CN103630072A - Layout optimization method for camera in binocular vision measuring system - Google Patents

Abstract

The invention discloses a layout optimization method for a camera in a binocular vision measuring system, belongs to the fields of computer vision detection and image detection, and particularly relates to the layout optimization method for the camera in the binocular vision measuring system for obtaining dimension parameters of a large-scale forging piece. In the binocular vision measuring system, image point extraction deviation caused by image sampling is considered, a mathematic relation model, namely a camera layout optimization mathematic model, is established between a measuring error which is caused by the image point extraction deviation and three structural parameters of a camera focal distance, a reference line distance and a camera deflection angle, and an optimized structural parameter combination is obtained by utilizing a genetic algorithm. According to the layout optimization method disclosed by the invention, the layout optimization design of the camera in the binocular vision measuring system is realized by utilizing the genetic algorithm, minimization of the measuring error caused by the image point extraction deviation is achieved, effective theoretical guidance and reference can be provided for reasonable layout of the camera under the situation that the camera is not calibrated, and the layout optimization method has the characteristics of good optimization effect and strong applicability.

Description

The layout optimization method of video camera in two CCD camera measure system

Technical field

The invention belongs to Computer Vision Detection and image detection field, particularly for obtaining the layout optimization method of the two CCD camera measure system video camera of large forgings dimensional parameters.

Background technology

Binocular vision is measured as a kind of real-time, non-contact measurement method that measuring accuracy is high, be widely used in the numerous areas such as industrial detection, target identification, especially in measuring in real time large forgings forging and stamping process, aspect hot physical dimension, there is incomparable advantage.Many scholars have carried out a large amount of research around how obtaining high-precision measurement result, yet these research work mainly concentrate on and improve the stated accuracy of camera system and the matching precision of unique point, often ignored the impact of the structural parameters of measuring system on measuring accuracy, and structural parameters have not only been determined the size of apparent field, and determining the measuring accuracy of diverse location in apparent field.While utilizing two CCD camera measure system to measure, target to be measured must be in apparent field.Therefore, analytical structure parameter during on the affecting of measuring error, does not consider that the research of carrying out under apparent field's constraint all has one-sidedness.In actual measurement process, once after system calibrating, it is relatively fixing that system just must keep, the structural parameters of system all can not change, so before starting to demarcate, be necessary system structure parameter to be optimized.By the installation position of reasonable Arrangement video camera, improve the measuring accuracy of two CCD camera measure system.

Existing Camera composition optimization method draws general conclusion by investigating one by one single structure parameter to the impact of measuring accuracy mostly, fail each structural parameters to consider to obtain optimum structural parameters combination, or utilize first order optimization method etc. to carry out video camera and optimize distribution, but be easily absorbed in local minimum point.In fact, current most of optimization method all belongs to local optimal searching category, and its effect of optimization depends on choosing of initial value to a great extent, and genetic algorithm is a kind of heuristic random searching algorithm, has efficient global optimizing ability.In addition the picture point that, seldom has focus of attention to produce by sampling is extracted the impact of deviation on final measuring error.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, for lack effective Camera composition optimization method at forging scene, and not by the problems such as each structural parameters of system consider, the layout optimization method of inventing video camera in a kind of two CCD camera measure system based on genetic algorithm.In two CCD camera measure system, consider that the picture point that image sampling causes extracts deviation, the present invention has set up by picture point and has extracted measuring error that deviation causes and the numerical relationship model between focal length of camera, parallax range and three structural parameters of video camera deflection angle.Distance between the Liang Tai video camera centre of perspectivity, is parallax range; The angle of two camera optical axis and Z axis, is video camera deflection angle.Considering under the constraints such as apparent field, the layout optimization problem of two CCD camera measure system is converted to the single goal optimization problem of belt restraining, and use genetic algorithm to carry out global optimizing, obtained the measuring system structural parameters of one group of optimum, made the measuring error being caused by picture point extraction deviation reach minimum.

