CN105654476A - Binocular calibration method based on chaotic particle swarm optimization algorithm - Google Patents

Abstract

The invention provides a binocular calibration method based on a chaotic particle swarm optimization algorithm. A plurality of sets of dot array planar calibration board image pairs with different poses are simultaneously photographed through two image cameras. On condition that distortion is not considered, initial values of inner parameters and outer parameters of a left image camera and a right image camera are obtained by means of a Zhang's planar template linear calibration method. Then on condition that a two-order radial distortion and a two-order tangential distortion are considered, a three-dimensional reprojection error is minimized by means of the chaotic particle swarm optimization algorithm, thereby obtaining final inner parameter and final outer parameter of the two image cameras. In an iteration optimization process, a global adaptive inertia weight (GAIW) is introduced. A particle local neighborhood is constructed by means of a dynamic annular topological relationship. Speed and current position are updated according to an optimal fitness value in the particle local neighborhood. Furthermore chaotic optimization is performed on the optimal position which corresponds with the optimal fitness value in the particle local neighborhood. The binocular calibration method effectively settles a problem of low calibration precision caused by a local extreme value in a previous particle swarm optimization algorithm, thereby improving binocular calibration precision and ensuring high precision in subsequent binocular three-dimensional reconstruction.

Description

Based on the binocular calibration method of chaotic particle swarm optimization algorithm

Technical field

The present invention relates to machine vision metrology field, in particular to a kind of binocular calibration method based on chaotic particle swarm optimization algorithm.

Background technology

Binocular vision is perceived distance technology the most important in passive ranging method, owing to its direct modeling human vision is to the processing mode of scene, take testee from different angles by two pick up cameras simultaneously, through binocular calibration and three-dimensional coupling, principle of triangulation is utilized to obtain the three-dimensional information of object. Wherein binocular calibration is as the most important integral part of binocular vision, and its essence is the relative pose relation determining between the inner parameter of two pick up cameras and two pick up cameras according to pick up camera geometry imaging model.

Existing camera marking method mainly contains linear approach, two-step approach, nonlinear optimization method etc., and wherein linear approach does not consider that camera lens distorts, and precision is not high; Two-step approach is one method comparatively flexibly between linear approach and nonlinear method, mainly contain the two-step approach of Tsai and the flat formwork method of Zhang, both linear solution initial parameters, then consider that distortion carries out nonlinear optimization, but still the requirement of industrial machine vision can not be met, stated accuracy increases; Nonlinear optimization method, owing to considering that distortion carries out successive ignition optimization, can obtain higher stated accuracy. Traditional nonlinear parameter optimization method has Levenberg-Marquardt method, gradient descent method, method of conjugate gradient, newton's method etc., but such method computation process is complicated, initial iterative value is responsive, parameter is by the constraint of non-linear factor, and poor astringency, easily it is absorbed in local optimum, it is not easy to obtain optimum solution. Numerous scholar proposes to utilize intelligent optimization algorithm to carry out nonlinear calibration, wherein particle cluster algorithm owing to realizing easily, precision height, restrain the advantage such as fast and be widely used in pick up camera and demarcate in parameter optimization, but easily it is absorbed in local extreme value, causes calibration result inaccurate.

Summary of the invention

The present invention is in order to determine the inside and outside parameter of left and right two pick up cameras in binocular vision system, it provides a kind of binocular calibration method based on chaotic particle swarm optimization algorithm.By taking the dot matrixes plane reference plate image of many group different positions and poses, image coordinate according to scaling board round dot center and the corresponding relation of world's coordinate thereof, flat formwork standardization based on Zhang Zhengyou obtains two camera interior and exterior parameter initial values, the three-dimensional re-projection error function of recycling chaotic particle swarm optimization algorithm iteration minimization, obtains the inside and outside parameter that two pick up cameras are final.

For reaching this object, the present invention is achieved through the following technical solutions:

(1) adopting the round dot edge profile of Canny operator extraction scaling board image, recycling Zernike square carries out sub-pixel edge extraction, tries to achieve round dot center sub-pix image coordinate by ellipse fitting;

(2) adopt pin hole imaging model to describe the linear model between the sub-pix image coordinate at round dot center and world's coordinate thereof, ask for the homography matrix that world's coordinate is tied to image coordinate system;

(3), when not considering that camera lens distorts, utilize the flat formwork standardization of Zhang Zhengyou to be demarcated respectively by left and right two pick up camera, obtain two camera interior and exterior parameter initial values;

(4) camera lens two rank radial direction and two rank circumferential distortions are considered, based on the two camera interior and exterior parameter initial values of (3), by constructing three-dimensional re-projection error function as optimization object function, chaos particle cluster algorithm is utilized to carry out the iteration optimization of inside and outside parameter. In optimizing process, introduce overall situation self-adaptation dynamic inertia weight (GAIW), simultaneously speed more the new stage according to the optimal-adaptive angle value renewal speed in particle local neighborhood and current position, and the optimal location that optimal-adaptive angle value in particle local neighborhood is corresponding is carried out chaos optimization, dynamically annular topology is wherein utilized to close series structure particle local neighborhood, neighborhood linearly increases along with iteration number of times, and last neighborhood extending is to whole population;

(5) judge termination condition, if objective function fitness value evolves to the precision �� set in advance, then terminate optimizing and the final inside and outside parameter result of two pick up cameras about exporting, otherwise return step (4).

