CN102980529A - Part shape difference detection method based on multi-scale mesh vertex average gradient - Google Patents

Abstract

The invention discloses a part shape difference detection method based on multi-scale mesh vertex average gradient, which mainly solves the problems that only simple geometrical shape features can be detected and the detection scale is single in the prior art. The method comprises the following steps: firstly, fixing control group Cg and study group Sg samples to prepare all parts, and obtaining three-dimensional images after scanning, secondly, obtaining a triangular mesh of each part through triangulation, thirdly, calculating the vertex average gradient Qp of all vertexes in K scale meshes of all samples of the control group Cg and the study group Sg, fourthly, performing two-sample T-detection to the vertex average gradient Qp, and obtaining a shape difference vertex group J after two times of screening, and fifthly, calculating vectors describing the size, the position and the reliability of shape difference aiming at vertexes in the group J. The method has the advantages of complete scales, accuracy, reliability and high anti-noise property, and is applicable to the shape defect screening and determination between two groups of part samples with different attributes.

Description

External Shape difference detecting method based on multiple dimensioned grid vertex mean inclination

Technical field

The invention belongs to the computer graphical field of measuring technique, the shape difference that relates to rejected part detects, a kind of External Shape group difference detection method based on multiple dimensioned grid vertex mean inclination specifically can be used for the occasion such as appearance defect examination or examination between the group of two groups of part samples with different attribute.

Background technology

Along with the development of science and technology and the raising of social demand, accuracy requirement to the object part of the industries such as machining in the actual production life is more and more higher, except the high-precision requirement to simple physical dimension, also day by day urgent to the accuracy requirement of shape simultaneously.This just requires in process of production, except detecting the conventional physical dimension of part, also needs the shape of part is carried out Difference test, thereby the level of crudy or processing technology is made measurement and judgement.But when the body form more complicated or when irregular, can't use simply geometry parameter, describe such as length, the shape difference of complex object also can't characterize and describe with simple dimensional measurement.

Existing 3 d part shape detecting method, mainly comprise two large classes: (1) contact type measurement, Typical Representative are coordinate measuring machine (CMM), and there is a lot of restrictions in this measuring method: sweep velocity is subject to the restriction of mechanical motion, measuring speed is slow, and needs the planning survey path before measuring; Bad to the soft material measurement effect, can't measure the impalpable surface of gauge head, such as endoporus, also can't measure the zone of the geometric properties such as some edges, wedge angle, very high to environmental requirement.Be difficult to satisfy current high-level efficiency, high precision, the detection of large profile shape needs.(2) non-contact measurement: Typical Representative is optical measuring method, and optical measuring method can be divided into two large classes according to the basic skills of obtaining three-dimensional information: passive type and active two large classes.Passive type is under the natural light condition, obtains the three-dimensional information of object by the 2-D gray image of the optical sensors such as video camera picked-up; Active is to utilize special controlled light source irradiation measured object, according to the three-dimensional information of the known structure acquisition of information scenery of active light source.The non-contact type measuring method precision is low, and the ability of its reliability and opposing random noise also needs to improve.

In addition, comprise that in employing said method carries out often can't knowing in advance size or the yardstick of shape difference, thereby usually can't selecting the detection method of appropriate yardstick in the process of 3 d part detection.At present usually determine yardstick according to subjective experience or according to the precision of survey instrument, can't portray all-sidedly and accurately shape difference, do not possess multiple dimensioned characteristic, may have the difference of omitting on certain yardstick.

In sum, the shape difference of the irregular three-D part that existing method can't detection of complex, large multiple dimensioned single, can't be quantitatively, describe out the irregularly shaped difference of complexity location and dimensioning.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of External Shape difference detecting method based on multiple dimensioned grid vertex mean inclination is proposed, with the limitation that only can detect specific simple feature that overcomes common mesh shape difference detecting method with detect the shortcoming that is confined to single yardstick, realizes that the part sample shape difference of or complex appearance irregular to two groups is carried out quantitatively, the accurate detection in location and dimensioning ground.