The technical scheme that the present invention takes is the layout optimization method of video camera in a kind of two CCD camera measure system, it is characterized in that, in two CCD camera measure system, image sampling can cause picture point extraction deviation, the measuring error that foundation is caused by picture point extraction deviation and focal length of camera f, parallax range D, video camera deflection angle

the numerical relationship model of three structural parameters, i.e. Camera composition optimized mathematical model, and utilize genetic algorithm to obtain optimum structural parameters combination.Concrete steps are as follows:

Step 1: in two CCD camera measure system, set up two Camera composition optimized mathematical models.

As shown in Figure 2, left side camera CCD1 and right side video camera CCD2 converge arranged in form with optical axis, the initial point O of world coordinate system OXYZ and the camera coordinate system O of left side camera _lx _ly _lz _linitial point O _loverlap.If the coordinate of a certain object point P in world coordinate system OXYZ is (X _w, Y _w, Z _w), at the camera coordinate system O of left side camera _lx _ly _lz _lcamera coordinate system O with right side video camera _rx _ry _rz _runder coordinate be respectively (X _l, Y _l, Z _l), (X _r, Y _r, Z _r), in left and right side video camera CCD1, CCD2 image planes, the image physical coordinates of picture point is respectively (x _l, y _l) and (x _r, y _r).

Object point P is at the camera coordinate system O of left and right side video camera _lx _ly _lz _l, O _rx _ry _rz _runder coordinate and the image physical coordinates of picture point there is following relation:

$\left\{\begin{array}{c}{x}_l=f\frac{X_l}{Z_l}\\ y_l=f\frac{Y_l}{Z_l}\\ x_r=f\frac{X_r}{Z_r}\\ y_r=f\frac{Y_r}{Z_r}\end{array}\right.---\left(1\right)$

Object point P is at the camera coordinate system O of left and right side video camera _lx _ly _lz _l, O _rx _ry _rz _runder coordinate and its coordinate under world coordinate system OXYZ there is following relation:

By formula (3) and formula (2) substitution formula (1), obtain the coordinate of object point P under world coordinate system OXYZ and the following relation of image physical coordinates existence of picture point:

Simultaneous formula (1)～formula (5), obtains the coordinate (X of object point P under world coordinate system OXYZ _w, Y _w, Z _w) as follows:

Wherein, establish the expression formula of Ψ as follows:

Consider that sampling causes the situation of maximum picture point deviation, suppose that Pixel Dimensions is δ, the actual left and right video camera obtaining as the extraction deviation existing between the picture point in plane and picture point is ideally:

ε _l＝ε _r＝±0.5δ (10)

The left and right video camera that actual extracting obtains is respectively as the picture point physical coordinates in plane

, itself and picture point physical coordinates (x ideally _l, y _l), (x _r, y _r) pass be:

The picture point physical coordinates being obtained by actual extracting obtains the coordinate of object point P under world coordinate system OXYZ

as follows:

Wherein, establish

expression formula as follows:

Setting up picture point extracts measuring error Q and the mathematical relation between structural parameters that deviation causes and is:

The measurement space that is used for obtaining forging ' s block dimension is as shown in the profile line region of Fig. 2, it is of a size of L * W * H, and L represents the size of length direction (X-direction), and W represents the size of Width (Z-direction), H represents the size of short transverse (Y-direction), Y-axis forward be vertical paper inwards.

In XOZ plane, the angle theta of the left and right visual field border line of camera optical axis and video camera is:

$\mathrm{\θ}=\arctan \left(\frac{\mathrm{\γ}}{2f}\right)---\left(17\right)$

Wherein, γ is effective image planes size.

