CN102980529B - 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

Based on the External Shape difference detecting method of multiple dimensioned grid vertex mean inclination

Technical field

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

Background technology

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

Existing 3 d part shape detecting method, mainly comprise two large classes: (1) contact type measurement, Typical Representative is coordinate measuring machine (CMM), and this measuring method exists a lot of restrictions: sweep velocity is subject to the restriction of mechanical motion, measuring speed is slow, and needs planning survey path before measuring; Bad to soft material measurement effect, cannot measure the impalpable surface of gauge head, as endoporus, also cannot measure the region of some geometric properties such as edge, wedge angle, very high to environmental requirement.Be difficult to satisfied current high-level efficiency, high precision, the detection of large profile shape needs.(2) non-contact measurement: Typical Representative is optical measuring method, optical measuring method can be divided into two large classes according to the basic skills obtaining three-dimensional information: passive type and active two large classes.Passive type is under natural light condition, is obtained the three-dimensional information of object by the 2-D gray image of the optical sensor picked-ups such as video camera; Active is utilize special controlled light source to irradiate measured object, according to the three-dimensional information of the known structure acquisition of information scenery of active light source.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 said method in employing and carry out in the process of 3 d part detection, often cannot know size or the yardstick of shape difference in advance, thus usually cannot select the detection method of appropriate yardstick.At present usually according to subjective experience or determine yardstick according to the precision of survey instrument, shape difference cannot be portrayed all-sidedly and accurately, not possess multiple dimensioned characteristic, the difference of omitting on certain yardstick may be there is.

In sum, existing method cannot the shape difference of irregular three-D part of detection of complex, large multiple dimensioned single, cannot quantitatively, location and dimensioning ground describes out the irregularly shaped difference of complexity.

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, to overcome the limitation that only can detect specific simple feature of common mesh shape difference detecting method and to detect the shortcoming being confined to single yardstick, realize part sample shape difference that is irregular to two groups or complex appearance and carry out quantitatively, locate and the accurately detection of dimensioning ground.

For achieving the above object, the present invention mainly comprises the following steps:

C _gthe x-axis coordinate mean value of interior all sample respective vertices, T _ycontrol group C _gthe y-axis coordinate mean value of interior all sample respective vertices, T _zcontrol group C _gthe z-axis 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 formula the x-axis coordinate of the summit p of m part, the y-axis coordinate of the summit p of m part, the z-axis coordinate of the summit p of m part, C _nfor control group C _gthe number of interior all part samples;

(10) for each summit p in difference vertex set J, the summit mean inclination Q on this summit is calculated _plevel of significance value g and the yardstick k at this place, summit, form fiduciary level vector F=(k, g) of characterizing shape difference;

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

Compared with prior art, tool has the following advantages in the present invention:

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

(2) the postsearch screening link that the present invention adopts can guarantee that the summit detected concentrates on one or several region, improves the reliability of testing result and the ability of opposing random noise;

(3) the present invention is owing to jointly depicting control group C by size vector U, position vector T and these three vectors of fiduciary level vector F _gwith seminar S _gshape difference between two groups of samples, provide the size of shape difference, position, yardstick and reliability information, testing result is accurately complete, and reliability is high.

Accompanying drawing explanation

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

Fig. 2 is triangular mesh generation schematic diagram of the present invention;

Fig. 3 is that the present invention calculates distance d _pschematic diagram;

Fig. 4 is summit mean inclination Q of the present invention _pcalculate schematic diagram.

Embodiment

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

The first step, is divided into two groups by all part samples, is called control group C _gwith seminar S _g.

In this step, all part samples are divided according to respective had different attribute, such as the processing coming from two different machines, although or selected different constituent materials from same machine, be divided into control group C according to actual needs _gwith seminar S _g.

When dividing sample group, the number of two groups of samples wants equal or close, and this is accuracy in order to ensure the result adopting statistical method analysis to obtain and reliability.

