abstract

The invention provides an improved depth data splicing method based on a least square method. The method includes the steps of firstly obtaining three-dimensional coordinates of gauge points in different coordinate systems, utilizing a 'point-plane-side-point' grading searching method to search out the corresponding gauge points in the different coordinate systems, and then using the improved least square method to carry out registration on a collection of the corresponding gauge points in the two coordinate systems to achieve splicing of depth data in the different coordinate systems. By the adoption of the method, matching errors of the corresponding gauge points are effectively eliminated, and the matching efficiency and the robustness of the registration of the depth data are improved.

Description

A kind of improved depth data joining method based on least square method

Technical field

The invention belongs to field of optical measuring technologies, relate to the some cloud problem under different coordinates, be specially a kind of improved depth data joining method based on least square method.

Background technology

In order to obtain the complete three-dimensional data in testee surface, need to testee, be measured from a plurality of angles, the depth data Unitary coordinate processing that then will repeatedly measure, complete the data splicing.In the depth data splicing, joining method based on gauge point is not subject to the restriction of testee shape, and it is low that gauge point is easy to cost of manufacture, positioning precision is high, be easy to the advantages such as identification, the stitching algorithm operand is little, does not need interative computation, can reach automatic high-precision data splicing requirement.

At first depth data joining method based on the non-coding gauge point need to obtain the corresponding relation of gauge point under different coordinates, then according to the depth data joining method, the depth data under different coordinates is spliced.The correctness that under different coordinates, the gauge point correspondence is searched and efficiency direct relation splicing precision and the real-time efficiency of measuring; In the situation that correspondence is searched is correct, the precision of stitching algorithm too also relation the precision of depth data splicing precision and optical measurement.

For the optical three-dimensional measuring method based on the non-coding gauge point, the corresponding relation and the more accurate joining method that accurately obtain in real time gauge point under different coordinates are the gordian techniquies of three dimensional optical measuring.The present invention proposes a kind of method and higher technology of data splicing robustness that accurately obtains in real time the corresponding relation of gauge point under different coordinates.

Summary of the invention

The technical matters solved

The problem existed for solving prior art, the present invention proposes a kind of improved depth data joining method based on least square method.

Technical scheme

The present invention adopts the non-coding gauge point to be spliced the depth data under different visual angles (coordinate system), at first need to obtain the three-dimensional coordinate of gauge point under different coordinates, utilize the hierarchical searching method of " point-face-limit-point " to search out the correspondence markings point under different coordinates, then adopt improved least square method to gather and carry out registration the correspondence markings point under two coordinate systems, realize the splicing of depth data under different coordinates.

Technical scheme of the present invention is:

Described a kind of improved depth data joining method based on least square method is characterized in that: adopt following steps:

Step 1: at testee surface binding mark point, shot object from two different visual angles, and twice shooting have overlappingly, and the gauge point of lap has 3 at least, obtain respectively the three-dimensional coordinate of gauge point under two visual angles, wherein the gauge point three-dimensional coordinate matrix under visual angle A shooting is P _a, the gauge point three-dimensional coordinate matrix under visual angle B takes is P _b;

Step 2: the gauge point three-dimensional coordinate matrix P two visual angles shootings that obtain from step 1 _a=[p ₁, p ₂... p _i..., p _n] ^t, P _b=[q ₁, q ₂... q _j..., q _m] ^tin find out the identical point under the frame of reference, matrix P wherein _ain element p _i={ x _pi, y _pi, z _pi, { x _pi, y _pi, z _pibe a p _icoordinate under the A coordinate system of visual angle, matrix P _bin element q _j={ x _qj, y _qj, z _qj, { x _qj, y _qj, z _qjbe a q _jcoordinate under the B coordinate system of visual angle:

According to matrix P _abuild distance matrix dA, wherein

The element da of matrix dA _ijrepresenting matrix P _ain element p _iand p _jdistance; According to matrix P _bbuild distance matrix dB, wherein