The front depth of field Δ L1 of video camera is:

$\mathrm{\&Delta;<figure-callout\; id="1"\; label="L"\; filenames="HDA0000401704150000012.png"\; state="\{\{state\}\}">L</figure-callout>}1=\frac{F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^2+F\&CenterDot;\mathrm{CoC}\&CenterDot;d}---\left(18\right)$

The rear depth of field Δ L2 of video camera is:

$\mathrm{\&Delta;L}2=\frac{F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^2-F\&CenterDot;\mathrm{CoC}\&CenterDot;d}---\left(19\right)$

The depth of field Δ L of video camera is:

$\mathrm{\&Delta;L}=\mathrm{\&Delta;<figure-callout\; id="1"\; label="L"\; filenames="HDA0000401704150000012.png"\; state="\{\{state\}\}">L</figure-callout>}1+\mathrm{\&Delta;L}2=\frac{{2f}^2\&CenterDot;F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^4-F^2\&CenterDot;{\mathrm{CoC}}^2\&CenterDot;d^2}---\left(20\right)$

Wherein, F is f-number, d=|O _la|=|O _rb| be focusing from, CoC, for allowing blur circle diameter, calculates by following formula:

CoC＝a/1730 (21)

Wherein, the catercorner length that a is effective image planes.

In XOZ coordinate system, build the equation of each place, border straight line, the form of straight-line equation is z=k ₀x+b, wherein k ₀for the slope of straight line, the intercept that b is straight line.

The equation of video camera CCD2 depth of field inner boundary l1 place, right side straight line is:

The equation of video camera CCD2 depth of field outer boundary l2 place, right side straight line is:

The equation of left side camera CCD1 depth of field inner boundary l3 place straight line is:

The equation of left side camera CCD1 depth of field outer boundary l4 place straight line is:

The equation of left margin l5 place, video camera CCD2 visual field, right side straight line is:

The equation of left margin l6 place, left side camera CCD1 visual field straight line is:

The equation of right margin l7 place, video camera CCD2 visual field, right side straight line is:

The equation of right margin l8 place, left side camera CCD1 visual field straight line is:

On measurement space length direction, the equation of left margin l9 (l9') place straight line is:

x＝D/2-L/2 (30)

On measurement space length direction, the equation of right margin l10 place straight line is:

x＝D/2+L/2 (31)

The statement of measurement space Width size W is divided into two kinds of situations: | CU|=W, | C'V'|=W.There is W=min{|CU|, | C'V'|}.Wherein,

According to the range of size of actual measurement Location of requirement measurement space, the size L>=L of length direction (X-direction) ₀, the size W>=W of Width (Z-direction) ₀, the size H>=H of short transverse (Y-direction) ₀, should meet L=L ₀time corresponding measurement space width

.Choose and be positioned at apparent field center L ₀* W ₀* H ₀in measurement space, an equally distributed p position is as test point, and the layout situation of test point is as follows: according to be divided into q the test plane being equally spaced along Z-direction direction from the close-by examples to those far off, test interplanar spacing is W ₀/ (q-1), each test plane is L ₀* H ₀，Ge region, region on choose that r is capable, s is listed as uniform test point.

Video camera adopts zoom lens, and the range of adjustment of focal distance f is [f ₁, f ₂]; The scope of parallax range D is [D ₁, D ₂]; Video camera depth of field Δ L>=W ₀; Distance between reference measure system and forging arranges suitable focusing from d; Video camera deflection angle

scope be [0, θ];

The layout optimization problem of this two CCD camera measure system is converted to the single goal optimization problem of following belt restraining:

Wherein, ∑ Q is the summation of p test point measuring error.Γ is the mean value of each test point measuring error, and it is objective function to be optimized.

for the reference position along two camera field of view laps of Z direction, its value is less than focusing from d.

Step 2: use genetic algorithm to find optimum solution, i.e. optimum structural parameters combination.

For the single goal optimization problem of the belt restraining obtaining in step 1, adopt genetic algorithm to carry out global optimizing.Detailed process is as follows:

(1) algorithm routine is write, and comprises and writes the objective function of optimization problem described in step 1 and the program file of non-linear constrain.

(2) optimized variable is focal distance f, parallax range D and video camera deflection angle

the span of each variable is respectively [f ₁, f ₂], [D ₁, D ₂] and

(3) Population Size is set, crossover probability, variation probability and algorithm end condition.

Population Size is elected PopSize as, and crossover probability is elected p as _c, variation probability is elected p as _m.The stop criterion of algorithm is: iterations reaches maximum iteration time MaxGen; Or when algorithm, stagnating in the algebraically ConGen of algebraically regulation, the weighted mean variation of fitness function is less than function franchise FunTol.