For achieving the above object, the present invention mainly may further comprise the steps:

C _gThe x axial coordinate mean value of interior all sample respective vertices, T _yControl group C _gThe y axial coordinate mean value of interior all sample respective vertices, T _zControl group C _gThe z axial coordinate mean value of interior all sample respective vertices, and

$T_x=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\Σ}}}{p}_x^m,$ $T_y=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\Σ}}}{p}_y^m,$ $T_z=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\Σ}}}{p}_z^m,p\∈J---1)$

In the formula

The x axial coordinate of the summit p of m part,

The y axial coordinate of the summit p of m part, The z axial coordinate of the summit p of m part, C _nBe control group C _gThe number of interior all part samples;

(10) for each the summit p in the difference vertex set J, calculate the summit mean inclination Q on this summit _pLevel of significance value g and the yardstick k at this place, summit, consist of the fiduciary level vector F=(k, g) that characterizes shape difference;

(11) jointly depict control group C with big or small vectorial U, position vector T and these three vectors of fiduciary level vector F _gWith the S of seminar _gShape difference between two groups of samples, namely for certain summit on the particular dimensions, depict on this summit the size of part shape difference between two groups of samples with the vectorial U of size, describe on this summit the position at part shape difference place between two groups of samples with position vector T, be described in the reliability that there is significant difference in shape under the mean inclination index of summit with fiduciary level vector F.

The present invention has following advantage compared with prior art:

(1) the present invention can check the appearance difference between the sample group effectively by the group difference of the summit mean inclination value of two groups of samples that possess different attribute relatively;

(2) the postsearch screening link of the present invention's employing can guarantee that the summit that detects concentrates on one or several zone, has improved the reliability of testing result and the ability of opposing random noise;

(3) the present invention is because by big or small vectorial U, position vector T and these three vectors of fiduciary level vector F depict control group C jointly _gWith the S of seminar _gShape difference between two groups of samples provides size, position, yardstick and the reliability information of shape difference, and testing result is complete accurately, and reliability is high.

Description of drawings

Fig. 1 is general flow chart of the present invention;

Fig. 2 is triangle gridding subdivision synoptic diagram of the present invention;

Fig. 3 is that the present invention calculates apart from d _pSynoptic diagram;

Fig. 4 is summit mean inclination Q of the present invention _pCalculate synoptic diagram.

Embodiment

With reference to Fig. 1, performing step of the present invention is as follows:

The first step is divided into two groups with all part samples, is called control group C _gWith the S of seminar _g

In this step, all part samples are divided according to the different attribute that has separately, such as being the processing that comes from two different machines, although perhaps selected different constituent materials from same machine, be divided into control group C according to actual needs _gWith the S of seminar _g

When dividing the sample group, the number of two groups of samples will equate or approach that this is accuracy and reliability in order to ensure the result who adopts the statistical method analysis to obtain.

Second step, according to geometric properties with control group C _gWith the S of seminar _gAll parts are registration in same rectangular coordinate system.

In this step, all samples comprise control group sample and seminar's sample, all must carry out registration in same three-dimensional cartesian coordinate system.In the specific implementation process, at first selected coordinate system is set one group of registration marks, then accurately registration marks is adjusted to same position in the coordinate system by rigid motions such as translation, rotations between different samples; For convenience's sake, usually select simple and stable geometric properties as the sign in the registration process, such as the border of part, the intersection on plane and the intersection point of intersection; In addition, area-of-interest during these geometric properties that are elected to be registration marks must detect with this shape difference is irrelevant, be in the testing process these geometric properties not to be carried out shape difference to detect, can assert that perhaps there is not shape difference in these geometric properties between two groups of samples.

In the 3rd step, all parts to behind the registration scan with three-dimensional camera, obtain the 3-D view of part.

In this step, use control group and seminar's sample after the three-dimensional camera shooting machine part scans registration, obtain simultaneously including the 3-D view of locus and depth information.In concrete implementation process, for guaranteeing the error consistency of scanning result, preferably select the video camera with equal resolution and imaging parameters to scan.According to actual needs, if the purpose of Detection task only is the shape difference that detects in the single view of part shape, then by can being met the 3-D view of requirement to the single pass of part, and camera position remains unchanged when scanning different part.