Second step, according to geometric properties by control group C _gwith seminar S _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 specific implementation process, first selected coordinate system, is set one group of registration marks, between different sample, then accurately registration marks is adjusted to the same position in coordinate system by the rigid motion such as translation, rotation; For convenience's sake, usually select simple and stable geometric properties as the mark in registration process, the intersection point of the border of such as part, the intersection of plane and intersection; In addition, area-of-interest during these geometric properties being elected to be registration marks must detect with this shape difference has nothing to do, namely in testing process, shape difference detection is not carried out to these geometric properties, or can assert that these geometric properties do not exist shape difference between two groups of samples.

3rd step, to all parts after registration, scans with three-dimensional camera, obtains the 3-D view of part.

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

Because more situation will carry out Difference test to the monnolithic case of part, then must carry out the 3-D scanning of multi-angle to each part, in the scanning process to each angle, position and the parameter of video camera all remain unchanged; By multi-angle scanning result by after ordinate transform and geometric transformation, obtain the overall 3-D view of sample.In multi-angle scanning process, same video camera can be adopted to complete, some video cameras with identical parameters also can be adopted to complete.

4th step, according to the 3-D view of part, adopts triangular mesh subdivision method step by step, sets up control group C _gwith seminar S _gthe triangular mesh of interior each part.

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

(4a) select initial level triangular mesh, and be defined as the 0th grade of triangular mesh, be designated as G ₀, G ₀for most coarse grids, initial level triangular mesh here selects regular polygon usually, such as has the regular dodecahedron on 12 summits;

(4b) carry out L level subdivision to initial triangle gridding, the total progression of setting subdivision is L, L>=1, and its subdivision process newly increases a j level grid vertex between certain two adjacent vertex in jth-1 grade of grid, newly-increased grid vertex P _jthe 3-D view outline of the Approximation of 3 D part more accurately of the grid after subdivision will be enable as much as possible.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, then the grid obtained after subdivision has more summits and little triangle, and the sign of grid to entity component is more accurate, and such as, total number of vertex of the grid of regular dodecahedron after f level subdivision is 10 × 4 ^f+ 2, triangle number is 20 × 4 ^f, 0≤f≤L.It should be noted that, be subject to the precision of 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) grid vertex P will be increased newly _jwith existing vertex merge, obtain jth level triangular mesh G _j, then have:

G _j=G _j-1UP _j，1≤j≤L 2）

Wherein U represents union of sets computing, and j is called grid G _jyardstick, the G obtained after L subdivision obviously _lfor most fine grid blocks.In this step, except the merging on summit, also need the triangle re-constructed out according to spatial relation on grid.

5th step, note jth level triangle gridding G _jin arbitrarily summit be p, the set that the summit in the 1-ring neighborhood of definition summit p is formed is E _p.

6th step, with set E _pinterior all summits structure obtains a plane f _p.

(6a) plane f is established _pequation be z=a ₀x+a ₁y+a ₂, wherein a ₀, a ₁, a ₂for plane undetermined coefficient, a ₀for the undetermined coefficient of x, a ₁for the undetermined coefficient of y, a ₂for 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 _pinterior all summits are to plane f _pskew sum of squares function S:

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

Wherein (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n, n are set E _pthe number on middle summit;

(6c) according to minimizing decision method, function S is utilized 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) be set E _pin the coordinate on i-th summit, i=1,2 ... n;

(6d) solution system of equations above obtains 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) by plane undetermined coefficient a ₀, a ₁, a ₂substitute into plane f _pequation z in, namely obtain the plane f that will construct _p, now gather E _pinterior all summits are to plane f _pskew sum of squares function S be minimal value.

7th step, with set E _pinterior all summits structure obtains an approximate circle C _p.

(7a) Spherical Surface S is established _pequation be x ²+ y ²+ z ²-Ax-By-Cz+D=0, wherein A, B, C, D are 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 _pinterior all summits are to Spherical Surface S _pskew sum of squares function V:

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

Wherein (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n, n are set E _pthe number on middle summit;

(7c) according to minimizing decision method, adopt matrix method respectively to the sphere undetermined coefficient A in function V, B, C, D ask local derviation, obtain 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) solution system of equations above obtains sphere undetermined coefficient A, and B, C, D are:

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

Wherein [] ^-1the inverse matrix of representing matrix [], wherein (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n, n are set E _pthe number on middle summit;

(7e) by sphere undetermined coefficient A, B, C, D substitute into Spherical Surface S _pequation

X ²+ y ²+ z ²in-Ax-By-Cz+D=0, namely obtain the Spherical Surface S that will construct _p, Spherical Surface S _pwith plane f _pintersection be the approximate circle C that will construct _p.