The invention has the beneficial effects as follows: the present invention provides a kind of binocular calibration method based on chaotic particle swarm optimization algorithm, chaotic particle swarm optimization algorithm application is optimized in binocular vision camera interior and exterior parameter, solve traditional nonlinear parameter optimization method computation process in vision calibration complicated, to initial iterative value sensitivity and to noise-sensitive, stated accuracy is not high, can not meet industrial requirements. In optimizing process, introduce overall situation self-adaptation dynamic inertia weight (GAIW), simultaneously speed more the new stage according to the optimal-adaptive angle value renewal speed in particle local neighborhood and current position, dynamically annular topology is wherein utilized to close series structure particle local neighborhood, and the optimal location that optimal-adaptive angle value in particle local neighborhood is corresponding is carried out chaos optimization, thus efficiently solve the problem that primary particle colony optimization algorithm is easily absorbed in local extreme value, thus improve binocular calibration precision and robustness, ensure the precision that follow-up binocular vision 3 D reconstructs.

Accompanying drawing explanation

Fig. 1 Binocular Stereo Vision System schematic diagram

Fig. 2 binocular camera demarcates schematic diagram

Fig. 3 population ring topology schematic diagram

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in further detail.

The present invention provides a kind of binocular calibration method based on chaotic particle swarm optimization algorithm, whole algorithm flow primarily of scaling board image round dot center sub-pix image coordinate is extracted, homography matrix is asked for, camera interior and exterior parameter initial value is determined, chaos particle cluster algorithm carries out inside and outside parameter optimization formation.

For further explanation, specific implementation step is as follows:

Step one: scaling board image round dot center sub-pix image coordinate is extracted

(1) many groups scaling board image that two pick up cameras are taken from different angles simultaneously is inputted respectively;

(2) respectively sequence is carried out the extraction of Canny edge by left and right scaling board image, then utilize Zernike square to carry out sub-pixel edge extraction, try to achieve round dot center sub-pix image coordinate by ellipse fitting, be designated as respectivelyWithWherein i=1,2 ..., 49, in every width scaling board image, round dot number is 49.

Step 2: homography matrix is asked for

(1) pin hole imaging model is adopted to describe the linear model between the sub-pix image coordinate at scaling board image round dot center and world's coordinate thereof, shown in (1), and by world system of coordinates Z_w=0 place plane is set to the measurement plane at scaling board place.

$s^j\left[\begin{array}{c}{u}_i^j\\ v_i^j\\ 1\end{array}\right]=A^j\left[\begin{array}{cc}{R}^j& T^j\end{array}\right]\left[\begin{array}{c}{X}_{wi}\\ Y_{wi}\\ Z_{wi}\\ 1\end{array}\right]=A^j\left[\begin{array}{ccc}{\mathrm{\α}}^j& {\mathrm{\β}}^j& T^j\end{array}\right]\left[\begin{array}{c}{X}_{wi}\\ Y_{wi}\\ 1\end{array}\right]---\left(1\right)$

In formula, j=l, r, the parameter of the corresponding left pick up camera of j=l, the parameter of the corresponding right pick up camera of j=r, s^jFor scale factor; A^jFor camera intrinsic parameter, it is designated as The normalization method focal length being respectively on x, y direction,For coefficient of torsion;For the pixel coordinate of pick up camera primary optical axis and image plane point of intersection, it is called principal point; R^jFor camera coordinate system rotation matrix orthogonal relative to world's system of coordinates 3 �� 3, it is external parameters of cameras, it is designated as $R^j=\left[\begin{array}{ccc}{r}_{11}^j& r_2^j& r_{13}^j\\ r_{21}^j& r_{22}^j& r_{23}^j\\ r_{31}^j& r_{32}^j& r_{33}^j\end{array}\right];$ ��^j, ��^j, ��^jIt is respectively rotation matrix R^jThree column vectors, be designated as ${\mathrm{\α}}^j={\left[\begin{array}{ccc}{r}_1^j& r_{21}^j& r_{31}^j\end{array}\right]}^T,$ ${\mathrm{\β}}^j={\left[\begin{array}{ccc}{r}_2^j& r_{22}^j& r_{32}^j\end{array}\right]}^T,$ ${\mathrm{\γ}}^j={\left[\begin{array}{ccc}{r}_3^j& r_{23}^j& r_{33}^j\end{array}\right]}^T;$ T^jFor camera coordinate system translates vector relative to world's system of coordinates 3 �� 1, it is external parameters of cameras, it is designated as ${\tilde{P}}_i={\left[\begin{array}{cccc}{X}_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1\end{array}\right]}^T$ It is respectively the homogeneous coordinate of scaling board round dot center in image coordinate system and world's system of coordinates.