The element db of matrix dB _ijrepresenting matrix P _bin element q _iand q _jdistance;

Each row in every a line of matrix dA and matrix dB is contrasted, and the number of identical element in two row that obtain comparing, further obtain the two row da that identical element is maximum _rwith db _s, representing matrix P _ar point and matrix P _bthe s point be the same point under the frame of reference, i.e. first group of corresponding point; Described identical element refers to that the difference of the element value of two elements is less than the three-dimensional coordinate extraction accuracy;

Step 3: by matrix P _arevise: by P _ain capable the 1st row of mentioning of r, by P _ain the former the 1st walk to that former r-1 is capable to be reduced to the 2nd to walk to r capable, obtain new gauge point coordinate set matrix P _a1; By P _a1point and P that middle the first row means _a1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _a,

Wherein

element sa _ijexpression is by P _a1point and P that middle the first row means _a1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _aturn to upper triangular matrix T _a;

By matrix P _brevise: by P _bin capable the 1st row of mentioning of s, by P _bin the former the 1st walk to that former s-1 is capable to be reduced to the 2nd to walk to s capable, obtain new gauge point coordinate set matrix P _b1, by P _b1point and P that middle the first row means _b1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _b,

Wherein

sb _ijexpression is by P _b1point and P that middle the first row means _b1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _bturn to upper triangular matrix T _b;

Step 4: by T _ain each nonzero element and T _bin each nonzero element make comparisons, if T wherein _amiddle element T _athe triangle of (i, j) representative and T _bmiddle element T _bthe triangle area compatibility of (r, t) representative and length of side compatibility, by matrix P _a1in the capable and capable corresponding point of j+1 of i+1 put into P _a1correspondence markings point set pA1 in, by matrix P _b1in the capable and capable corresponding point of t+1 of r+1 put into P _b1correspondence markings point set pB1 in, wherein area is compatible as follows with the compatible determination methods of the length of side:

Set area relative error limit ε _sif meet

t is described _athe triangle of (i, j) representative and T _bthe triangle area compatibility of (r, t) representative;

T _athe limit of first group of corresponding point of leg-of-mutton two mistakes of (i, j) representative is L _a(i, 1), L _a(j, 1), T _bthe limit of first group of corresponding point of leg-of-mutton two mistakes of (r, t) representative is L _b(r, 1), L _b(t, 1), if

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(r,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(t,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, and

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(r,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(t,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, mean T _athe triangle of (i, j) representative and T _bthe triangle length of side compatibility of (r, t) representative, wherein ε _lmean length relative error limit;

Step 5: by improved least square method obtain under two visual angles correspondence markings point between transition matrix R and T:

Compute matrix P _a1correspondence markings point set pA1={p _i| p _i∈ pAl, i=1,2 ... the barycenter C of N} _pwith matrix P _b1correspondence markings point set pB1={q _i| q _i∈ pB1, i=1,2 ... the barycenter C of N} _q; Correspondence markings in pA1 and pB1 point is done with respect to the translation of barycenter separately $\left\{\begin{array}{c}{\mathrm{\&alpha;}}_i=p_i-C_p\\ {\mathrm{\&beta;}}_i=q_i-C_q\end{array}\right.,$ Make C ₁=[α ₁, α ₂... α _i... α _n] ^t, C ₂=[β ₁, β ₂... β _i... β _n] ^t, solving equation C ₁r=C ₂minimum least square solution, and obtain

meet objective function

minimize, and obtain translation vector T=C _q-RC _p.

Beneficial effect

Adopt method of the present invention, effectively eliminated correspondence markings point matching error, improve the efficiency of coupling and the robustness of depth data registration.

The accompanying drawing explanation

Fig. 1: left and right two pictures under the A of visual angle;

Fig. 2: left and right two pictures under the B of visual angle;

Fig. 3: the hierarchical searching method diagram of " point-face-limit-point ";

Fig. 4: the average error skew diagram of three kinds of joining methods under random noise average 0.05;

Fig. 5: the average error skew diagram of three kinds of joining methods under random noise average 0.1.

