CN103438803B - Computer vision technique accurately measures the method for Rectangular Parts size across visual field - Google Patents

Abstract

The invention discloses computer vision technique accurately measures Rectangular Parts size method across visual field; comprise: Rectangular Parts to be measured is positioned on rectangle reference block; axis of symmetry O and axis of symmetry O ' is parallel to each other or mutual α at a certain angle, and 0 °≤α & lt; 15 °; Guarantee that part does not exceed the edge of rectangle reference block; Utilize the length of rectangle reference block middle conductor EE ', FF ', GG ', HH ', EF, line segment EI, I in conjunction with utilizing the Computer Image Processing program that pre-sets accurately to detect ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H ' length, calculates the edge line size of Rectangular Parts to be measured.The precision of testing result of the present invention is high, and reduces the cost of detection system, can be applicable to accurately measure Rectangular Parts size.

Description

Computer vision technique accurately measures the method for Rectangular Parts size across visual field

Technical field

The present invention relates to the accurate fields of measurement of computer vision, refer in particular to a kind of computer vision technique accurately measures Rectangular Parts size method across the visual field.

Background technology

The actual measurement size of industrial products part is the important evidence judging its quality, and the size controlling part is the important means ensureing quality of finished in the error range of design.At present, the detection of industrial products accessory size comprises contact measurement method and the large class of contactless measurement two.Contact measurement method mainly contains vernier caliper, milscale, three-coordinates measuring machine etc., although the result of this type of measuring method is accurate, measuring process time and effort consuming, easily damages, the surface of scratching products part, is difficult to meet the large demand of producing of industry.Contactless measurement mainly contains laser optical method and computer vision measurement method, and this type of measuring method has favorable reproducibility, and detection speed is fast, easily realizes the advantages such as on-line checkingi; Wherein computer vision measurement method can detect multiple dimensional parameters on product parts surface simultaneously, has been widely used the size detection in industrial products part.

At present, computer vision has been used to the fine feature accurately detecting object to be measured in fixing visual field.Patent " a kind of high precision microscopic fatigue tester " (application number: 200810207563.2) disclose a kind of method utilizing Computer Vision Detection microfissure size.The method amplifies the image in sample fatigue crack region in visual field by microscope, and the image under this visual field taken by camera also sends into computing machine, is accurately measured the length of sample crackle in visual field by image processing techniques.When whole piece crackle to be measured does not exceed microscopical visual field, the method can measure the length of crackle accurately; When certain part of crackle to be measured is beyond microscopical visual field, then the method is difficult to the length measuring crackle, and therefore the method can not accurately detect the fine feature exceeding fixing field of view.

When utilizing computer vision accurately to measure, in order to effectively catch the local feature of sample, camera or microscopical visual field size limited often, the length of visual field or be widely generally 2mm ~ 5mm, and the length, width, thickness etc. of characteristic parameter to be measured as product parts often exceed camera or microscopical field of view, how accurately to detect across visual field the difficult point that above-mentioned characteristic parameter is computer vision measurement field.For this problem, patent " a kind of part vision detection device " (application number: 200910079737.6) disclose a kind of computer vision detects surface defects of parts and appearance and size device across visual field.This device utilizes CCD camera and enlarging objective etc. to form imaging system, is fixed on displacement platform by part to be measured, and pick-up unit is provided with the detection system of recorded bit moving stage displacement simultaneously.The fringe region continuous print of part is sent in the visual field of imaging system by displacement platform by this device, calculates the appearance and size of part eventually through the part edge image of imaging system shooting and the displacement of displacement detection system record.Because the measuring accuracy of this device is not only relevant with the visual identity precision of part edge image, and closely related with the registration accuracy of displacement detection system to mechanical shift platform stroke, therefore can not realize high-acruracy survey.Patent " a kind of digital displacement measuring instrument " (application number: 201120026446.3) disclose and a kind ofly utilize multiple camera coupling to carry out the method for computer vision high-acruracy survey.First the method obtains the image information of object regional area to be measured in each viewing field of camera, then utilize image mosaic technology that the local area image that each camera obtains is spliced into the panoramic picture of an object to be measured, and then utilize computer vision technique to carry out high-acruracy survey to object to be measured.Although the measuring accuracy of this pick-up unit can not be subject to the impact of mechanical shift platform, but when larger than viewing field of camera tens times of parameter to be measured, hundreds of times, even more time, the coupling of needs tens, even more polyphaser up to a hundred just can complete measurement, easily causes testing cost higher.

