CN105654476B - Binocular calibration method based on Chaos particle swarm optimization algorithm - Google Patents
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Abstract
The binocular calibration method based on Chaos particle swarm optimization algorithm that the present invention provides a kind of, shoot the dot matrixes plane reference plate image pair of multiple groups different positions and pose simultaneously by two video cameras, in the case where not considering distortion, two camera interior and exterior parameter initial values of left and right are obtained using Zhang Zhengyou plane template linear calibration's method；Then in the case where considering second order radial distortion and second order tangential distortion, using Chaos particle swarm optimization algorithm iteration minimization three-dimensional re-projection error, the final inside and outside parameter of two video cameras is obtained.In iterative optimization procedure, introduce global adaptive dynamic inertia weight (GAIW), by constructing particle local neighborhood using Dynamic Annular topological relation, according in particle local neighborhood adaptive optimal control angle value renewal speed and current location, and chaos optimization is carried out to the corresponding optimal location of adaptive optimal control angle value in particle local neighborhood, efficiently solve the problems, such as that primary particle colony optimization algorithm is easily trapped into local extremum and causes stated accuracy not high, to improve binocular calibration precision, guarantee the precision of subsequent binocular three-dimensional reconstruct.
Description
Technical field
The present invention relates to machine vision metrology field, in particular to a kind of Bi-objective based on Chaos particle swarm optimization algorithm
Determine method.
Background technique
Binocular vision is most important perceived distance technology in passive ranging method, since it directly simulates human vision pair
The processing mode of scene can shoot testee simultaneously from different perspectives by two video cameras, by binocular calibration and solid
Matching obtains the three-dimensional information of object using principle of triangulation.Wherein binocular calibration is as the most important composition of binocular vision
Part, essence be determined according to video camera geometry imaging model it is opposite between the inner parameter of two video cameras and two video cameras
Position orientation relation.
Existing camera marking method mainly linear method, two-step method, nonlinear optimization method etc., wherein linear approach is not examined
Consider lens distortion, precision is not high；Two-step method is a kind of more flexible method between linear approach and nonlinear method, is mainly had
The two-step method of Tsai and the plane template method of Zhang, both linear solution initial parameter, it is non-thread then to consider that distortion carries out
Property optimization, but still be not able to satisfy the requirement of industrial machine vision, stated accuracy increases；Nonlinear optimization method is abnormal due to considering
Become and carry out successive ignition optimization, higher stated accuracy can be obtained.Traditional nonlinear parameter optimization method has Levenberg-
Marquardt method, gradient descent method, conjugate gradient method, Newton method etc., but such method calculating process is complicated, to primary iteration
Value is sensitive, and parameter and poor astringency, is easily trapped into local optimum by the constraint of non-linear factor, it is not easy to obtain optimal solution.It is many
More scholars propose that wherein particle swarm algorithm is due to realizing that easy, precision is high, receiving using intelligent optimization algorithm progress nonlinear calibration
The parameter optimization that the advantages that fast is widely used in camera calibration is held back, but is easily trapped into local extremum, calibration is caused to be tied
Fruit inaccuracy.
Summary of the invention
The present invention controls the inside and outside parameter of two video cameras in order to determine in binocular vision system, provide a kind of based on chaos
The binocular calibration method of particle swarm optimization algorithm.By shooting the dot matrixes plane reference plate image of multiple groups different positions and pose, root
According to the image coordinate at scaling board dot center and its corresponding relationship of world coordinates, the plane template standardization based on Zhang Zhengyou is obtained
To two camera interior and exterior parameter initial values, Chaos particle swarm optimization algorithm iteration minimization three-dimensional re-projection error letter is recycled
Number, obtains the final inside and outside parameter of two video cameras.