Embodiment

Below in conjunction with specific embodiment, the present invention is described:

A kind of improved depth data joining method based on least square method in the present embodiment adopts following steps:

Step 1: build experiment porch, on surface, tested tool box, paste the non-coding gauge point.Demarcate two cameras (model DMK-21BUO4) and obtain inside and outside parameter, take tool box with two cameras simultaneously, obtain left and right two pictures under the A of first visual angle, as shown in Figure 1, extract the gauge point two-dimensional coordinate of left and right two figure, then carry out the two dimension coupling, obtain the three-dimensional coordinate of gauge point under this coordinate system by trigonometry, the gauge point three-dimensional coordinate matrix formed under visual angle A shooting is P _a, separate the depth data that phase place obtains Xia tool box, this visual angle.Take tested tool box left and right two figure under two cameras of translation or tested tool box ，Cong visual angle B, as shown in Figure 2, solve the three-dimensional coordinate of gauge point taken under the B of visual angle, the gauge point three-dimensional coordinate matrix formed under visual angle B shooting is P _b, and separate the depth data that phase place obtains tool box under this visual angle.Wherein under visual angle A and visual angle B, take have overlapping, at least 3 of the gauge points of lap.

Step 2: the gauge point three-dimensional coordinate matrix P two visual angles shootings that obtain from step 1 _a=[p ₁, p ₂... p _i..., p _n] ^t, P _b=[q ₁, q ₂... q _j..., q _m] ^tin find out the identical point under the frame of reference, matrix P wherein _ain element p _i={ x _pi, y _pi, z _pi, { x _pi, y _pi, z _pibe a p _icoordinate under the A coordinate system of visual angle, matrix P _bin element q _j={ x _qj, y _qj, z _qj, { x _qj, y _qj, z _qjbe a q _jcoordinate under the B coordinate system of visual angle:

According to matrix P _abuild distance matrix dA, wherein

The element da of matrix dA _ijrepresenting matrix P _ain element p _iand p _jdistance; According to matrix P _bbuild distance matrix dB, wherein

The element db of matrix dB _ijrepresenting matrix P _bin element q _iand q _jdistance;

Each row in every a line of matrix dA and matrix dB is contrasted, and the number of identical element in two row that obtain comparing, further obtain the two row da that identical element is maximum _rwith db _s, representing matrix P _ar point and matrix P _bthe s point be the same point under the frame of reference, i.e. first group of corresponding point; Described identical element refers to that the difference of the element value of two elements is less than the three-dimensional coordinate extraction accuracy.

Step 3: by matrix P _arevise: by P _ain capable the 1st row of mentioning of r, by P _ain the former the 1st walk to that former r-1 is capable to be reduced to the 2nd to walk to r capable, obtain new gauge point coordinate set matrix P _a1; By P _a1point and P that middle the first row means _a1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _a,

Wherein

element sa _ijexpression is by P _a1point and P that middle the first row means _a1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _aturn to upper triangular matrix T _a;

By matrix P _brevise: by P _bin capable the 1st row of mentioning of s, by P _bin the former the 1st walk to that former s-1 is capable to be reduced to the 2nd to walk to s capable, obtain new gauge point coordinate set matrix P _b1, by P _b1point and P that middle the first row means _b1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _b,

Wherein sb _ijexpression is by P _b1point and P that middle the first row means _b1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _bturn to upper triangular matrix T _b.