Because more situation is to carry out Difference test to the monnolithic case of part, then must carry out to each part the 3-D scanning of multi-angle, in the scanning process to each angle, position and the parameter of video camera all remain unchanged; With the multi-angle scanning result by coordinate system conversion and geometric transformation after, obtain the whole 3-D view of sample.In the multi-angle scanning process, can adopt same video camera to finish, also can adopt the some video cameras with identical parameters to finish.

The 4th step, according to the 3-D view of part, adopt step by step subdivision method of triangular mesh, set up control group C _gWith the S of seminar _gThe triangular mesh of interior each part.

With reference to Fig. 2, being implemented as follows of this step:

(4a) select the initial level triangular mesh, and be defined as the 0th grade of triangular mesh, be designated as G ₀, G ₀Be coarse grids, the initial level triangular mesh is here selected regular polygon usually, such as the regular dodecahedron with 12 summits;

(4b) initial triangle gridding is carried out L level subdivision, setting the total progression of subdivision is L, L 〉=1, and its subdivision process is to increase a j level grid vertex newly, newly-increased grid vertex P between certain two adjacent vertex in j-1 level grid _jTo make as much as possible the grid 3-D view outline of Approximation of 3 D part more accurately behind the subdivision.The total progression L of subdivision can determine according to the full accuracy of actual needs and 3-D view.Total progression of subdivision is more, and the grid that then obtains behind the subdivision has more summits and little triangle, and grid is more accurate to the sign of entity component, such as, total number of vertex of the grid behind the regular dodecahedron process f level subdivision is 10 * 4 ^f+ 2, the triangle number is 20 * 4 ^f, 0≤f≤L.Need to prove that be subject to the precision of the 3-D view that obtains in the 3rd step and the restriction of resolution, the total progression of subdivision is not more high better.

(4c) will increase grid vertex P newly _jMerge with existing summit, obtain j level triangular mesh G _j, then have:

G _j=G _j-1UP _j，1≤j≤L 2）

Wherein U represents the union of sets computing, and j is called grid G _jYardstick, obviously at the G that obtains later on through L subdivision _LBe fine grid blocks.In this step, except the merging on summit, also need to re-construct out triangle on the grid according to spatial relation.

In the 5th step, remember j level triangle gridding G _jIn arbitrarily the summit be p, the set that the summit in the 1-ring neighborhood of definition summit p consists of is E _p

The 6th step is with set E _pAll interior summits structures obtain a plane f _p

(6a) establish plane f _pEquation be z=a ₀X+a ₁Y+a ₂, a wherein ₀, a ₁, a ₂Be plane undetermined coefficient, a ₀Be the undetermined coefficient of x, a ₁Be the undetermined coefficient of y, a ₂Be the undetermined coefficient of constant term, x, y are independent variable, and z is dependent variable;

(6b) for determining plane undetermined coefficient a ₀, a ₁, a ₂, construction set E _pAll interior summits are to plane f _pSkew sum of squares function S:

$S=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(a_0{x}_i+a_1{y}_i+a_2-z_i)}^2,---3)$

(x wherein _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n, n is set E _pThe number on middle summit;

(6c) according to minimizing decision method, utilize function S respectively to plane undetermined coefficient a ₀, a ₁, a ₂Ask local derviation, obtain following system of equations:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)x_i=0\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)y_i=0\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)=0\end{array}\right.$

Wherein, (x _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n;

(6d) separate top system of equations and obtain plane undetermined coefficient a ₀, a ₁, a ₂For:

$\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left[\begin{array}{ccc}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i& n\end{array}\right]}^{-1}\left(\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i\end{array}\right),---4)$

Wherein [] ^-1The inverse matrix of representing matrix [];

(6e) with plane undetermined coefficient a ₀, a ₁, a ₂Substitution plane f _pEquation z in, namely obtained the plane f that will construct _p, gather E this moment _pAll interior summits are to plane f _pSkew sum of squares function S be minimal value.