For this purpose, the present invention is achieved through the following technical solutions:
(1) the dot edge contour for using Canny operator extraction scaling board image recycles Zernike square to carry out sub- picture
Plain edge extracting acquires dot center sub-pix image coordinate by ellipse fitting；
(2) it is described using pin-hole imaging model linear between the sub-pix image coordinate and its world coordinates at dot center
Model, seek world coordinate system to image coordinate system homography matrix；
(3) in the case where not considering camera lens distortion, left and right two is taken the photograph using the plane template standardization of Zhang Zhengyou
Camera is demarcated respectively, obtains two camera interior and exterior parameter initial values；
(4) consider that camera lens second order is radial and second order tangential distortion, two camera interior and exterior parameters based on (3) are initial
Value carries out inside and outside parameter using Chaos particle swarm optimization algorithm by constructing three-dimensional re-projection error function as optimization object function
Iteration optimization.In optimization process, introduce global adaptive dynamic inertia weight (GAIW), at the same the speed more new stage according to
Adaptive optimal control angle value renewal speed and current location in particle local neighborhood, and to adaptive optimal control angle value in particle local neighborhood
Corresponding optimal location carries out chaos optimization, wherein construct particle local neighborhood using Dynamic Annular topological relation, neighborhood with
The number of iterations linearly increases, last neighborhood extending to entire population；
(5) judge termination condition, if objective function fitness value evolves to preset precision ε, terminate optimization simultaneously
The final inside and outside parameter of two video cameras of output left and right is as a result, otherwise return step (4).
The beneficial effects of the present invention are: the present invention provides a kind of binocular calibration sides based on Chaos particle swarm optimization algorithm
Chaos particle swarm optimization algorithm is optimized applied to binocular vision camera interior and exterior parameter, solves traditional non-linear ginseng by method
Number optimization methods calculating process in vision calibration is complicated, sensitive to primary iteration value and to noise-sensitive, and stated accuracy is not high,
It is not able to satisfy industrial requirements.In optimization process, global adaptive dynamic inertia weight (GAIW) is introduced, while updating rank in speed
Section according in particle local neighborhood adaptive optimal control angle value renewal speed and current location, wherein utilize Dynamic Annular topological relation
Particle local neighborhood is constructed, and chaos optimization is carried out to the corresponding optimal location of adaptive optimal control angle value in particle local neighborhood, from
And solve the problems, such as that primary particle colony optimization algorithm is easily trapped into local extremum, to improve binocular calibration precision and Shandong
Stick guarantees the precision of subsequent binocular vision 3 D reconstruct.
Detailed description of the invention
Fig. 1 Binocular Stereo Vision System schematic diagram
Fig. 2 binocular camera demarcates schematic diagram
Fig. 3 population ring topology schematic diagram
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer with reference to specific embodiments and reference
Attached drawing, invention is further described in detail.
The binocular calibration method based on Chaos particle swarm optimization algorithm that the present invention provides a kind of, entire algorithm flow are main
By the sub-pix image coordinate at scaling board image dot center is extracted, homography matrix is sought, camera interior and exterior parameter initial value
It determines, Chaos particle swarm optimization algorithm carries out inside and outside parameter optimization and constitutes.
To further illustrate, the specific implementation steps are as follows:
Step 1: scaling board image dot center sub-pix image coordinate is extracted
(1) the multiple groups scaling board image that two video cameras are shot simultaneously from different perspectives is inputted respectively；
(2) Canny edge extracting is carried out to sequence to left and right scaling board image respectively, is then carried out using Zernike square
Sub-pixel edge extracts, and acquires dot center sub-pix image coordinate by ellipse fitting, is denoted as respectivelyWithWherein i=1,2 ..., 49, every width scaling board Circle in Digital Images point number are 49.
Step 2: homography matrix is sought
(1) the sub-pix image coordinate and its world coordinates at scaling board image dot center are described using pin-hole imaging model
Between linear model, as shown in formula (1), and by world coordinate system ZwMeasurement where=0 place plane is set as scaling board is flat
Face.