Summary of the invention

Computer vision technique is the object of the present invention is to provide accurately to measure the method for Rectangular Parts size across visual field, to realize accurately measuring the size of Rectangular Parts.

In order to eliminate mechanical shift platform to the impact of measuring accuracy and the cost effectively controlling detection system, the technical solution used in the present invention is as follows:

The present invention is the device accurately measuring Rectangular Parts size based on computer vision technique across the visual field, comprises rectangle reference block ABCD, Rectangular Parts A ' B ' C ' D ' to be measured, Vision imaging system, computing machine, mechanical shift platform composition;

The length breadth ratio of described rectangle reference block ABCD is identical with the length breadth ratio of Rectangular Parts A ' B ' C ' D ' standard component to be measured, and the area large 5% ~ 20% of the area ratio Rectangular Parts A ' to be measured B ' C ' D ' standard component of rectangle reference block ABCD; Rectangle reference block ABCD is provided with the reference line EE ' of two horizontal directions and the reference line GG ' of FF ' and two vertical direction and HH ', and the length L of reference line EE ' _{eE '}, reference line FF ' length L _{fF '}, reference line GG ' length L _{gG '}, reference line HH ' length L _{hH '}, length L between reference point E and reference point F _eF, length L between reference point G and reference point H _gH, rectangle reference block ABCD the length L of four edges edge line AB, BC, CD, DA _aB, L _bC, L _cD, L _dAbe known; Dotted line O is rectangle reference block ABCD axis of symmetry in the vertical direction;

Described Rectangular Parts A ' B ' C ' D ' to be measured axis of symmetry is in the vertical direction dotted line O '; Described Vision imaging system is made up of camera, camera lens, light source, image pick-up card and data line, and Vision imaging system is fixedly installed on mechanical shift platform; The image processing program that described built-in computer is developed in advance, can obtain, stores, processes the image of Vision imaging system acquisition; Described mechanical shift platform can carry Vision imaging system and above rectangle reference block ABCD, do tangential movement along the path of setting.

Accurately measure the method for Rectangular Parts size based on computer vision technique across visual field, it is characterized in that comprising the following steps:

Step one, is positioned over Rectangular Parts A ' B ' C ' D ' to be measured on rectangle reference block ABCD, axis of symmetry O and axis of symmetry O ' is parallel to each other or mutual α at a certain angle, and 0 °≤α <15 °;

Step 2, checks whether any part of Rectangular Parts A ' B ' C ' D ' to be measured exceeds the edge of rectangle reference block ABCD, concrete point of following three processes:

Process one, mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A in the surface level of distance rectangle reference block ABCD upper surface 2mm ~ 200mm, in the process of movement, Vision imaging system takes the image of four edges edge line AB, BC, CD, DA of rectangle reference block ABCD continuously, and is stored in computing machine;

Process two, computing machine is processed by the image of four edges edge line AB, BC, CD, DA to rectangle reference block ABCD, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process three, if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, then returns step one; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, then enter step 3;

Step 3, mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface 2mm ~ 200mm, obtain reference line EE ', FF ', GG ', HH ' respectively not by the image of Rectangular Parts A ' B ' C ' D ' cover part to be measured, H ' is complete appears in the visual field of Vision imaging system for take 8 width images altogether, shooting process makes line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P '.Wherein I, I ' is respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' be respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' be respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4, utilizes the line segment length in the Computer Image Processing program accurate detecting step 38 width image pre-set, obtains the length L of line segment EI respectively _eI, line segment I ' E ' length L _{i ' E '}, line segment FJ length L _fJ, line segment J ' F ' length L _{j ' F '}, line segment GK length L _gK, line segment K ' G ' length L _{k ' G '}, line segment HP length L _hP, line segment P ' H ' length L _{p ' H '};

Step 5, utilize the length of rectangle reference block ABCD middle conductor EE ', FF ', GG ', HH ', EF, the length of line segment EI, I of obtaining in integrating step four ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H ', calculates the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '};

The edge line size L of described Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '}below point, two kinds of modes calculate:

Mode one: when satisfying condition time (0.0001<x<0.05), can think that the axis of symmetry O of rectangle reference block ABCD and the axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured is parallel to each other, then L _{a ' B '}and L _{a ' D '}computing formula be respectively:

L _A’B’=L _II’=L _EE’-L _EI-L _I’E’

L _A’D’=L _KK’=L _GG’-L _GK-L _K’G’