(2) the round dot center sub-pix image coordinate that step one is extracted is utilizedWithAnd the world coordinate P of picture point_i=(X_wiY_wiZ_wi)^T, obtain, according to formula (2), the homography matrix H that world's coordinate is tied to left and right cameras image coordinate system respectively^lAnd H^r��

H^j=A^j[��^j��^jT^j], j=l, r (2)

Step 3: camera interior and exterior parameter initial value is determined

(1) due to ��^jAnd ��^jIt is unit orthogonal vector, by H^jMatrix is write asObtain the intrinsic parameter constraint condition shown in formula (3).

$\begin{array}{c}{h^T}_1^j{A}^{-T_j}{A}^{-1_j}{h}_2^j=0\\ {h^T}_1^j{A}^{-T_j}{A}^{-1_j}{h}_1^j={h^T}_2^j{A}^{-T_j}{A}^{-1_j}{h}_2^j\end{array}---\left(3\right)$

When linear solution camera interior and exterior parameter initial value, order:

$B^j=A^{-T_j}{A}^{-1_j}=\left[\begin{array}{ccc}{B}_{11}^j& B_{12}^j& B_{13}^j\\ B_{12}^j& B_{22}^j& B_{23}^j\\ B_{13}^j& B_{23}^j& B_{33}^j\end{array}\right]---\left(4\right)$

Wherein B^jFor 3*3 symmetric matrix.

On the basis of formula (3) and formula (4), Zhang Zhengyou template planar linear standardization is utilized to derive camera intrinsic parameter, shown in (5).

In formula, $c^j=B_{33}^j-\[{B^2}_{13}^j+v_0^j(B_{12}^j{B}_{13}^j-B_{11}^j{B}_{23}^j)\]/{B^2}_{11}^j,j=l,r.$

(2), after obtaining the intrinsic parameter initial value of pick up camera, external parameters of cameras initial value is asked for according to homography matrix.

Can obtain by formula (2):

$h_1^j=A^j{\mathrm{\α}}^j,h_2^j=A^j{\mathrm{\β}}^j,h_3^j=A^j{T}^j---\left(6\right)$

On formula (6) basis, Zhang Zhengyou template planar linear standardization is utilized to derive external parameters of cameras, shown in (7).

$\begin{array}{c}{\mathrm{\λ}}^j=1/\left|\right|A^{-1_j}{h}_1^j\left|\right|=1/\left|\right|a^{-1_j}{h}_2^j\left|\right|\\ {\mathrm{\α}}^j={\mathrm{\λ}}^j{A}^{-1_j}{h}_1^j\\ {\mathrm{\β}}^j={\mathrm{\λ}}^j{A}^{-1_j}{h}_2^j\\ {\mathrm{\γ}}^j={\mathrm{\α}}^j\×{\mathrm{\β}}^j\\ T^j={\mathrm{\λ}}^j{A}^{-1_j}{h}_3^j\end{array}---\left(7\right)$

Step 4: the two camera interior and exterior parameter optimizations considering distortion

(1) considering two rank radial distortions and two rank circumferential distortions, distortion model is such as formula shown in (8).

$\left\{\begin{array}{c}{u}_i^{\′j}=u_i^j+u_i^j(k_1^j{r}^2+k_2^j{r}^4)+2p_1^j{u}_i^j{v}_i^j+p_2^j(r^2+2{u^2}_i^j)\\ {v^{\′}}_i^j=v_i^j+v_i^j(k_1^j{r}^2+k_2^j{r}^4)+2p_2^j{u}_i^j{v}_i^j+p_1^j(r^2+2{v^2}_i^j)\end{array}\right.---\left(8\right)$

In formula, j=l, r,For round dot center real image coordinate,For round dot center ideal image coordinate, For coefficient of radial distortion, For tangential distortion coefficient.

The two camera interior and exterior parameter initial value A that integrating step three obtains^l��R^l��T^lAnd A^r��R^r��T^r, all inside and outside parameter of demarcation can with vector table illustrated as ��, shown in (9).