In formula, j=l, r, j=l correspond to the parameter of left video camera, and j=r corresponds to the parameter of right video camera, sjFor ratio because
Son；AjFor camera intrinsic parameter, the normalization focal length being denoted as on the respectively direction x, y,
For coefficient of torsion；For the pixel coordinate of video camera primary optical axis and plane of delineation intersection point, referred to as principal point；RjFor video camera seat
Mark system is external parameters of cameras, is denoted as relative to the orthogonal spin matrix of world coordinate system 3 × 3αj, βj,
γjRespectively spin matrix RjThree column vectors, be denoted as TjIt is camera coordinate system relative to 3 × 1 translation vector of world coordinate system, is external parameters of cameras,
It is denoted asRespectively scaling board dot center is in image
Homogeneous coordinates in coordinate system and world coordinate system.
(2) the dot center sub-pix image coordinate extracted using step 1WithAnd its
The world coordinates P of picture pointi=(Xwi Ywi Zwi)T, world coordinate system is found out according to formula (2) respectively and is sat to left and right cameras image
Mark the homography matrix H of systemlAnd Hr。
Hj=Aj[αj βj Tj], j=l, r (2)
Step 3: camera interior and exterior parameter initial value determines
(1) due to αjAnd βjIt is unit orthogonal vectors, by HjMatrix is write asIt obtains in shown in formula (3)
Parameter constraints.
In linear solution camera interior and exterior parameter initial value, enable:
Wherein BjFor 3*3 symmetrical matrix.
On the basis of formula (3) and formula (4), camera intrinsic parameter is exported using Zhang Zhengyou stencil plane linear calibration's method,
As shown in formula (5).
In formula,
(2) after the intrinsic parameter initial value for obtaining video camera, external parameters of cameras initial value is sought according to homography matrix.
It can be obtained by formula (2):
On the basis of formula (6), external parameters of cameras is exported using Zhang Zhengyou stencil plane linear calibration's method, such as formula (7) institute
Show.
Step 4: consider the two camera interior and exterior parameters optimization of distortion
(1) second order radial distortion and second order tangential distortion are considered, shown in distortion model such as formula (8).
In formula, j=l, r,For dot center real image coordinate,For dot center ideal image seat
Mark, For coefficient of radial distortion, For tangential distortion coefficient.
The two camera interior and exterior parameter initial value A obtained in conjunction with step 3l、Rl、TlAnd Ar、Rr、Tr, calibration it is all inside and outside
Parameter can be θ with vector representation, as shown in formula (9).
Wherein,
(2) two camera interior and exterior parameter optimizations are carried out based on Chaos particle swarm optimization algorithm, steps are as follows:
Step1: the scaling board image dot centre coordinate extracted according to step 1WithAnd it will
Distortion factorWithValue is initialized as 0, acquires dot according to distortion model formula (8)
Center ideal image coordinateWith
Step2: the projection matrix M of two video cameras is acquired according to formula (11)lAnd Mr。
Mj=Aj[RjTj], j=l, r (11)
Wherein, projection matrix MjFor 3 × 4 matrix, it is denoted as
Step3: ideal coordinates are based onWithWith the projection matrix M of binocular cameralAnd Mr, root
Spatial point three-dimensional coordinate P ' is acquired according to formula (12)~(17)i=[X 'wi Y′wi Z′wi]T。
Note Respectively with P 'iHomogeneous seat
Mark, can obtain according to formula (1):
Association type (12) and formula (13) eliminate slAnd srIt can obtain:
KiPi=Ui (14)
Formula (14) indicates optical path O in Fig. 1lalAnd OraiIntersect at target point P 'i, KiFor 4 × 3 matrixes, P 'iIt is unknown three
Dimensional vector, UiFor 4 × 1 vectors, solving formula (17) by least square method can be obtained target point P 'iWorld coordinates.