8th step, calculates summit p to plane f _pdistance d _p.

Plane f is obtained by the 6th step _pequation z=a ₀x+a ₁y+a ₂, with reference to accompanying drawing 3, appoint 1 q in face of making even, if its coordinate is (x ', y ', z '), then have z '=a ₀x '+a ₁y '+a ₂; If the coordinate of summit p is (x _p, y _p, z _p), connect Vertex p and q point, and q point is plane f excessively _punit normal vector required summit p is to plane f _pdistance d _pfor vector with inner product numerical values recited, that is:

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

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

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

9th step, calculates approximate circle C _pradius R _p.

(9a) Spherical Surface S is calculated _pthe centre of sphere to plane f _pdistance d ₀, the Spherical Surface S obtained by the 7th step _pthe coordinate of the known centre of sphere of equation be the summit p obtained according to the 8th step is to plane f _pdistance d _pcomputing formula can obtain the centre of sphere to plane f _pdistance d ₀for:

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

(9b) Spherical Surface S obtained by the 7th step _pthe known Spherical Surface S of equation _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:

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

Tenth step, according to summit p to plane f _pdistance d _pand Spherical Surface S _pradius R _p, with reference to accompanying drawing 4, calculate the summit mean inclination Q of summit p _pfor:

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

11 step, to the summit mean inclination Q on each summit on each yardstick grid _pvalue carries out two Samples T-Test, is gone out the 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 H is the progression needing to carry out shape difference analysis, and 1≤H≤L, k is the yardstick needing the grid carrying out shape difference analysis, control group C _gwith seminar S _gthe subset that the summit on k yardstick between two groups of samples with significant difference is formed, (L-H+1)≤k≤L,

In formula, s is k yardstick grid G _kinterior arbitrary summit, control group C _gthe summit mean inclination value of summit s on k yardstick in interior all sample grid, seminar S _gthe summit mean inclination value of summit s on k yardstick in interior all sample grid, sig (,) represent and the level of significance value that two Samples T-Test obtains is carried out to given two vectors, α is setting level of significance threshold value, 0< α≤0.05.

12 step, to difference vertex set J ₀in summit carry out postsearch screening, namely according to difference vertex set J ₀the region that the interior summit be connected with summit p is formed and given threshold value T _n=t, t>1, opposite vertexes p is handled as follows:

If difference vertex set J ₀the interior summit be connected with summit p forms a region, and the number on the summit comprised in this region is more than or equal to given threshold value T _n, then summit p is retained;

If difference vertex set J ₀the interior summit be connected with summit p forms a region, but the number on the summit comprised in this region is less than given threshold value T _n, then summit p is deleted;

If difference vertex set J ₀the interior summit be connected with summit p does not form a region, then summit p is deleted.

13 step, for each summit p in set J, calculates control group C respectively _gwith seminar S _gthe mean inclination Q on this summit in two groups of samples _pthe average of value and standard deviation, form the size vector of characterizing 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.

It should be noted that, average and standard deviation are statistical characteristic values the most frequently used in statistics, and these two characteristic quantities can rationally and effectively reflect control group C _gwith seminar S _gmiddle summit mean inclination Q _pthe reasonable fiducial interval of value, thus the size cases of the shape difference of respective vertices between two groups of samples can be depicted quantitatively.

14 step, for each summit p in set J, calculates control group C _gthe coordinate mean value of interior all sample respective vertices, forms position vector T=(k, the T of characterizing shape difference _x, T _y, T _z),

Wherein, k is the yardstick of p place, summit grid, T _xcontrol group C _gthe x-axis coordinate mean value of interior all sample respective vertices, T _ycontrol group C _gthe y-axis coordinate mean value of interior all sample respective vertices, T _zcontrol group C _gthe z-axis 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-axis coordinate of the summit p of m part, the y-axis coordinate of the summit p of m part, the z-axis coordinate of the summit p of m part, C _nfor control group C _gthe number of interior all part samples.