(4) move the program of genetic algorithm, draw the optimum solution of optimization problem, i.e. optimum structural parameters combination, makes the measuring error in whole measurement space reach minimum.

The invention has the beneficial effects as follows and utilize genetic algorithm to realize the layout optimization design of video camera in two CCD camera measure system, make the measuring error being caused by picture point extraction error reach minimum, in the situation that video camera not being demarcated, the rational deployment that can be video camera provides effective theoretical direction and reference, there is effect of optimization good, the feature such as application is strong.

Accompanying drawing explanation

Fig. 1 is the schematic diagram that analog image is sampled as digital picture.(a) analog image that figure is unique point, (b) figure is corresponding digital picture after unique point sampling, wherein: 1-unique point, 2-boost line, 3-pixel, 4-unique point place pixel.

Fig. 2 is the structural representation of two CCD camera measure system, the distribution schematic diagram that Fig. 3 is test point.Wherein: CCD1-left side camera, CCD2-right side video camera, O _lx _ly _lz _lthe camera coordinate system of-left side camera, O _l-left side camera the centre of perspectivity, O _lz _l-left side camera optical axis, | O _lthe focusing of A|-left side camera is from, O _rx _ry _rz _rthe camera coordinate system of-right side video camera, O _rthe video camera centre of perspectivity ,-right side, O _rz _r-right side camera optical axis, | O _rthe video camera focusing of B|-right side is from, OXYZ-world coordinate system, O-world coordinate system initial point, and D-parallax range, f-focal length of camera,

-video camera deflection angle, the angle of θ-camera optical axis and camera field of view boundary line, L-measurement space length, W-measurement space width, Z ₀-along the reference position of two camera field of view laps of Z direction, the Δ L-video camera depth of field, l1-right side video camera depth of field inner boundary, l2-right side video camera depth of field outer boundary, l3-left side camera depth of field inner boundary, l4-left side camera depth of field outer boundary, l5-right side camera field of view left margin, l6-left side camera visual field left margin, l7-right side camera field of view right margin, l8-left side camera visual field right margin, left margin on l9-measurement space length direction, the intersection point of C-l9 and l2, the intersection point of U-l9 and l3, the intersection point of V-l9 and l5, right margin on l10-measurement space length direction, left margin on measurement space length direction in the another kind of situation of l9'-, the intersection point of C'-l9' and l2, the intersection point of U'-l9' and l3, the intersection point of V'-l9' and l5, P _{k, (i, j)}the test point that in-k test plane, the capable j of i lists.

Embodiment

Below in conjunction with accompanying drawing and technical scheme, further describe the specific embodiment of the present invention.

As shown in Figure 1, after only having analog image (a) sampling of a unique point 1, obtain unique point 1 corresponding digital picture (b), continuous image planes by discrete be many square region, pixel 3.Characteristic point positioning method for Pixel-level precision, can only obtain the positional information of unique point 1 place pixel 4, if think that the position of this pixel is the position of unique point 1, will exist the picture point being caused by image sampling to extract deviation so.The system structure parameter that the present invention considers is the deflection angle of focal length of camera f, parallax range D and video camera

the present invention has set up by picture point and has extracted measuring error that deviation causes and the numerical relationship model of said structure parameter, it is Camera composition optimized mathematical model, considering, under apparent field's constraint, to use genetic algorithm to carry out global optimizing, the measuring system structural parameters of one group of optimum have been obtained.Concrete steps are as follows:

Step 1: in two CCD camera measure system, set up two Camera composition optimized mathematical models.

The imaging device that the present invention selects is Princeton MegaPlus II ES4020 type black-white CCD video camera, and its resolution is 2048 * 2048, and Pixel Dimensions is δ=7.4 μ m; Effectively image planes are of a size of 15.2mm * 15.2mm, i.e. γ=15.2mm, catercorner length for adapting to different visual field demands, two video cameras are all furnished with Tamron Di-II LD zoom lens, and the range of adjustment of its focal distance f is [f ₁, f ₂]=[18,250], unit is mm.The range of adjustment of the f-number F of this camera lens is [3.5,6.3], and for making logical light quantity large as far as possible, to obtain image clearly, lens aperture value F selects 3.5.The parameters of supposing two video cameras is identical.