The 7th step is with set E _pAll interior summits structures obtain an approximate circle C _p

(7a) establish Spherical Surface S _pEquation be x ²+ y ²+ z ²-Ax-By-Cz+D=0, A wherein, B, C, D are the sphere undetermined coefficient, and A is the undetermined coefficient of x, and B is the undetermined coefficient of y, and C is the undetermined coefficient of z, and D is the undetermined coefficient of constant term, and x, y are independent variable, and z is dependent variable;

(7b) for determining sphere undetermined coefficient A, B, C, D, construction set E _pAll interior summits are to Spherical Surface S _pSkew sum of squares function V:

$V=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{({x_i}^2+{y_i}^2+{z_i}^2-A{x}_i-B{y}_i-C{z}_i+D)}^2,---5)$

(x wherein _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n, n is set E _pThe number on middle summit;

(7c) according to minimizing decision method, adopt matrix method respectively to the sphere undetermined coefficient A among the function V, B, C, D asks local derviation, obtains following system of equations:

$\left[\begin{array}{ccccccc}{x}_1& & y_1& & z_1& & -1\\ & \·& & \·& \·& \·& \\ & \·& & \·& \·& \·& \\ & \·& & \·& \·& \·& \\ x_n& & y_n& & z_n& & -1\end{array}\right]\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]=\left[\begin{array}{c}{x}_1^2+y_1^2+z_1^2\\ \·\\ \·\\ \·\\ x_n^2+y_n^2+z_n^2\end{array}\right],$

(7d) separate top system of equations and obtain sphere undetermined coefficient A, B, C, D is:

$\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]={\left[\begin{array}{cccc}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{z}_i& -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i^2& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{z}_i& -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{z}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{z}_i& \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i^2& -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i\\ -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i& -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i& -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i& n\end{array}\right]}^{-1}\left[\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i(x_i^2+y_i^2+z_i^2)\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i(x_i^2+y_i^2+z_i^2)\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i(x_i^2+y_i^2+z_i^2)\\ -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i^2+y_i^2+z_i^2)\end{array}\right]---6)$

Wherein [] ^-1The inverse matrix of representing matrix [], wherein (x _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n, n is set E _pThe number on middle summit;

(7e) with sphere undetermined coefficient A, B, C, D substitution Spherical Surface S _pEquation

x ²+ y ²+ z ²Among-the Ax-By-Cz+D=0, namely obtained the Spherical Surface S that to construct _p, Spherical Surface S _pWith plane f _pIntersection be the approximate circle C that will construct _p

In the 8th step, calculate summit p to plane f _pApart from d _p

Obtained plane f by the 6th step _pEquation z=a ₀X+a ₁Y+a ₂, with reference to accompanying drawing 3, appoint 1 q in the face of making even, establish its coordinate and be (x ', y ', z '), z '=a is then arranged ₀X '+a ₁Y '+a ₂If the coordinate of summit p is (x _p, y _p, z _p), connect Vertex p and q point, and cross the q point and be plane f _pUnit normal vector

Required summit p is to plane f _pApart from d _pBe vector

With

The inner product numerical values recited, that is:

$d_p=|<\stackrel{\&RightArrow;}{\mathrm{pq}},\stackrel{\&RightArrow;}{n}>|=\frac{|a_0(x_p-x^{\&prime;})+a_1(y_p-y^{\&prime;})-(z_p-z^{\&prime;})|}{\sqrt{{a_0}^2+{a_1}^2+1}}$

$=\frac{|a_0{x}_p+a_1{y}_p-z_p-(a_0{x}^{\&prime;}+a_1{y}^{\&prime;}-z^{\&prime;})|}{\sqrt{{a_0}^2+{a_1}^2+1}}$

$=\frac{|a_0{x}_p+a_1{y}_p-z_p+a_2|}{\sqrt{{a_0}^1+{a_1}^2+1}}.$

In the 9th step, calculate approximate circle C _pRadius R _p

(9a) calculate Spherical Surface S _pThe centre of sphere to plane f _pApart from d ₀, go on foot the Spherical Surface S that obtains by the 7th _pEquation as can be known the coordinate of the centre of sphere be

According to the 8th summit p that obtain of step to plane f _pApart from d _pComputing formula can get the centre of sphere to plane f _pApart from d ₀For:

$d_0=\frac{|a_{0}A+a_{1}B-C+2a_2|}{2\sqrt{{a_0}^2+{a_1}^2+1}};---7)$

The Spherical Surface S that (9b) is obtained by the 7th step _pEquation Spherical Surface S as can be known _pRadius be