The calculating of position vector only only used the sample in control group, because as one of standard group of sample when control group compares between normally organizing, the position that the position vector obtained like this characterizes is clearer and more definite, also more convincing.

15 step, for each summit p in set J, the yardstick at the level of significance value selecting this summit to calculate in the 7th step and this place, summit, forms fiduciary level vector F=(k, g) of characterizing shape difference,

Wherein, k is this vertex correspondence yardstick, and g is mean inclination Q on the p of summit _pthe level of significance value of two Samples T-Test between the group of value.

It should be noted that, for certain summit specific, its mean inclination Q _pvalue may calculate under several yardsticks, and thus this summit may show significant difference statistically on several yardsticks.

In addition, Corpus--based Method general knowledge, level of significance numerical value is less means that the possibility with significant difference is larger, the thus mean inclination Q on summit _pthe level of significance value obtained when sample compares between the group of value, can reflect that this summit place exists the reliability of significant difference really.

16 step, depicts control group C jointly with these three vectors of size vector U, position vector T and fiduciary level vector F _gwith seminar S _gshape difference between two groups of samples, namely depicts the size of part shape difference degree between two groups of samples, describes the position at difference place with position vector T with size vector U, describe yardstick and the reliability at difference place with fiduciary level vector F.Such as, suppose that summit 1 and summit 2 are all the summits in set J, the summit mean inclination Q of all samples _pvalue is as table 1:

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

Control group C in reckoner 1 _gwith seminar S _gthe summit mean inclination Q of two groups of samples _pthe average of value and standard deviation, be used for representing control group C _gwith seminar S _gthe size of the shape difference between two groups of samples, calculates control group C _gwith seminar S _gthe coordinate average weight on the summit of two groups of samples, is used for representing control group C _gwith seminar S _gthe position of the shape difference between two groups of samples, and control group C in his-and-hers watches 1 _gwith seminar S _gthe summit mean inclination Q of two groups of samples _pvalue carries out two Samples T-Test, control group C _gwith seminar S _gthe size of the shape difference between two groups of samples, position and level of significance result are as table 2:

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

As shown in Table 2, level of significance value is 0.0010 and 0.0033, all meet the requirement that level of significance value is less than 0.05, namely opposite vertexes 1 can be thought, significant shape difference is there is in two groups of samples on yardstick 6, and then there is significant shape difference on yardstick 5 in opposite vertexes 2, two groups of samples.

It should be noted that, for all summits on grid, all can calculate the size vector of shape difference, position vector and fiduciary level vector, but only have the summit in the set J obtained through postsearch screening just to have practical significance.

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

Claims (5)

1., based on an External Shape difference detecting method for multiple dimensioned grid vertex mean inclination, comprise the steps:

(1) part of different attribute is divided into two groups, is called control group C _gwith seminar S _g, the number of two groups of samples is equal;

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

(3) with each part after three-dimensional camera scanning registration, the 3-D view of part is obtained;

(4) triangular mesh subdivision method is step by step adopted, to initial level triangular mesh G ₀carry out L level subdivision and obtain each rank G _j, 1≤j≤L, j is called grid G _jyardstick, and G _lfor most fine grid blocks, G ₀for most coarse grids;

(5) jth level triangle gridding G is remembered _jin arbitrarily summit be p, the set that the summit in the 1-ring neighborhood of definition summit p is formed is E _p, and with gathering E _pinterior all summits construct respectively and obtain a plane f _pwith approximate circle C _p, calculate summit p respectively to this plane f _pdistance d _pwith approximate circle C _pradius R _p;

(6) according to distance d _pand radius R _p, calculate the summit mean inclination Q of 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 carries out two Samples T-Test, and preliminary screening goes out the difference vertex set J on each yardstick ₀, then to difference vertex set J ₀in summit carry out postsearch screening, obtain difference vertex set J;