Step4: the distortion factor for being 0 according to two camera interior and exterior parameter initial values and all initial values is to grain in population
Son speed and position carry out random initializtion, usually initialize Searching point position and speed be in initial value neighborhood space with
Machine generates, and it is Ω=100 that number of particles, which is arranged, and search space dimension is D=28, and corresponding calibration inside and outside parameter to be optimized is total
Number.
Step5: calculating the fitness value f (θ) of each particle, i.e., brings each particle into formula (18) and acquire optimization aim
Functional value utilizes the calibration point three-dimensional of actual measurement that is, by constructing three-dimensional re-projection error function as optimization object function
Coordinate (Xwi Ywi Zwi)TWith the three-dimensional coordinate (X ' being calculated by modelwi Y′wi Z′wi)TBetween residual error indicate.
In formula, θ is that the D of each particle ties up position vector, and N represents the quantity of calibration point on dot scaling board image.
Step6: the speed of particle and position are updated according to formula (19)~(21).
In formula, i=1,2 ..., Ω, d=1,2 ..., D, xI, d(t) particle i d in the t times iteration in group is indicated
The position of dimension, vI, dIt (t+1) is corresponding speed；c1、c2For acceleration constant (learning rate), general value range is [0,2], often
Take fixed value 2；r1(t)、r2It (t) is [0,1] equally distributed random number；PbestI, dIt (t) is particle i personal best particle vector
D tie up element, Gbestd(t) element is tieed up for the d of entire population global optimum position vector；ω (t) is inertia weight,
It determines influence of the particle historical speed information to present speed information, and t is current iteration number, tmaxFor total the number of iterations,
Generally take ωmax=0.9, ωmm=0.4.
Faster more accurately to find global extreme point, to improve the essence that camera interior and exterior parameter optimizes in binocular calibration
Degree introduces global adaptive dynamic inertia weight (GAIW), as shown in formula (22).
In formula, Gbest (t+1) is the t+1 times iteration global optimum position vector, and Gbest (t) is that the t times iteration is global
Optimal location vector, f (Gbest (t+1)) and f (Gbest (t)) respectively correspond the overall situation of Gbest (t+1) and the position Gbest (t)
Adaptive optimal control angle value.The value of ω (t) is updated according to global optimum's fitness value of history iteration and current iteration.If particle
Search process in do not find more preferably global fitness value position, then ω (t) is set 0, if being for the value of ω (t) continuous K time 0,
ω (t) value then is updated according to formula (21), so that particle is searched near the corresponding position of current global optimum's fitness value.
Step7: particle i desired positions Pbest experienced is calculatedi(t) namely having of being lived through of particle is optimal suitable
The position for answering angle value, as shown in formula (23).
In formula, xiIt (t+1) is the t+1 times iteration optimal location vector of particle i, f (xiIt (t+1)) is the adaptation of corresponding position
Angle value.
Step8: calculating all particles in group and live through desired positions, that is, has global optimum's fitness value corresponding complete
Office optimal location Gbest (t).
Due to the particle swarm algorithm fast convergence rate of global version, but it is easily trapped into local optimum.The present invention is using dynamic
Ring topology constructs the distribution of particle, a ring as shown in Figure 3 is formed between particle, with all grains in particle i neighborhood
The local optimum position Gbest of soni(t) global optimum position Gbest (t) is replaced, the speed and position to particle i carry out more
Newly.Wherein, particle i neighborhood is determined in the way of linear increment, for the t times iteration, the corresponding Size of Neighborhood of particle i is
2t, until expanding to entire particle group.By taking particle 1 as an example, when the 0th iteration, neighborhood is itself；It is adjacent when the 1st iteration
Domain is 2,8；When the 2nd iteration, neighborhood is 2,3,7,8, and so on, up to neighborhood extending to entire particle group.