Mode two: when satisfying condition (0.0001<x<0.05), time, the axis of symmetry O of rectangle reference block ABCD and the mutual α at a certain angle of axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured can be thought; In order to determine the size of angle α, be that starting point is made vertical line to line segment EI and intersects at Q point with EI with J, then α=∠ IJQ, can obtain thus $\cos \mathrm{\&alpha;}=\frac{L_{\mathrm{JQ}}}{L_{\mathrm{JI}}}=\frac{L_{\mathrm{JQ}}}{\sqrt{L_{\mathrm{JQ}}^2+L_{\mathrm{QI}}^2}}=\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}};$ Due to the existence of angle α, make LA ' B ' ≠ LII ', be therefore starting point with I to B ' C ' make vertical line and and B ' C ' intersect at Q ' point, and ∠ Q ' II '=∠ IJQ=α; Then L _{a ' B '}computing formula be:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{\mathrm{EI}}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

In like manner L can be obtained _{a ' D '}computing formula be:

$L_{A^{,}{D}^{,}}=L_{K{K}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{\mathrm{GK}}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

The present invention has beneficial effect.The present invention, by arranging corresponding reference point and reference line on rectangle reference block, has carried out accurate measurement in conjunction with computer vision technique to the Rectangular Parts size much larger than Vision imaging system single visual field size.Although in the process detected, zones of different that Vision imaging system moves to rectangle reference block carries out image taking to need Mechanical Moving platform to carry, but do not need the travel parameters inputting mechanical mobile platform in the computing formula of rectangular dimension to be measured, therefore the precision of testing result is no longer subject to the impact of mobile platform kinematic accuracy.Do not need the collaborative of multiple camera can complete accurately measuring across visual field of large scale parameter simultaneously in testing process, effectively control the cost of detection system.

Accompanying drawing explanation

Fig. 1 is rectangle reference block schematic diagram;

Fig. 2 is Rectangular Parts schematic diagram to be measured;

Fig. 3 is that computer vision accurately measures the schematic diagram of Rectangular Parts size across visual field.

Embodiment

Describe the present invention below by way of each embodiment.But these embodiments do not limit the present invention, the structure that those of ordinary skill in the art makes according to these embodiments, method or conversion functionally are all included in protection scope of the present invention.

Computer vision technique accurately measures a method for Rectangular Parts size across the visual field, comprises rectangle reference block ABCD, Rectangular Parts A ' B ' C ' D ' to be measured, Vision imaging system, computing machine, mechanical shift platform composition.

As shown in Figure 1, the length breadth ratio of rectangle reference block ABCD and Rectangular Parts A ' B ' C ' D ' standard component to be measured is 1:2, and the area large 14.79% of the area ratio Rectangular Parts A ' to be measured B ' C ' D ' standard component of rectangle reference block ABCD; The length L of reference line EE ' _{eE '}the length L of=60mm, reference line FF ' _{fF '}the length L of=60mm, reference line GG ' _{gG '}the length L of=120mm, reference line HH ' _{hH '}=120mm, length L between reference point E and reference point F _eF=80mm, length L between reference point G and reference point H _gHthe length L of four edges edge line AB, BC, CD, DA of=35mm, rectangle reference block ABCD _aB=L _cD=60mm, L _bC=L _dA=120mm; Dotted line O is rectangle reference block ABCD axis of symmetry in the vertical direction;

As shown in Figure 2, Rectangular Parts A ' B ' C ' D ' to be measured axis of symmetry is in the vertical direction dotted line O ';

In Vision imaging system, the model of camera is BasleracA1600-20gm, the model of camera lens is OPTOTC2312, the model of light source is CSTCOL-040-R, the model of image pick-up card is ADLinkGIE64+;

The model of mechanical shift platform is HY10DY (50-500) C, and Vision imaging system is fixedly installed on mechanical shift platform and the distance of camera lens distance rectangle reference block ABCD is 78mm;

The present invention is based on computer vision technique accurately measures Rectangular Parts size method across the visual field, the concrete implementation step of measuring process is as follows.

Step one: Rectangular Parts A ' B ' C ' D ' to be measured is positioned on rectangle reference block ABCD, axis of symmetry O and axis of symmetry O ' is parallel to each other or mutual α at a certain angle, i.e. 0 °≤α <15 °, as shown in Figure 3;

Step 2: check whether any part of Rectangular Parts A ' B ' C ' D ' to be measured exceeds the edge of rectangle reference block ABCD;

This step divides following three processes:

Process (1): mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A at the surface level of rectangle reference block ABCD upper surface certain altitude, in the process of movement, Vision imaging system takes the image of four edges edge line AB, BC, CD, DA of rectangle reference block ABCD continuously, and is stored in computing machine;