(8) for each summit p in difference vertex set J, control group C is calculated respectively _gwith seminar S _gthe summit mean inclination Q on this summit in two groups of samples _pthe average of value and standard deviation, form the size vector of characterizing 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 summit p in difference vertex set J, control group C is calculated _gthe coordinate mean value of interior all sample respective vertices, forms the position vector of characterizing 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-axis coordinate mean value of interior all sample respective vertices, T _ycontrol group C _gthe y-axis coordinate mean value of interior all sample respective vertices, T _zcontrol group C _gthe z-axis 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 formula the x-axis coordinate of the summit p of m part, the y-axis coordinate of the summit p of m part, the z-axis coordinate of the summit p of m part, C _nfor control group C _gthe number of interior all part samples;

(10) for each summit p in difference vertex set J, the summit mean inclination Q on this summit is calculated _plevel of significance value g and the yardstick k at this place, summit, form fiduciary level vector F=(k, g) of characterizing shape difference;

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

2. method according to claim 1, with set E in wherein said step (5) _pinterior all summits structure obtains a plane f _p, carry out as follows:

(5a) plane f is established _pequation be z=a ₀x+a ₁y+a ₂, wherein a ₀, a ₁, a ₂for plane undetermined coefficient, a ₀for the undetermined coefficient of x, a ₁for the undetermined coefficient of y, a ₂for 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 _pinterior all summits are to plane f _pskew sum of squares function S:

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

Wherein (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n, n are set E _pthe number on middle summit;

(5c) according to minimizing decision method, function S is utilized 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) be set E _pin the coordinate on i-th summit, i=1,2 ... n;

(5d) solution system of equations above obtains plane undetermined coefficient a ₀, a ₁, a ₂for:

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

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

(5e) by plane undetermined coefficient a ₀, a ₁, a ₂substitute into plane f _pequation z in, namely obtain the plane f that will construct _p, now gather E _pinterior all summits are to plane f _pskew sum of squares function S be minimal value.

3. method according to claim 1, with set E in wherein said step (5) _pinterior all summits matching obtains approximate circle C _p, carry out as follows:

(5f) Spherical Surface S is established _pequation be x ²+ y ²+ z ²-Ax-By-Cz+D=0, wherein A, B, C, D are 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 _pinterior all summits are to Spherical Surface S _pskew sum of squares function V:

$V=\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{({x_i}^2+{y_i}^2+{z_i}^2-{\mathrm{Ax}}_i-{\mathrm{By}}_i-{\mathrm{Cz}}_i+D)}^2,$

Wherein (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n, n are set E _pthe number on middle summit;

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

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

(5i) solution system of equations above obtains sphere undetermined coefficient A, and B, C, D are:

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

Wherein [] ^-1the inverse matrix of representing matrix [], (x _i, y _i, z _i) be set E _pin the coordinate on i-th summit, i=1,2 ... n;

(5j) by sphere undetermined coefficient A, B, C, D substitute into Spherical Surface S _peQUATION x ²+ y ²+ z ²in-Ax-By-Cz+D=0, namely obtain the Spherical Surface S that will construct _p, Spherical Surface S _pwith plane f _pintersection be the approximate circle C that will construct _p.

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

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

Wherein L is total progression of subdivision, and H is the progression needing to carry out shape difference analysis, and 1≤H≤L, k is the yardstick needing the grid carrying out shape difference analysis, control group C _gwith seminar S _gthe subset that the summit on k yardstick between two groups of samples with significant difference is formed, (L-H+1)≤k≤L,

In formula, s is k yardstick grid G _kinterior arbitrary summit, control group C _gthe summit mean inclination value of summit s on k yardstick in interior all sample grid, seminar S _gthe summit mean inclination value of summit s on k yardstick in interior all sample grid, sig (,) represent and the level of significance value that two Samples T-Test obtains is carried out to given two vectors, 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 summit carry out postsearch screening, carry out as follows:

(7a) according to difference vertex set J ₀the region that the interior summit be connected with summit p is formed and given threshold value T _n=t, t>1, opposite vertexes p is handled as follows:

If difference vertex set J ₀the interior summit be connected with summit p forms a region, and the number on the summit comprised in this region is more than or equal to given threshold value T _n, then summit p is retained;

If difference vertex set J ₀the interior summit be connected with summit p forms a region, but the number on the summit comprised in this region is less than given threshold value T _n, then summit p is deleted;

If difference vertex set J ₀the interior summit be connected with summit p does not form a region, then summit p is deleted.