$\begin{array}{c}\mathrm{\θ}=({\mathrm{\θ}}^l,{\mathrm{\θ}}^r)=(f_x^l,f_y^l,u_0^l,v_0^l,k_1^l,k_2^l,p_1^l,p_2^l,{\mathrm{\α}}^l,{\mathrm{\β}}^l,{\mathrm{\γ}}^l,t_x^l,t_y^l,t_z^l,\\ f_x^r,f_y^r,u_0^r,v_0^r,k_1^r,k_2^r,p_1^r,p_2^r,{\mathrm{\α}}^r,{\mathrm{\β}}^r,{\mathrm{\γ}}^r,t_x^r,t_y^r,t_z^r)\end{array}---\left(9\right)$

Wherein,

$\begin{array}{c}{\mathrm{\θ}}^l=(f_x^l,f_y^l,u_0^l,v_0^l,k_1^l,k_2^l,p_1^l,p_2^l,{\mathrm{\α}}^l,{\mathrm{\β}}^l,{\mathrm{\γ}}^l,t_x^l,t_y^l,t_z^l)\\ {\mathrm{\θ}}^r=(f_x^r,f_y^r,u_0^r,v_0^r,k_1^r,k_2^r,p_1^r,p_2^r,{\mathrm{\α}}^r,{\mathrm{\β}}^r,{\mathrm{\β}}^r,{\mathrm{\γ}}^r,t_x^r,t_y^r,t_z^r)\end{array}---\left(10\right)$

(2) carrying out two camera interior and exterior parameter optimizations based on chaos particle cluster algorithm, step is as follows:

Step1: the scaling board image round dot centre coordinate extracted according to step oneWithAnd by distortion factorWithValue is initialized as 0, tries to achieve round dot center ideal image coordinate according to distortion model formula (8)With

Step2: the projection matrix M trying to achieve two pick up cameras according to formula (11)^lAnd M^r��

M^j=A^j[R^jT^j], j=l, r (11)

Wherein, projection matrix M^jIt is the matrix of 3 �� 4, it is designated as $M^j=\left[\begin{array}{cccc}{m}_{11}^j& m_{12}^j& m_{13}^j& m_{14}^j\\ m_{21}^j& m_{22}^j& m_{23}^j& m_{24}^j\\ m_{31}^j& m_{32}^j& m_{33}^j& m_{34}^j\end{array}\right];$

Step3: based on desirable coordinateWithWith the projection matrix M of binocular camera^lAnd M^r, try to achieve spatial point three-dimensional coordinate P ' according to formula (12)��(17)_i=[X '_wiY��_wiZ��_wi]^T��

Note $\widetilde{{a^{\′}}_i^l}={\left[\begin{array}{ccc}{u^{\′}}_i^l& {v^{\′}}_i^l& 1\end{array}\right]}^T,$ $\widetilde{{a^{\′}}_i^r}={\left[\begin{array}{ccc}{u^{\′}}_i^r& {v^{\′}}_i^r& 1\end{array}\right]}^T,$ $\widetilde{{P^{\′}}_i}={\left[\begin{array}{cccc}{X^{\′}}_{wi}& {Y^{\′}}_{wi}& {Z^{\′}}_{wi}& 1\end{array}\right]}^T,$ It is respectively With P '_iHomogeneous coordinate, can obtain according to formula (1):

$s^l\widetilde{{a^{\′}}_i^l}=M^l\widetilde{{P^{\′}}_i}---\left(12\right)$

$s^r\widetilde{{a^{\′}}_i^r}=M^r\widetilde{{P^{\′}}_i}---\left(13\right)$

Association type (12) and formula (13), cancellation s^lAnd s^rCan obtain:

K_iP_i=U_i(14)

$K_i=\left[\begin{array}{ccc}{u^{\′}}_i^l{m}_{31}^l-m_{11}^l& {u^{\′}}_i^l{m}_{32}^l-m_{12}^l& {v^{\′}}_i^l{m}_{33}^l-m_{13}^l\\ {v^{\′}}_i^l{m}_{31}^l-m_{21}^l& {v^{\′}}_i^l{m}_{32}^l-m_{22}^l& {v^{\′}}_i^l{m}_{33}^l-m_{23}^l\\ {u^{\′}}_i^r{m}_{31}^r-m_{11}^r& {u^{\′}}_i^r{m}_{32}^r-m_{12}^r& {u^{\′}}_i^r{m}_{33}^r-m_{13}^r\\ {v^{\′}}_i^r{m}_{31}^r-m_{21}^r& {v^{\′}}_i^r{m}_{32}^r-m_{22}^r& {v^{\′}}_i^r{m}_{33}^r-m_{23}^r\end{array}\right]---\left(15\right)$

$U_i={\left[\begin{array}{cccc}{m}_{14}^l-{u^{\′}}_i^l{m}_{34}^l& m_{24}^l-{v^{\′}}_i^l{m}_{34}^l& m_{14}^r-{u^{\′}}_i^r{m}_{34}^r& m_{24}^r-{v^{\′}}_i^r{m}_{34}^r\end{array}\right]}^T---\left(16\right)$

Formula (14) represents light path O in Fig. 1_la_lAnd O_ra_iIntersect at object point P '_i, K_iIt is 4 �� 3 matrixes, P '_iFor the three-dimensional vector of the unknown, U_iIt is 4 �� 1 vectors, solves formula (17) by method of least squares and can obtain object point P '_iWorld's coordinate.