Step 4: by T _ain each nonzero element and T _bin each nonzero element make comparisons, if T wherein _amiddle element T _athe triangle of (i, j) representative and T _bmiddle element T _bthe triangle area compatibility of (r, t) representative and length of side compatibility, by matrix P _a1in the capable and capable corresponding point of j+1 of i+1 put into P _a1correspondence markings point set pA1 in, by matrix P _b1in the capable and capable corresponding point of t+1 of r+1 put into P _b1correspondence markings point set pB1 in, wherein area is compatible as follows with the compatible determination methods of the length of side:

Set area relative error limit ε _sif meet

t is described _athe triangle of (i, j) representative and T _bthe triangle area compatibility of (r, t) representative;

T _athe limit of first group of corresponding point of leg-of-mutton two mistakes of (i, j) representative is L _a(i, 1), L _a(j, 1), T _bthe limit of first group of corresponding point of leg-of-mutton two mistakes of (r, t) representative is L _b(r, 1), L _b(t, 1), if

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(r,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(t,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, and

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(r,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(t,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, mean T _athe triangle of (i, j) representative and T _bthe triangle length of side compatibility of (r, t) representative, wherein ε _lmean length relative error limit.

Step 5: by improved least square method obtain under two visual angles correspondence markings point between transition matrix R and T, realize the splicing of depth data:

The correspondence markings point set pA1={p of compute matrix PA1 _i| p _i∈ pA1, i=1,2 ... the barycenter C of N} _pwith matrix P _b1correspondence markings point set barycenter C _q, the geometrical mean that three coordinates of barycenter described here are each element respective coordinates in the set of respective markers point; Correspondence markings in pA1 and pB1 point is done with respect to the translation of barycenter separately $\left\{\begin{array}{c}{\mathrm{\&alpha;}}_i=p_i-C_p\\ {\mathrm{\&beta;}}_i=q_i-C_q\end{array}\right.,$ Make C ₁=[α ₁, α ₂... α _i... α _n] ^t, C ₂=[β ₁, β ₂... β _i... β _n] ^t, solving equation C1R=C ₂minimum least square solution, and obtain

meet objective function

minimize, and obtain translation vector T=C _q-RC _p.

The set pA1 that obtains in step 4 and set pB1 are added to random noise, by the improved least square method of step 5 and SVD method and least square method in the situation that the same comparison of random noise average stitching error drift condition, as shown in Figure 4 and Figure 5.

In actual measurement environment, grating is incident upon the testee surface, and camera is taken testee, and the noisy existence of meeting, affect the extraction accuracy at gauge point center and follow-up splicing precision.By contrast improved least square method with SVD method and least square method the error deviation figure in the consistent situation of noise average, can clearly find: improved least square method is in the situation that the random noise existence, the stitching error variation range is less, and precision all can remain on below the random noise average, precision is higher, noise is had to better robustness, be applicable to practical engineering application.Institute of the present invention elaboration method has improved accuracy and the real-time of correspondence markings point coupling, has overcome the unstable and low problem of precision of stitching error that exists under noise situations.

Claims (1)

1. the improved depth data joining method based on least square method is characterized in that: adopt following steps:

Step 1: at testee surface binding mark point, shot object from two different visual angles, and twice shooting have overlappingly, and the gauge point of lap has 3 at least, obtain respectively the three-dimensional coordinate of gauge point under two visual angles, wherein the gauge point three-dimensional coordinate matrix under visual angle A shooting is P _a, the gauge point three-dimensional coordinate matrix under visual angle B takes is P _b;

Step 2: the gauge point three-dimensional coordinate matrix P two visual angles shootings that obtain from step 1 _a=[p ₁, p ₂... p _i..., p _n] ^t, P _b=[q ₁, q ₂... q _j..., q _m] ^tin find out the identical point under the frame of reference, matrix P wherein _ain element p _i={ x _pi, y _pi, z _pi, { x _pi, y _pi, z _pibe a p _icoordinate under the A coordinate system of visual angle, matrix P _bin element q _j={ x _qj, y _qj, z _qj, { x _qj, y _qj, z _qjbe a q _jcoordinate under the B coordinate system of visual angle:

According to matrix P _abuild distance matrix dA, wherein

The element dai of matrix dA _jrepresenting matrix P _ain element p _iand p _jdistance; According to matrix P _bbuild distance matrix dB, wherein