Process (2): computing machine is processed by the image of four edges edge line AB, BC, CD, DA to rectangle reference block ABCD, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process (3): if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, then return step one; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, then enter step 3;

Step 3: mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface certain altitude, obtain reference line EE ', FF ', GG ', HH ' respectively not by the image of Rectangular Parts A ' B ' C ' D ' cover part to be measured, H ' is complete appears in the visual field of Vision imaging system for take 8 width images altogether, shooting process makes line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P '.Wherein I, I ' is respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' be respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' be respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4: utilize the line segment length in 8 width images in the accurate detecting step three of Computer Image Processing program pre-set, obtain the length L of line segment EI respectively _eIthe length L of=2.5174mm, line segment I ' E ' _{i ' E '}the length L of=1.5436mm, line segment FJ _fJthe length L of=1.5433mm, line segment J ' F ' _{j ' F '}the length L of=2.5171mm, line segment GK _gKthe length L of=3.2558mm, line segment K ' G ' _{k ' G '}the length L of=4.5354mm, line segment HP _hPthe length L of=4.5356mm, line segment P ' H ' _{p ' H '}=3.2554mm;

Step 5: the known parameters in above-mentioned steps is substituted into find that it meets (namely the value of x is 0.01), so according to the edge line size L of following formulae discovery Rectangular Parts A ' B ' to be measured C ' D ' _{a ' B '}and L _{a ' D '}value:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{\mathrm{EI}}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

$L_{A^{,}{D}^{,}}=L_{K{K}^{,}}\&CenterDot;\cos \mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{\mathrm{GK}}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}$

Wherein

$\cos \mathrm{\&alpha;}=\frac{L_{\mathrm{JQ}}}{L_{\mathrm{JI}}}=\frac{L_{\mathrm{JQ}}}{\sqrt{L_{\mathrm{JQ}}^2+L_{\mathrm{QI}}^2}}=\frac{L_{\mathrm{EF}}}{\sqrt{L_{\mathrm{EF}}^2+{(L_{\mathrm{EI}}-L_{\mathrm{FJ}})}^2}}=\frac{80}{\sqrt{{80}^2+{(2.5174-1.5433)}^2}}=0.999926$

Known parameters is substituted into L _{a ' B '}and L _{a ' D '}computing formula, obtain L _{a ' B '}=55.9349mm, L _{a ' D '}=112.2005mm.The L calculated _{a ' B '}and L _{a ' D '}the stroke of length and mechanical shift platform has nothing to do, and therefore Rectangular Parts size detecting method provided by the invention can not be subject to the impact of mechanical shift platform kinematic accuracy, and computer vision can be utilized accurately to measure the size of part.

Claims (3)

1. computer vision technique accurately measures the method for Rectangular Parts size across visual field, described method accurately measures the device of Rectangular Parts size across the visual field based on computer vision technique, comprise rectangle reference block ABCD, Rectangular Parts A ' B ' C ' D ' to be measured, Vision imaging system, computing machine, mechanical shift platform; The length breadth ratio of described rectangle reference block ABCD is identical with the length breadth ratio of Rectangular Parts A ' B ' C ' D ' standard component to be measured, and the area large 5% ~ 20% of the area ratio Rectangular Parts A ' to be measured B ' C ' D ' standard component of rectangle reference block ABCD;

It is characterized in that comprising the following steps:

Step one, is positioned over Rectangular Parts A ' B ' C ' D ' to be measured on rectangle reference block ABCD, axis of symmetry O and axis of symmetry O ' is parallel to each other or mutual α at a certain angle, and 0 °≤α <15 °;

Step 2: any part checking Rectangular Parts A ' B ' C ' D ' to be measured, guarantees the edge not exceeding rectangle reference block ABCD;

Step 3, mechanical shift platform carries Vision imaging system and moves in the surface level of distance rectangle reference block ABCD upper surface 2mm ~ 200mm, obtain reference line EE ', FF ', GG ', HH ' respectively not by the image of Rectangular Parts A ' B ' C ' D ' cover part to be measured, H ' is complete appears in the visual field of Vision imaging system for take 8 width images altogether, shooting process makes line segment EI, I ' E ', FJ, J ' F ', GK, K ' G ', HP, P '; I, I ' be respectively the point of crossing of reference line EE ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', J, J ' be respectively the point of crossing of reference line FF ' and Rectangular Parts edge line A ' D ' to be measured, B ' C ', K, K ' be respectively the point of crossing of reference line GG ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ', P, P ' are respectively the point of crossing of reference line HH ' and Rectangular Parts edge line A ' B ' to be measured, D ' C ';