${P^{\′}}_i={\left({K_i}^T{K}_i\right)}^{-1}{K_i}^T{U}_i---\left(17\right)$

Step4: according to two camera interior and exterior parameter initial values and all initial values be 0 distortion factor the speed of particle in population and position are carried out random initializtion, the position of usual initialize Searching point and speed produce at random in initial value neighborhood space, and to arrange number of particles be ��=100, search space dimension is D=28, demarcation inside and outside parameter sum corresponding to be optimized.

Step5: the fitness value f (��) calculating each particle, bring formula (18) into by each particle and try to achieve optimization object function value, namely by the three-dimensional re-projection error function of structure as optimization object function, the actual demarcation point three-dimensional coordinate (X measured is utilized_wiY_wiZ_wi)^TWith calculate by model three-dimensional coordinate (X '_wiY��_wiZ��_wi)^TBetween residual error represent.

$f\left(\mathrm{\θ}\right)=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}\[{(X_{wi}-{X^{\′}}_{wi})}^2+{(Y_{wi}-{Y^{\′}}_{wi})}^2+{(Z_{wi}-{Z^{\′}}_{wi})}^2\]}---\left(18\right)$

In formula, the D that �� is each particle ties up position vector, and N represents the quantity of round dot scaling board image subscript fixed point.

Step6: the speed of particle and position are upgraded according to formula (19)��(21).

$v_{i,d}(t+1)=\left(\mathrm{\ω}\right)v_{i,d}\left(t\right)+c_1{r}_1\left(t\right)\[{\mathrm{Pbest}}_{i,d}\left(t\right)-x_{i,d}\left(t\right)\]+c_2{r}_2\left(t\right)\[{\mathrm{Gbest}}_d\left(t\right)-x_{i,d}\left(t\right)\]---\left(19\right)$

$x_{i,d}(t+1)=x_{i,d}\left(t\right)+v_{i,d}(t+1)---\left(20\right)$

$\mathrm{\ω}\left(t\right)={\mathrm{\ω}}_{max}-t\×\frac{{\mathrm{\ω}}_{max}-{\mathrm{\ω}}_{min}}{t_{max}}---\left(21\right)$

In formula, i=1,2 ..., ��, d=1,2 ..., D, x_{I, d}T () represents the position of particle i d dimension in the t time iteration in colony, v_{I, d}(t+1) it is corresponding speed; c₁��c₂For acceleration constant (learning rate), general span is [0,2], often gets fixed value 2; r₁(t)��r₂T () is [0,1] equally distributed randomized number; Pbest_{I, d}T d that () is particle i personal best particle vector ties up element, Gbest_dT d dimension element that () is whole population overall situation optimal location vector; �� (t) is inertia weight, which determines particle historical speed information to the impact of present speed information, and t is current iteration number of times, t_maxFor total iteration number of times, generally get ��_max=0.9, ��_mm=0.4.

For finding global extremum point more accurately sooner, thus improve the precision that in binocular calibration, camera interior and exterior parameter is optimized, introduce overall situation self-adaptation dynamic inertia weight (GAIW), shown in (22).

$\mathrm{\ω}(t+1)=\left\{\begin{array}{cc}0.9& ift=0\\ f\left(Gbest\right(t+1\left)\right)-f\left(Gbest\right(t\left)\right)& ift>0\end{array}\right.---\left(2\right)$

In formula, Gbest (t+1) is the t+1 time iteration overall situation optimal location vector, Gbest (t) is the t time iteration overall situation optimal location vector, the overall optimal-adaptive angle value of the corresponding Gbest (t+1) of f (Gbest (t+1)) and f (Gbest (t)) difference and Gbest (t) position. The value of �� (t) upgrades according to the overall optimal-adaptive angle value of history iteration and current iteration. If the search procedure of particle does not find more excellent overall fitness value position, then �� (t) is set to 0, if the value of �� (t) is 0 continuous K time, then upgrade �� (t) value according to formula (21) so that particle search near the position that current overall situation optimal-adaptive angle value is corresponding.

Step7: calculate the desired positions Pbest that particle i experiences_iT (), the position with optimal-adaptive angle value that also namely particle was experienced, shown in (23).

${\mathrm{Pbest}}_i(t+1)=\left\{\begin{array}{c}{x}_i(t+1),f\left(x_i\right(t+1\left)\right)<{\mathrm{Pbest}}_i\left(t\right)\\ {\mathrm{pbest}}_i\left(t\right),f\left(x_i\right(t+1\left)\right)\&GreaterEqual;{\mathrm{Pbest}}_i\left(t\right)\end{array}\right.---\left(23\right)$

In formula, x_i(t+1) it is particle i the t+1 time iteration optimal location vector, f (x_i(t+1)) it is the fitness value of correspondence position.