The element dbi of matrix dB _jrepresenting matrix P _bin element q _iand q _jdistance;

Each row in every a line of matrix dA and matrix dB is contrasted, and the number of identical element in two row that obtain comparing, further obtain the two row da that identical element is maximum _rwith db _s, representing matrix P _ar point and matrix P _bthe s point be the same point under the frame of reference, i.e. first group of corresponding point; Described identical element refers to that the difference of the element value of two elements is less than the three-dimensional coordinate extraction accuracy;

Step 3: by matrix P _arevise: by P _ain capable the 1st row of mentioning of r, by P _ain the former the 1st walk to that former r-1 is capable to be reduced to the 2nd to walk to r capable, obtain new gauge point coordinate set matrix P _a1; By P _a1point and P that middle the first row means _a1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _a,

Wherein

element sa _ijexpression is by P _a1point and P that middle the first row means _a1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _aturn to upper triangular matrix T _a;

By matrix P _brevise: by P _bin capable the 1st row of mentioning of s, by P _bin the former the 1st walk to that former s-1 is capable to be reduced to the 2nd to walk to s capable, obtain new gauge point coordinate set matrix P _b1, by P _b1point and P that middle the first row means _b1in the point of other any two line displays form triangle, and obtain triangle area, form the area matrix S _b,

Wherein

sb _ijexpression is by P _b1point and P that middle the first row means _b1in the triangle area that forms of the point of the capable and j+1 line display of i+1; By S _bturn to upper triangular matrix T _b;

Step 4: by T _ain each nonzero element and T _bin each nonzero element make comparisons, if T wherein _amiddle element T _athe triangle of (i, j) representative and T _bmiddle element T _bthe triangle area compatibility of (r, t) representative and length of side compatibility, by matrix P _a1in the capable and capable corresponding point of j+1 of i+1 put into P _a1correspondence markings point set pA1 in, by matrix P _b1in the capable and capable corresponding point of t+1 of r+1 put into P _b1correspondence markings point set pB1 in, wherein area is compatible as follows with the compatible determination methods of the length of side:

Set area relative error limit ε _sif meet

t is described _athe triangle of (i, j) representative and T _bthe triangle area compatibility of (r, t) representative;

T _athe limit of first group of corresponding point of leg-of-mutton two mistakes of (i, j) representative is L _a(i, 1), L _a(j, 1), T _bthe limit of first group of corresponding point of leg-of-mutton two mistakes of (r, t) representative is L _b(r, 1), L _b(t, 1), if

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(r,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(i,1)-L_B(t,1)}{L_A(i,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, and

$-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(r,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ With $-{\mathrm{\&epsiv;}}_l<\frac{L_A(j,1)-L_B(t,1)}{L_A(j,1)}<{\mathrm{\&epsiv;}}_l$ At least one establishment, mean T _athe triangle of (i, j) representative and T _bthe triangle length of side compatibility of (r, t) representative, wherein ε _lmean length relative error limit;

Step 5: by improved least square method obtain under two visual angles correspondence markings point between transition matrix R and T:

Compute matrix P _a1correspondence markings point set pA1={p _i| p _i∈ pA1, i=1,2 ... the barycenter C of N} _pwith matrix P _b1correspondence markings point set pB1={q _i| q _i∈ pB1, i=1,2 ... the barycenter C of N} _q; Correspondence markings in pA1 and pB1 point is done with respect to the translation of barycenter separately $\left\{\begin{array}{c}{\mathrm{\&alpha;}}_i=p_i-C_p\\ {\mathrm{\&beta;}}_i=q_i-C_q\end{array}\right.,$ Make C ₁=[α ₁, α ₂... α _i... α _n] ^t, C ₂=[β ₁, β ₂... β _i... β _n] ^t, solving equation C ₁r=C ₂minimum least square solution, and obtain meet objective function

minimize, and obtain translation vector T=C _q-RC _p.

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