$r=\sqrt{{\left(\frac{A}{2}\right)}^2+{\left(\frac{B}{2}\right)}^2+{\left(\frac{C}{2}\right)}^2-D},$

According to Pythagorean theorem, calculate approximate circle C _pRadius R _pFor:

$R_p=\sqrt{r^2-{d_0}^2}.---8)$

In the tenth step, arrive plane f according to summit p _pApart from d _pAnd Spherical Surface S _pRadius R _p, with reference to accompanying drawing 4, calculate the summit mean inclination Q of summit p _pFor:

$Q_p=\frac{d_p}{R_p}.---9)$

The 11 step is to the summit mean inclination Q on each summit on each yardstick grid _pValue is carried out two sample T-checks, goes out difference vertex set J on each yardstick by following formula preliminary screening ₀:

$J_0=\{V_{L-H+1}^0,...,V_k^0,...,V_L^0\},(L-H+1)\&le;k\&le;L---10)$

Wherein, L is total progression of subdivision, and the progression that H analyzes for carrying out shape difference, 1≤H≤L, k are the yardstick that need to carry out the grid of shape difference analysis,

Control group C _gWith the S of seminar _gHave the subset that the summit of significant difference consists of at the k yardstick between two groups of samples,

(L-H+1)≤k≤L,

In the formula, s is k yardstick grid G _kInterior arbitrary summit,

Control group C _gThe summit mean inclination value of summit s on the k yardstick on interior all sample grid,

The S of seminar _gThe summit mean inclination value of summit s on the k yardstick on interior all sample grid, sig () expression is carried out the level of significance value that two sample T-checks obtain to given two vectors, and α is setting level of significance threshold value, 0＜α≤0.05.

The 12 step is to difference vertex set J ₀In the summit carry out postsearch screening, namely according to difference vertex set J ₀The zone that the interior summit that is connected with summit p consists of and given threshold value T _N=t, t〉1, p is handled as follows to the summit:

If difference vertex set J ₀In zone of summit formation of being connected with summit p, and the number on the summit that comprises in should the zone is more than or equal to given threshold value T _N, then keep summit p;

If difference vertex set J ₀In zone of summit formation of being connected with summit p, but the number on the summit that comprises in should the zone is less than given threshold value T _N, then summit p is deleted;

If difference vertex set J ₀The interior summit that is connected with summit p does not consist of a zone, and then summit p is deleted.

In the 13 step, for each summit p in the set J, calculate respectively control group C _gWith the S of seminar _gThe mean inclination Q on this summit in two groups of samples _pAverage and the standard deviation of value consist of the size vector that characterizes shape difference Wherein k is the yardstick of p place, summit grid,

That summit p is at control group C _gIn summit mean inclination Q _pAverage,

That summit p is at control group C _gIn summit mean inclination Q _pStandard deviation,

That summit p is at control group S _gIn summit mean inclination Q _pAverage,

That summit p is at control group S _gIn summit mean inclination Q _pStandard deviation.

Need to prove that average and standard deviation are statistical characteristic values the most frequently used in the statistics, these two characteristic quantities can rationally and effectively reflect control group C _gWith the S of seminar _gMiddle summit mean inclination Q _pThe reasonable fiducial interval of value, thus can depict quantitatively the size cases of the shape difference of respective vertices between two groups of samples.

In the 14 step, for each summit p in the set J, calculate control group C _gThe coordinate mean value of interior all sample respective vertices consists of the position vector T=(k, the T that characterize shape difference _x, T _y, T _z),

Wherein, k is the yardstick of p place, summit grid, T _xControl group C _gThe x axial coordinate mean value of interior all sample respective vertices, T _yControl group C _gThe y axial coordinate mean value of interior all sample respective vertices, T _zControl group C _gThe z axial coordinate mean value of interior all sample respective vertices, and:

$T_x=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_x^m,$ $T_y=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_y^m,$ $T_z=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_z^m,p\&Element;J---11)$

Wherein,

The x axial coordinate of the summit p of m part,

The y axial coordinate of the summit p of m part,

The z axial coordinate of the summit p of m part, C _nBe control group C _gThe number of interior all part samples.