Step8: calculate all particles in colony and experienced desired positions, namely there is overall optimal location Gbest (t) that overall optimal-adaptive angle value is corresponding.

Due to the particle cluster algorithm fast convergence rate of overall situation version, but easily it is absorbed in local optimum. The present invention adopts the distribution of dynamic ring topology structure particle, forms as shown in Figure 3 a ring, with the local optimum position Gbest of all particles in particle i neighborhood between particle_iT () replaces overall situation optimal location Gbest (t), speed and position to particle i upgrade. Wherein, determining particle i neighborhood according to the mode of linear increment, for the t time iteration, the Size of Neighborhood that particle i is corresponding is 2t, until expanding to whole particle colony.For particle 1, during the 0th iteration, neighborhood is that it is own; During the 1st iteration, neighborhood is 2,8; During the 2nd iteration, neighborhood is 2,3,7,8, analogizes with this, until neighborhood extending is to whole particle colony.

Occur for preventing some particle stagnating in iteration, cause the local optimum position Gbest in above-mentioned particle i neighborhood_iT () solves inaccurate, take chaotic maps equation to local optimal location Gbest here_iT () carries out chaos optimization. Algorithm utilizes the ergodicity of Chaos Variable, based on the local optimum position searched in particle i neighborhood, iteration produces a chaos sequence, then optimum particle position in this sequence replace a certain particle position in current particle i neighborhood carry out iteration at random, thus solve particle and stagnate the algorithm premature convergence problem caused, concrete steps are as follows:

I. by formula (24) by Gbest_iT () maps in the field of definition [0,1] arriving chaotic maps equation (25), and remember

$\begin{array}{c}{\mathrm{Gbest}}_i\left(t\right)=\&lsqb;{\mathrm{Gbest}}_{i,1}\left(t\right),{\mathrm{Gbest}}_{i,2}\left(t\right),\mathrm{...},{\mathrm{Gbest}}_{i,d}\left(t\right),...,{\mathrm{Gbest}}_{l,D}\left(t\right)\&rsqb;,d=1,2,...,D;\\ y_{i,d}^1\left(t\right)=\frac{{\mathrm{Gbest}}_{i,d}\left(t\right)-R_{i,d}^{\min }\left(t\right)}{R_{i,d}^{\max }\left(t\right)-R_{i,d}^{\min }\left(t\right)}\end{array}---\left(24\right)$

$\begin{array}{c}{R}_{i,d}^{\min }\left(t\right)=\min \left\{{\mathrm{Gbest}}_i\left(t\right)\right\},R_{i,d}^{\max }\left(t\right)-\max \left\{{\mathrm{Gbest}}_i\left(t\right)\right\}\\ y_{i,d}^{n+1}\left(t\right)=\left\{\begin{array}{cc}{y}_{i,d}^n\left(t\right)/0.4,& 0<y_{i,d}^n\left(t\right)\&le;0.4\\ (1-y_{i,d}^n(t\left)\right)/(1-0.4),& 0.4\&le;y_{i,d}^n\left(t\right)<1\end{array}\right.\end{array}---\left(25\right)$

Ii. rightCarry out Q iteration by chaotic maps equation (25), obtain such as formula the chaos sequence shown in (26);

Iii. chaos sequence is returned former solution space by formula (27) inverse mapping, obtain a Chaos Variable feasible solution sequenceShown in (28);

Iv. feasible solution sequence is calculatedIn each feasible solution vectorFitness value, and retain fitness value optimum time feasible solution vector, be designated as Gbest '_i(t);

V. random from current particle i neighborhood a particle is selected, and with Gbest '_iT the position vector of () replaces the position vector of this particle.

Step9: judge termination condition, if the fitness value of objective function evolves to the precision �� set in advance, then terminates optimizing and Output rusults, otherwise returns Step5.

Claims (2)

1. based on the binocular calibration method of chaotic particle swarm optimization algorithm, it is characterized in that, two pick up cameras are by the dot matrixes plane reference plate image pair of shooting many groups different positions and pose simultaneously, image coordinate according to scaling board round dot center and the corresponding relation of world's coordinate thereof, flat formwork standardization based on Zhang Zhengyou obtains two camera interior and exterior parameter initial values, the three-dimensional re-projection error of recycling chaotic particle swarm optimization algorithm iteration minimization, obtain the inside and outside parameter that two pick up cameras are final, there is higher stated accuracy, thus ensure the precision that follow-up binocular vision 3 D reconstructs, mainly comprise following several steps:

(1) adopting the round dot edge profile of Canny operator extraction scaling board image, recycling Zernike square carries out sub-pixel edge extraction, tries to achieve round dot center sub-pix image coordinate by ellipse fitting;

(2) adopt pin hole imaging model to describe the linear model between the sub-pix image coordinate at scaling board image round dot center and world's coordinate thereof, ask for the homography matrix that world's coordinate is tied to image coordinate system;

(3), when not considering that camera lens distorts, utilize flat formwork linear calibration's method of Zhang Zhengyou that left and right two pick up camera is carried out linear calibration respectively, obtain two camera interior and exterior parameter initial value A respectively^l��R^l��T^lAnd A^r��R^r��T^r;

(4) camera lens two rank radial direction and two rank circumferential distortions are considered, based on the two camera interior and exterior parameter initial values of (3), by constructing three-dimensional re-projection error function as optimization object function, chaos particle cluster algorithm is utilized to carry out the iteration optimization of inside and outside parameter, in optimizing process, introduce overall situation self-adaptation dynamic inertia weight (GAIW), simultaneously speed more the new stage according to the optimal-adaptive angle value renewal speed in particle local neighborhood and current position, and the optimal location that optimal-adaptive angle value in particle local neighborhood is corresponding is carried out chaos optimization, dynamically annular topology is wherein utilized to close series structure particle local neighborhood, neighborhood linearly increases along with iteration number of times, last neighborhood extending is to whole population,

(5) judge termination condition, if the fitness value of objective function evolves to the precision �� set in advance, then terminate optimizing and export the inside and outside parameter result of left and right cameras, otherwise return step (4).

2. according to claim 1 based on the binocular calibration method of chaotic particle swarm optimization algorithm, utilizing chaotic particle swarm optimization algorithm to carry out the inside and outside parameter iteration optimization of two pick up cameras in described step (4)��(5), its feature is as follows:

The first step, obtain two camera interior and exterior parameter initial values according to step (3) and all initial values be 0 distortion factor the speed of particle in population and position are carried out random initializtion, and to arrange number of particles be ��=100, search space dimension is D=28, the sum of corresponding demarcation inside and outside parameter to be optimized;

2nd step, the fitness value f (��) calculating each particle, each particle is brought into formula (27) and tries to achieve optimization object function value, namely by the three-dimensional re-projection error function of structure as optimization object function, the actual demarcation point three-dimensional coordinate (X measured is utilized_wiY_wiZ_wi)^TWith calculate by model three-dimensional coordinate (X '_wiY��_wiZ��_wi)^TBetween residual error represent;

$f\left(\mathrm{\&theta;}\right)=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\&Sigma;}}\&lsqb;{(X_{wi}-{X^{\&prime;}}_{wi})}^2+{(Y_{wi}-{Y^{\&prime;}}_{wi})}^2+{(Z_{Wi}-{Z^{\&prime;}}_{wi})}^2\&rsqb;}---\left(27\right)$

3rd step, formula (28)��(30) are utilized the speed of particle and position to be upgraded;

v_{I, d}(t+1)=�� (t) v_{I, d}(t)+c₁r₁(t)[Pbest_{I, d}(t)-x_{I, d}(t)]+c₂r₂(t)[Gbest_d(t)-x_{I, d}(t)](28)

x_{I, d}(t+1)=x_{I, d}(t)+v_{I, d}(t+1)(29)

$\mathrm{\&omega;}\left(t\right)={\mathrm{\&omega;}}_{max}-t\&times;\frac{{\mathrm{\&omega;}}_{max}-{\mathrm{\&omega;}}_{min}}{t_{max}}---\left(30\right)$

Global extremum point must be found for faster more accurate, thus improve the precision that in binocular calibration, camera interior and exterior parameter is optimized, introduce overall situation self-adaptation dynamic inertia weight (GAIW), shown in (31);

$\mathrm{\&omega;}(t+1)=\left\{\begin{array}{ccc}0.9& if& t=0\\ f\left(Gbest\right(t+1\left)\right)-f\left(Gbest\left(t\right)\right)& if& t>0\end{array}\right.---\left(31\right)$

In formula, the value of �� (t) upgrades according to the overall optimal-adaptive angle value of history iteration and current iteration, if not finding more excellent overall fitness value position in the search procedure of particle, is then set to 0 by �� (t), if the value of �� (t) is 0 continuous K time, then basisUpgrade �� (t) value so that particle search near the position that current overall situation optimal-adaptive angle value is corresponding;

The desired positions Pbest that 4th step, calculating particle i experience_i(t), the position with optimal-adaptive angle value that also namely particle was experienced, shown in (32);