The derivation of aforesaid formula (1)～formula (9) is to be all based upon on the basis that meets perspective projection relation ideally, and object point is in space continuous distribution.Yet, the continuous object point in space is sampled as picture point discrete in digital camera image planes, cause and exist picture point to extract deviation, consider to cause in sampling process the situation of maximum deviation, by formula (10), try to achieve and between picture point in the actual left and right picture plane of obtaining and picture point ideally, have extraction deviation:

ε _l＝ε _r＝±3.7μm

By formula (21), calculate and allow blur circle diameter CoC to be:

$\mathrm{CoC}=a/1730=15.2\sqrt{2}/1730\mathrm{mm}=0.0124\mathrm{mm}$

While utilizing binocular vision system to measure, target to be measured must refer to the overlapped fov in two video camera field depths in apparent field Nei， apparent field, as shown in the shadow region in Fig. 2.The measurement space that is used for obtaining forging ' s block dimension is as shown in the profile line region of Fig. 2.According to practical measurement requirement, require measurement space to meet: L ₀=3000mm, W ₀=3000mm, H ₀=3000mm, i.e. the size L>=3000mm of length direction (X-direction), the size W>=1000mm of Width (Z-direction), the size H>=3000mm of short transverse (Y-direction).

The measuring error of two CCD camera measure system is inhomogeneous in the distribution of measurement space, for without loss of generality, choose and be positioned at equally distributed 180 location points of apparent field center 3000mm * 1000mm * 3000mm measurement space (the shade rectangular parallelepiped region shown in Fig. 3) as test point, be i.e. p=180.Test point is numbered according to following rule: according to be divided into 5 tests plane, i.e. q=5 that are equally spaced along Z-direction direction from the close-by examples to those far off.Interplanar spacing is 1000/4=250mm, and each test plane is chosen the uniform test point of 6 row * 6 row on the ，Ge region, region that is 3000mm * 3000mm, i.e. r=6, s=6.Test point coding rule in each test plane is consistent with the pixel coordinate coding of image, and the upper left corner is coordinate origin, and (i, j) represents the test point that the capable j of i lists, and the sequence number of row increases progressively from top to bottom, and the sequence number of row increases progressively from left to right, uses P _{k, (i, j)}represent the test point that k the capable j of i in test plane lists.Therefore, can obtain the value of all test points each coordinate components in the ideal coordinates under world coordinate system, X _wvalue have: { D/2-1500, D/2-900, D/2-300, D/2+300, D/2+900, D/2+1500}, Y _wvalue have: 1500 ,-900 ,-300,300,900,1500}, Z _wvalue according to intersection point C (C'), U (U') and V (V') relatively video camera focusing from the position at d place, $[\frac{1000(Z_C-d^{\&prime;})}{Z_C-Z_U}+d^{\&prime;},d^{\&prime;}-\frac{1000(d^{\&prime;}-Z_U)}{Z_C-Z_U}]$ In scope, evenly choose 5 be worth and be spaced apart 250mm or $[\frac{1000(Z_C-d^{\&prime;})}{Z_C-Z_V}+d^{\&prime;},d^{\&prime;}-\frac{1000(d^{\&prime;}-Z_V)}{Z_C-Z_V}]$ In scope, evenly choose 5 and be worth and be spaced apart 250mm.The expression formula of wherein, establishing d' is:

Under XOZ coordinate system, solve the Z-direction coordinate of intersection point C (C'), U (U') and V (V'):

The Z-direction coordinate of C (C') point is:

The Z-direction coordinate of U (U') point is:

The Z-direction coordinate of V (V') point is:

According to forging on-site actual situations, consideration equipment install and avoid equipment because of some constraint conditions that obtain other compared with the factor such as near and overheated apart from hot large forgings as follows: the statement of the size W of measurement space Width is divided into two kinds of situations, a kind of situation is that the distance between C and U equals W, | CU|=W, another kind of situation is when on measurement space length direction, left margin l9' is near apparent field's right side edge, distance between C' and V' equals W, , there is W=min{|CU|, | C'V'|}.During measurement space lengthwise dimension L=3000mm, corresponding measurement space Width size W _l=3000=min{|CU| _l=3000, | C'V'| _l=3000and W _l=3000>=W ₀therefore, have | CU| _l=3000>=1000 and | C'V'| _l=3000>=1000.Consider the compactedness requirement of two CCD camera measure system, in conjunction with the restriction of video camera self size and erecting bed size, parallax range D span is [D ₁, D ₂]=[100,2000], unit is mm.Because measurement space is arranged in the overlapped fov of two video camera field depths, therefore, video camera depth of field Δ L must be greater than the width W of measurement space ₀, have Δ L>=1000mm.For avoiding high temperature to cause damage to measuring equipment, measuring system is at least d apart from anvil block center under forge press ₁=8000mm is far away, with reference to d ₁choose video camera focusing from d=8000mm.For making full use of apparent field, video camera deflection angle

scope is [0, θ].By formula (17), in conjunction with focal range [f ₁, f ₂] and the span that effectively image planes size γ calculates θ be [1.74 °, 22.89 °].

In sum, the layout optimization problem of this two CCD camera measure system is converted to the single goal optimization problem of following belt restraining:

Wherein, Q _{k, (i, j)}be the measuring error that k the capable j of i in test plane lists test point, Z ₀for along the overlapping reference position of Z direction two camera field of view, should there is Z ₀< 8000mm.

Step 2: use genetic algorithm to find optimum solution, i.e. optimum structural parameters combination.

For the single goal optimization problem of the belt restraining obtaining in step 1, adopt genetic algorithm to carry out global optimizing.From initial population, use genetic operator, select operator, crossover operator and mutation operator to produce population of future generation, so make population evolve towards the direction of optimization solution, until meet the end condition of setting.Detailed process is as follows:

(1) algorithm routine is write, and comprises and writes the objective function of optimization problem described in step 1 and the program file of non-linear constrain.

(2) optimized variable is focal distance f, parallax range D and video camera deflection angle

each variable-value scope is respectively [18,250], [100,2000] and [0,22.89], and unit is respectively millimeter, millimeter and degree.

(3) Population Size is set, crossover probability, variation probability and algorithm end condition

Algorithm parameter is set as PopSize=500, p _c=0.78, p _m=0.008, MaxGen=2000, ConGen=500, FunTol=10 ^-12, that is: Population Size elects 500 as, and crossover probability elects 0.78 as, and variation probability elects 0.008 as.The stop criterion of algorithm is: iterations reaches maximum iteration time 2000; Or when algorithm, stagnating in the algebraically 500 of algebraically regulation, the weighted mean variation of fitness function is less than function franchise 10 ^-12.

(4) call genetic algorithm master routine, draw the optimum solution of optimization problem, i.e. optimum structural parameters combination, makes the measuring error in whole measurement space reach minimum.

In step 1, the optimum solution of optimization problem is focal length of camera f=42.552mm, parallax range D=2000mm, video camera deflection angle

target function value converges to minimum value 5.834mm.Above-mentioned experiment is carried out on the computing machine of 1.99GB internal memory, 2.09GHz processor, and average consuming time is 2.8h.

In two CCD camera measure system, image sampling can cause picture point extraction deviation, the present invention extracts measuring error that deviation causes and the mathematical relation between structural parameters by setting up picture point, consider measurement space, equipment install and avoid equipment because of apart from large forgings radiation compared with the factor such as near and overheated, for video camera and the fixed two CCD camera measure system of camera lens, adopt genetic algorithm to carry out the layout optimization design of video camera, rely on the efficient global optimizing ability of genetic algorithm can obtain the structural parameters combination of global optimum.