The sample in the control group has only been used in the calculating of position vector because control group normally organize between relatively the time as one group of sample of standard, the position that the position vector that obtains like this characterizes is clearer and more definite, also more convincing.

The 15 step, for each summit p in the set J, select the yardstick at this summit level of significance value that calculates and this place, summit in the 7th step, consist of the fiduciary level vector F=(k, g) that characterizes shape difference,

Wherein, k is the corresponding yardstick in this summit, and g is the upper mean inclination Q of summit p _pThe level of significance value of two sample T-checks between the group of value.

Need to prove, for specific certain summit, its mean inclination Q _pValue may be calculated under several yardsticks, thereby this summit may show statistically significant difference at several yardsticks.

In addition, based on statistics general knowledge, level of significance numerical value is less to mean that the possibility with significant difference is larger, thereby the mean inclination Q on summit _pResulting level of significance value when sample compares between the group of value can reflect that there is the reliability of significant difference really in this place, summit.

In the 16 step, jointly depict control group C with big or small vectorial U, position vector T and these three vectors of fiduciary level vector F _gWith the S of seminar _gShape difference between two groups of samples namely depicts the size of part shape difference degree between two groups of samples with big or small vectorial U, describe the position at difference place with position vector T, describes yardstick and the reliability at difference place with fiduciary level vector F.Such as, suppose that summit 1 and summit 2 all are the summits in the set J, the summit mean inclination Q of all samples _pBe worth such as table 1:

The summit mean inclination Qp value of all samples of table 1

Control group C in the reckoner 1 _gWith the S of seminar _gThe summit mean inclination Q of two groups of samples _pAverage and the standard deviation of value are used for representing control group C _gWith the S of seminar _gThe size of the shape difference between two groups of samples is calculated control group C _gWith the S of seminar _gThe coordinate average weight on the summit of two groups of samples is used for representing control group C _gWith the S of seminar _gThe position of the shape difference between two groups of samples, and control group C in the his-and-hers watches 1 _gWith the S of seminar _gThe summit mean inclination Q of two groups of samples _pValue is carried out two sample T-checks, control group C _gWith the S of seminar _gSize, position and level of significance result such as the table 2 of the shape difference between two groups of samples:

The result of the size of table 2 shape difference, position and level of significance

As shown in Table 2, the level of significance value is 0.0010 and 0.0033, all meet the level of significance value less than 0.05 requirement, namely can think for summit 1, there is significant shape difference in two groups of samples at yardstick 6, and then there is significant shape difference in 2, the two groups of samples in summit at yardstick 5.

Need to prove, for all summits on the grid, all can calculate size vector, position vector and the fiduciary level vector of shape difference, but only have the summit among the set J that obtains through postsearch screening just to have practical significance.

One of ordinary skill in the art, according to content of the present invention and thought, the part that on embodiment, all may change, this description not should be understood to limitation of the present invention.

Claims (5)

1. the External Shape difference detecting method based on multiple dimensioned grid vertex mean inclination comprises the steps:

(1) part with different attribute is divided into two groups, is called control group C _gWith the S of seminar _g, the number of two groups of samples equates or approaches;

(2) set the three dimensions rectangular coordinate system, and according to geometric properties with all parts registration in the same coordinate system;

(3) with each part behind the three-dimensional camera scanning registration, obtain the 3-D view of part;

(4) adopt step by step subdivision method of triangular mesh, to initial level triangular mesh G ₀Carry out L level subdivision and obtain each rank G _j, 1≤j≤L, j are called grid G _jYardstick, and G _LBe fine grid blocks, G ₀Be coarse grids;

(5) note j level triangle gridding G _jIn arbitrarily the summit be p, the set that the summit in the 1-ring neighborhood of definition summit p consists of is E _p, and with gathering E _pAll interior summits are constructed respectively and are obtained a plane f _pWith approximate circle C _p, calculate respectively summit p to this plane f _pApart from d _pWith approximate circle C _pRadius R _p

(6) foundation is apart from d _pAnd radius R _p, the summit mean inclination Q of calculating summit p _pValue:

$Q_p=\frac{d_p}{R_p};---1)$

(7) to the summit mean inclination Q on each summit on each yardstick grid _pValue is carried out two sample T-checks, and preliminary screening goes out the difference vertex set J on each yardstick ₀, again to difference vertex set J ₀In the summit carry out postsearch screening, obtain difference vertex set J;