${\mathrm{Pbest}}_i(t+1)=\left\{\begin{array}{c}{x}_i(t+1),f\left(x_i\right(t+1\left)\right)<{\mathrm{Pbest}}_i\left(t\right)\\ {\mathrm{pbest}}_i\left(t\right),f\left(x_i\right(t+1\left)\right)\&GreaterEqual;{\mathrm{Pbest}}_i\left(t\right)\end{array}\right.---\left(32\right)$

In 5th step, calculating colony, all particles experienced desired positions, namely there is overall optimal location Gbest (t) that overall optimal-adaptive angle value is corresponding, due to the particle cluster algorithm fast convergence rate of overall situation version, easily being absorbed in local optimum, the present invention adopts the local optimum position Gbest of all particles in particle i neighborhood_iT () replaces overall situation optimal location Gbest (t). Being constructed the distribution of particle by dynamic ring topology, determine the neighborhood of particle in iteration optimization process according to the mode of linear increment, for the t time iteration, the Size of Neighborhood that particle i is corresponding is 2t, until expansion is to whole particle colony;

Occur in iteration for preventing some particle stagnating, to the local optimum position Gbest in above-mentioned particle i neighborhood_iT () carries out chaos optimization according to chaotic maps equation, utilize the ergodicity of Chaos Variable, based on the local optimum position searched in particle i neighborhood, iteration produces a chaos sequence, then optimum particle position in sequence replace the position of a certain particle in current particle i neighborhood carry out iteration at random, thus solve particle and stagnate the algorithm premature convergence problem caused, concrete steps are as follows:

I. by formula (33) by Gbest_iT () maps in the field of definition [0,1] arriving chaotic maps equation (34), and remember

Gbest_i(t)=[Gbest_{I, 1}(t), Gbest_{I, 2}(t) ..., Gbest_{I, d}(t) ..., Gbest_{I, D}(t)], d=1,2 ..., D;

$y_{i,d}^1\left(t\right)=\frac{{\mathrm{Gbest}}_{i,d}\left(t\right)-R_{i,d}^{\min }\left(t\right)}{R_{i,d}^{\max }\left(t\right)-R_{i,d}^{\min }\left(t\right)}---\left(33\right)$

$R_{i,d}^{\min }\left(t\right)=min\left\{{\mathrm{Gbest}}_i\left(t\right)\right\},R_{i,d}^{\max }\left(t\right)=max\left\{{\mathrm{Gbest}}_i\left(t\right)\right\}$

$y_{i,d}^{n+1}\left(t\right)=\left\{\begin{array}{cc}{y}_{i,d}^n\left(t\right)/0.4,& 0<y_{i,d}^n\left(t\right)\&le;0.4\\ (1-y_{i,d}^n(t\left)\right)/(1-0.4),& 0.4\&le;y_{i,d}^n\left(t\right)\&le;1\end{array}\right.,n=1,2,\mathrm{...}---\left(34\right)$

Ii. rightCarry out Q iteration by chaotic maps equation (34), obtain such as formula the chaos sequence shown in (35);

$y_{i,d}\left(t\right)=\&lsqb;y_{i,d}^1\left(t\right),y_{i,d}^2\left(t\right),...y_{i,d}^q\left(t\right),...,y_{i,d}^Q\left(t\right)\&rsqb;,q=1,2,...,Q---\left(35\right)$

Iii. chaos sequence is returned former solution space by formula (36) inverse mapping, obtain a Chaos Variable feasible solution sequenceShown in (37);

${\mathrm{Gbest}}_{i,d}^q\left(t\right)=R_{i,d}^{\min }\left(t\right)+\left(K_{i,d}^{\max }\right(t)-R_{i,d}^{\min }(t\left)\right)y_{i,d}^q\left(t\right)---\left(36\right)$

${\mathrm{Gbest}}_i^{*}\left(t\right)=\&lsqb;{\mathrm{Gbest}}_i^1\left(t\right),{\mathrm{Gbest}}_i^2\left(t\right),...,{\mathrm{Gbest}}_i^q\left(t\right),...,{\mathrm{Gbest}}_i^Q\left(t\right)\&rsqb;$

(37)

${\mathrm{Gbest}}_i^q\left(t\right)=\&lsqb;{\mathrm{Gbest}}_{i,1}^q\left(t\right),{\mathrm{Gbest}}_{i,2}^q\left(t\right),\mathrm{...},{\mathrm{Gbest}}_{i,d}^q\left(t\right),...,{\mathrm{Gbest}}_{i,D}^q\left(t\right)\&rsqb;$

Iv. feasible solution sequence is calculatedIn each feasible solution vectorFitness value, and retain fitness value optimum time feasible solution vector, be designated as Gbest '_i(t);

V. random from current particle i neighborhood a particle is selected, and with Gbest '_iT the position vector of () replaces the position vector of this particle;

6th step, judge termination condition, if the fitness value of objective function evolves to the precision �� set in advance, then terminate optimizing and export the inside and outside parameter result of left and right cameras, otherwise return the 2nd step.