Step 4, the line segment length in 8 width images described in the accurate detecting step three of Computer Image Processing program that utilization pre-sets, obtains the length L of line segment EI respectively _eI, line segment I ' E ' length L _{i ' E '}, line segment FJ length L _fJ, line segment J ' F ' length L _{j ' F '}, line segment GK length L _gK, line segment K ' G ' length L _{k ' G '}, line segment HP length L _hP, line segment P ' H ' length L _{p ' H '};

Step 5, utilize the length of rectangle reference block ABCD middle conductor EE ', FF ', GG ', HH ', EF, the length of line segment EI, I of obtaining in integrating step four ' E ', FJ, J ' F ', GK, K ' G ', HP, P ' H ', calculates the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured _{a ' B '}and L _{a ' D '}.

2. computer vision technique as claimed in claim 1 accurately measures the method for Rectangular Parts size across visual field, it is characterized in that described step 2 is specially further:

Process one, mechanical shift platform carries Vision imaging system and moves one week along A → B → C → D → A at the surface level of rectangle reference block ABCD upper surface 2mm ~ 200mm, in the process of movement, Vision imaging system takes the image of four edges edge line AB, BC, CD, DA of rectangle reference block ABCD continuously, and is stored in computing machine;

Process two, computing machine is processed by the image of four edges edge line AB, BC, CD, DA to rectangle reference block ABCD, judges whether edge line AB, BC, CD, DA are covered by Rectangular Parts A ' B ' C ' D ' to be measured;

Process three, if any point of edge line AB, BC, CD, DA is covered by Rectangular Parts A ' B ' C ' D ' to be measured, then returns step one; If any point of edge line AB, BC, CD, DA is not all covered by Rectangular Parts A ' B ' C ' D ' to be measured, then enter step 3.

3. computer vision technique as claimed in claim 1 accurately measures the method for Rectangular Parts size across visual field, it is characterized in that: the edge line size L of Rectangular Parts A ' B ' C ' D ' to be measured in described step 5 _{a ' B '}and L _{a ' D '}below point, two kinds of modes calculate:

Mode one, when satisfying condition time (0.0001<x<0.05), can think that the axis of symmetry O of rectangle reference block ABCD and the axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured is parallel to each other, then L _{a ' B '}and L _{a ' D '}computing formula be respectively:

L _A’B’＝L _II’＝L _EE’-L _EI-L _I’E’

L _A’D’＝L _KK’＝L _GG’-L _GK-L _K’G’

Mode two, when satisfying condition $\frac{\left|L_{\mathrm{EI}}-L_{\mathrm{FJ}}\right|}{(L_{\mathrm{EI}}+L_{\mathrm{FJ}})/2}>x\%,(0.0001<x<0.05)$ Time, can think the axis of symmetry O of rectangle reference block ABCD and the mutual α at a certain angle of axis of symmetry O ' of Rectangular Parts A ' B ' C ' D ' to be measured; In order to determine the size of angle α, be that starting point is made vertical line to line segment EI and intersects at Q point with EI with J, then α=∠ IJQ, can obtain thus $cos\mathrm{\&alpha;}=\frac{L_{JQ}}{L_{JI}}=\frac{L_{JQ}}{\sqrt{L_{JQ}^2+L_{QI}^2}}=\frac{L_{EF}}{\sqrt{L_{EF}^2+{(L_{EI}-L_{FJ})}^2}};$ Due to the existence of angle α, make L _{a ' B '}≠ L _{iI '}, be therefore starting point with I to B ' C ' make vertical line and and B ' C ' intersect at Q ' point, and ∠ Q ' II '=∠ IJQ=α; Then L _{a ' B '}computing method be:

$L_{A^{,}{B}^{,}}=L_{{\mathrm{II}}^{,}}\&CenterDot;cos\mathrm{\&alpha;}=(L_{{\mathrm{EE}}^{,}}-L_{EI}-L_{I^{,}{E}^{,}})\&CenterDot;\frac{L_{EF}}{\sqrt{L_{EF}^2+{(L_{EI}-L_{FJ})}^2}}$

In like manner L can be obtained _{a ' D '}computing method be:

$L_{A^{,}{D}^{,}}=L_{{\mathrm{KK}}^{,}}\&CenterDot;cos\mathrm{\&alpha;}=(L_{{\mathrm{GG}}^{,}}-L_{GK}-L_{K^{,}{G}^{,}})\&CenterDot;\frac{L_{EF}}{\sqrt{L_{EF}^2+{(L_{EI}-L_{FJ})}^2}}.$