(8) for each the summit p in the difference vertex set J, calculate respectively control group C _gWith the S of seminar _gThe summit mean inclination Q on this summit in two groups of samples _pAverage and the standard deviation of value consist of the size vector that characterizes shape difference

Wherein k is the yardstick of p place, summit grid, That summit p is at control group C _gIn summit mean inclination Q _pThe average of value, That summit p is at control group C _gIn summit mean inclination Q _pThe standard deviation of value,

That summit p is at control group S _gIn summit mean inclination Q _pThe average of value,

That summit p is at control group S _gIn summit mean inclination Q _pThe standard deviation of value;

(9) for each the summit p in the difference vertex set J, calculate control group C _gThe coordinate mean value of interior all sample respective vertices consists of the position vector that characterizes shape difference: T=(k, T _x, T _y, T _z),

Wherein, k is the yardstick of p place, summit grid, T _xControl group C _gThe x axial coordinate mean value of interior all sample respective vertices, T _yControl group C _gThe y axial coordinate mean value of interior all sample respective vertices, T _zControl group C _gThe z axial coordinate mean value of interior all sample respective vertices, and

$T_x=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_x^m,$ $T_y=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_y^m,$ $T_z=\frac{1}{C_n}\underset{m=1}{\overset{C_n}{\mathrm{\&Sigma;}}}{p}_z^m,p\&Element;J---2)$

In the formula

The x axial coordinate of the summit p of m part,

The y axial coordinate of the summit p of m part,

The z axial coordinate of the summit p of m part, C _nBe control group C _gThe number of interior all part samples;

(10) for each the summit p in the difference vertex set J, calculate the summit mean inclination Q on this summit _pLevel of significance value g and the yardstick k at this place, summit, consist of the fiduciary level vector F=(k, g) that characterizes shape difference;

(11) jointly depict control group C with big or small vectorial U, position vector T and these three vectors of fiduciary level vector F _gWith the S of seminar _gShape difference between two groups of samples, namely for certain summit on the particular dimensions, depict on this summit the size of part shape difference between two groups of samples with the vectorial U of size, describe on this summit the position at part shape difference place between two groups of samples with position vector T, be described in the reliability that there is significant difference in shape under the mean inclination index of summit with fiduciary level vector F.

2. method according to claim 1 is used set E in the wherein said step (5) _pAll interior summits structures obtain a plane f _p, carry out as follows:

(5a) establish plane f _pEquation be z=a ₀X+a ₁Y+a ₂, a wherein ₀, a ₁, a ₂Be plane undetermined coefficient, a ₀Be the undetermined coefficient of x, a ₁Be the undetermined coefficient of y, a ₂Be the undetermined coefficient of constant term, x, y are independent variable, and z is dependent variable;

(5b) for determining plane undetermined coefficient a ₀, a ₁, a ₂, construction set E _pAll interior summits are to plane f _pSkew sum of squares function S:

$S=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(a_0{x}_i+a_1{y}_i+a_2-z_i)}^2,---3)$

(x wherein _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n, n is set E _pThe number on middle summit;

(5c) according to minimizing decision method, utilize function S respectively to plane undetermined coefficient a ₀, a ₁, a ₂Ask local derviation, obtain following system of equations:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)x_i=0\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)y_i=0\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}2(a_0{x}_i+a_1{y}_i+a_2-z_i)=0\end{array}\right.$

Wherein, (x _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n;

(5d) separate top system of equations and obtain plane undetermined coefficient a ₀, a ₁, a ₂For:

$\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left[\begin{array}{ccc}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y_i}^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& n\end{array}\right]}^{-1}\left(\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{z}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_i\end{array}\right),---4)$

Wherein [] ^-1The inverse matrix of representing matrix [];

(5e) with plane undetermined coefficient a ₀, a ₁, a ₂Substitution plane f _pEquation z in, namely obtained the plane f that will construct _p, gather E this moment _pAll interior summits are to plane f _pSkew sum of squares function S be minimal value.