Claims (1)

1. the layout optimization method of video camera in a two CCD camera measure system, it is characterized in that, in two CCD camera measure system, consider the picture point extraction deviation that image sampling causes, the numerical relationship model of the measuring error that foundation is caused by picture point extraction deviation and focal length of camera, parallax range, three structural parameters of video camera deflection angle, be Camera composition optimized mathematical model, and utilize genetic algorithm to obtain optimum structural parameters combination; Concrete steps are as follows:

Step 1: in two CCD camera measure system, set up two Camera composition optimized mathematical models;

Left side camera CCD1 and right side video camera CCD2 converge arranged in form with optical axis, the initial point O of world coordinate system OXYZ and the camera coordinate system O of left side camera _lx _ly _lz _linitial point O _loverlap; If the coordinate of a certain object point P in world coordinate system OXYZ is (X _w, Y _w, Z _w), at the camera coordinate system O of left side camera _lx _ly _lz _lcamera coordinate system O with right side video camera _rx _ry _rz _runder coordinate be respectively (X _l, Y _l, Z _l), (X _r, Y _r, Z _r), in left and right side video camera CCD1, CCD2 image planes, the image physical coordinates of picture point is respectively (x _l, y _l) and (x _r, y _r);

Object point P is at the camera coordinate system O of left and right side video camera _lx _ly _lz _l, O _rx _ry _rz _runder coordinate and the image physical coordinates of its picture point there is following relation:

$\left\{\begin{array}{c}{x}_l=f\frac{X_l}{Z_l}\\ y_l=f\frac{Y_l}{Z_l}\\ x_r=f\frac{X_r}{Z_r}\\ y_r=f\frac{Y_r}{Z_r}\end{array}\right.---\left(1\right)$

Object point P is at the camera coordinate system O of left and right side video camera _lx _ly _lz _l, O _rx _ry _rz _runder coordinate and its coordinate under world coordinate system OXYZ there is following relation:

By formula (3) and formula (2) substitution formula (1), obtain the coordinate of object point P under world coordinate system OXYZ and the following relation of image physical coordinates existence of picture point:

Simultaneous formula (1)～formula (5), obtains the coordinate (X of object point P under world coordinate system OXYZ _w, Y _w, Z _w) as follows:

Wherein, establish the expression formula of Ψ as follows:

Consider that sampling causes the situation of maximum picture point deviation, suppose that Pixel Dimensions is δ, the actual left and right video camera obtaining as the extraction deviation existing between the picture point in plane and picture point is ideally:

ε _l＝ε _r＝±0.5δ (10)

The left and right video camera that actual extracting obtains is respectively as the picture point physical coordinates in plane

, itself and picture point physical coordinates (x ideally _l, y _l), (x _r, y _r) pass be:

The picture point physical coordinates being obtained by actual extracting obtains the coordinate of object point P under world coordinate system OXYZ

as follows:

Wherein, establish

expression formula as follows:

Setting up picture point extracts measuring error Q and the mathematical relation between structural parameters that deviation causes and is:

For the measurement space that obtains forging ' s block dimension, be of a size of L * W * H, L represents the size of length direction (X-direction), and W represents the size of Width (Z-direction), and H represents the size of short transverse (Y-direction), Y-axis forward be vertical paper inwards;

In XOZ plane, the angle theta of the left and right visual field border line of camera optical axis and video camera is:

$\mathrm{\&theta;}=\arctan \left(\frac{\mathrm{\&gamma;}}{2f}\right)---\left(17\right)$

Wherein, γ is effective image planes size;

The front depth of field Δ L1 of video camera is:

$\mathrm{\&Delta;L}1=\frac{F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^2+F\&CenterDot;\mathrm{CoC}\&CenterDot;d}---\left(18\right)$

The rear depth of field Δ L2 of video camera is:

$\mathrm{\&Delta;L}2=\frac{F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^2-F\&CenterDot;\mathrm{CoC}\&CenterDot;d}---\left(19\right)$

The depth of field Δ L of video camera is:

$\mathrm{\&Delta;L}=\mathrm{\&Delta;L}1+\mathrm{\&Delta;L}2=\frac{{2f}^2\&CenterDot;F\&CenterDot;\mathrm{CoC}\&CenterDot;d^2}{f^4-F^2\&CenterDot;{\mathrm{CoC}}^2\&CenterDot;d^2}---\left(20\right)$

Wherein, F is f-number, d=|O _la|=|O _rb| be focusing from, CoC, for allowing blur circle diameter, calculates by following formula:

CoC＝a/1730 (21)

Wherein, the catercorner length that a is effective image planes;

In XOZ coordinate system, build the equation of each place, border straight line, the form of straight-line equation is z=k ₀x+b, wherein k ₀for the slope of straight line, the intercept that b is straight line;

The equation of video camera CCD2 depth of field inner boundary l1 place, right side straight line is:

The equation of video camera CCD2 depth of field outer boundary l2 place, right side straight line is:

The equation of left side camera CCD1 depth of field inner boundary l3 place straight line is:

The equation of left side camera CCD1 depth of field outer boundary l4 place straight line is:

The equation of left margin l5 place, video camera CCD2 visual field, right side straight line is:

The equation of left margin l6 place, left side camera CCD1 visual field straight line is:

The equation of right margin l7 place, video camera CCD2 visual field, right side straight line is:

The equation of right margin l8 place, left side camera CCD1 visual field straight line is:

On measurement space length direction, the equation of left margin l9 (l9') place straight line is:

x＝D/2-L/2 (30)

On measurement space length direction, the equation of right margin l10 place straight line is:

x＝D/2+L/2 (31)

The statement of measurement space Width size W is divided into two kinds of situations: | CU|=W or | C'V'|=W, have W=min{|CU|, | C'V'|}; Wherein,

According to the range of size of actual measurement Location of requirement measurement space, the size L>=L of length direction (X-direction) ₀, the size W>=W of Width (Z-direction) ₀, the size H>=H of short transverse (Y-direction) ₀, should meet L=L ₀time corresponding measurement space width W _l=L0>=W ₀; Choose and be positioned at apparent field center L ₀* W ₀* H ₀in measurement space, an equally distributed p position is as test point, and the layout situation of test point is as follows: according to be divided into q the test plane being equally spaced along Z-direction direction from the close-by examples to those far off, test interplanar spacing is W ₀/ (q-1), each test plane is L ₀* H ₀，Ge region, region on choose that r is capable, s is listed as uniform test point;

Video camera adopts zoom lens, and the range of adjustment of focal distance f is [f ₁, f ₂]; The scope of parallax range D is [D ₁, D ₂]; Video camera depth of field Δ L>=W ₀; Distance between reference measure system and forging arranges suitable focusing from d; Video camera deflection angle

scope be [0, θ];

The layout optimization problem of this two CCD camera measure system is converted to the single goal optimization problem of following belt restraining:

Wherein, ∑ Q is the summation of p test point measuring error; Γ is the mean value of each test point measuring error, and it is objective function to be optimized; for the reference position along two camera field of view laps of Z direction, its value is less than focusing from d;

Step 2: use genetic algorithm to find optimum solution, i.e. optimum structural parameters combination;

For the single goal optimization problem of the belt restraining obtaining in step 1, adopt genetic algorithm to carry out global optimizing; Detailed process is as follows:

(1) algorithm routine is write, and comprises and writes the objective function of optimization problem described in step 1 and the program file of non-linear constrain;

(2) optimized variable is focal distance f, parallax range D and video camera deflection angle

the span of each variable is respectively [f ₁, f ₂], [D ₁, D ₂] and

(3) Population Size is set, crossover probability, variation probability and algorithm end condition;

Population Size is elected PopSize as, and crossover probability is elected p as _c, variation probability is elected p as _m; The stop criterion of algorithm is: iterations reaches maximum iteration time MaxGen; Or when algorithm, stagnating in the algebraically ConGen of algebraically regulation, the weighted mean variation of fitness function is less than function franchise FunTol;

(4) move the program of genetic algorithm, draw the optimum solution of optimization problem, i.e. optimum structural parameters combination, makes the measuring error in whole measurement space reach minimum.

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