3. method according to claim 1 is used set E in the wherein said step (5) _pAll interior summit matches obtain approximate circle C _p, carry out as follows:

(5f) establish Spherical Surface S _pEquation be x ²+ y ²+ z ²-Ax-By-Cz+D=0, A wherein, B, C, D are the sphere undetermined coefficient, and A is the undetermined coefficient of x, and B is the undetermined coefficient of y, and C is the undetermined coefficient of z, and D is the undetermined coefficient of constant term, and x, y are independent variable, and z is dependent variable;

(5g) for determining sphere undetermined coefficient A, B, C, D, construction set E _pAll interior summits are to Spherical Surface S _pSkew sum of squares function V:

$V=\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{({x_i}^2+{y_i}^2+{z_i}^2-A{x}_i-B{y}_i-C{z}_i+D)}^2,$

(x wherein _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n, n is set E _pThe number on middle summit;

(5h) according to minimizing decision method, adopt matrix method respectively to the sphere undetermined coefficient A among the function V, B, C, D asks local derviation, obtains following system of equations:

$\left[\begin{array}{ccccccc}{x}_1& & y_1& & z_1& & -1\\ & \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;& \\ & \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;& \\ & \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;& \\ x_n& & y_n& & z_n& & -1\end{array}\right]\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]=\left[\begin{array}{c}{x}_1^2+y_1^2+z_1^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_n^2+y_n^2+z_n^2\end{array}\right]$

(5i) separate top system of equations and obtain sphere undetermined coefficient A, B, C, D is:

$\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]={\left[\begin{array}{cccc}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{z}_i& -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i^2& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{z}_i& -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{z}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{z}_i& \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_i^2& -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_i\\ -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i& -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i& -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_i& n\end{array}\right]}^{-1}\left[\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i(x_i^2+y_i^2+z_i^2)\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i(x_i^2+y_i^2+z_i^2)\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{z}_i(x_i^2+y_i^2+z_i^2)\\ -\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(x_i^2+y_i^2+z_i^2)\end{array}\right]---5)$

Wherein [] ^-1The inverse matrix of representing matrix [], (x _i, y _i, z _i) for gathering E _pIn the coordinate on i summit, i=1,2 ... n;

(5j) with sphere undetermined coefficient A, B, C, D substitution Spherical Surface S _pEQUATION x ²+ y ²+ z ²Among-the Ax-By-Cz+D=0, namely obtained the Spherical Surface S that to construct _p, Spherical Surface S _pWith plane f _pIntersection be the approximate circle C that will construct _p

4. method according to claim 1, wherein the described preliminary screening of step (7) goes out the difference vertex set J on each yardstick ₀, undertaken by following formula:

$J_0=\{V_{L-H+1}^0,...,V_k^0,...,V_L^0\},$ (L-H+1)≤k≤L 6）

Wherein L is total progression of subdivision, and the progression that H analyzes for carrying out shape difference, 1≤H≤L, k are the yardstick that need to carry out the grid of shape difference analysis,

Control group C _gWith the S of seminar _gHave the subset that the summit of significant difference consists of at the k yardstick between two groups of samples,

(L-H+1)≤k≤L,

In the formula, s is k yardstick grid G _kInterior arbitrary summit,

Control group C _gThe summit mean inclination value of summit s on the k yardstick on interior all sample grid,

The S of seminar _gThe summit mean inclination value of summit s on the k yardstick on interior all sample grid, sig () expression is carried out the level of significance value that two sample T-checks obtain to given two vectors, and α is setting level of significance threshold value, 0＜α≤0.05.

5. method according to claim 1, wherein step (7) is described to difference vertex set J ₀In the summit carry out postsearch screening, carry out as follows:

(7a) according to difference vertex set J ₀The zone that the interior summit that is connected with summit p consists of and given threshold value T _N=t, t〉1, p is handled as follows to the summit:

If difference vertex set J ₀In zone of summit formation of being connected with summit p, and the number on the summit that comprises in should the zone is more than or equal to given threshold value T _N, then keep summit p;

If difference vertex set J ₀In zone of summit formation of being connected with summit p, but the number on the summit that comprises in should the zone is less than given threshold value T _N, then summit p is deleted;

If difference vertex set J ₀The interior summit that is connected with summit p does not consist of a zone, and then summit p is deleted.

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