To prevent certain particles to stagnate in iteration, lead to the local optimum position in above-mentioned particle i neighborhood
Gbesti(t) inaccuracy is solved, takes chaotic maps equation to local optimal location Gbest herei(t) chaos optimization is carried out.It calculates
Method utilizes the ergodic of Chaos Variable, and based on the local optimum position searched in particle i neighborhood, iteration generates one and mixes
Then optimum particle position in the sequence is replaced a certain particle position in current particle i neighborhood to change by ignorant sequence at random
Generation, to solve algorithm premature convergence problem caused by particle is stagnated, the specific steps are as follows:
I. pass through formula (24) for Gbesti(t) it is mapped in the domain [0,1] of chaotic maps equation (25), and remembers
Ii. rightQ iteration is carried out by chaotic maps equation (25), obtains the chaos sequence as shown in formula (26)
Column；
Iii. chaos sequence is returned into former solution space by formula (27) inverse mapping, obtains the feasible solution sequence of Chaos VariableAs shown in formula (28)；
Iv. feasible solution sequence is calculatedIn each feasible solution vectorFitness value, and retain adaptation
Feasible solution vector when angle value is optimal, is denoted as Gbest 'i(t)；
V. a particle is randomly choosed from current particle i neighborhood, and with Gbest 'i(t) position vector replaces the grain
The position vector of son.
Step9: judging termination condition, if the fitness value of objective function evolves to preset precision ε, terminates excellent
Change and exports as a result, otherwise returning to Step5.
Claims (2)
1. the binocular calibration method based on Chaos particle swarm optimization algorithm, characterized in that two video cameras pass through while shooting is more
The dot matrixes plane reference plate image pair of group different positions and pose, according to the image coordinate at dot matrixes plane reference plate dot center
And its corresponding relationship of world coordinates, the plane template standardization based on Zhang Zhengyou obtain two camera interior and exterior parameter initial values,
Chaos particle swarm optimization algorithm iteration minimization three-dimensional re-projection error is recycled, the final inside and outside parameter of two video cameras is obtained,
Stated accuracy with higher mainly includes the following steps to guarantee the precision of subsequent binocular vision 3 D reconstruct:
(1) the dot edge contour for using Canny operator extraction dot matrixes plane reference plate image, recycles Zernike square
Sub-pixel edge extraction is carried out, dot center sub-pix image coordinate is acquired by ellipse fitting；
(2) using pin-hole imaging model describe dot matrixes plane reference plate image dot center sub-pix image coordinate and its
Linear model between world coordinates, seek world coordinate system to image coordinate system homography matrix；
(3) in the case where not considering camera lens distortion, using the plane template standardization of Zhang Zhengyou to two video cameras of left and right
Linear calibration is carried out respectively, respectively obtains two camera interior and exterior parameter initial value Al、Rl、TlAnd Ar、Rr、Tr；
(4) consider that camera lens second order is radial and second order tangential distortion, two camera interior and exterior parameters based on step (3) are initial
Value carries out inside and outside parameter using Chaos particle swarm optimization algorithm by constructing three-dimensional re-projection error function as optimization object function
Iteration optimization；In optimization process, introduce global adaptive dynamic inertia weight (GAIW), at the same the speed more new stage according to
Adaptive optimal control angle value renewal speed and current location in particle local neighborhood, and to adaptive optimal control angle value in particle local neighborhood
Corresponding optimal location carries out chaos optimization, wherein construct particle local neighborhood using Dynamic Annular topological relation, neighborhood with
The number of iterations linearly increases, last neighborhood extending to entire population；
(5) judge termination condition, if the fitness value of objective function evolves to preset precision ε, terminate optimization and it is defeated
The inside and outside parameter of left and right cameras is as a result, otherwise return step (4) out.
2. the binocular calibration method based on Chaos particle swarm optimization algorithm according to claim 1, the step (4) is middle to be utilized
Chaos particle swarm optimization algorithm carries out the inside and outside parameter iteration optimization of two video cameras, its feature is as follows:
The first step obtains the distortion factor that two camera interior and exterior parameter initial values and all initial values are 0 according to step (3) to grain
The speed of particle and position carry out random initializtion in subgroup, and it is Ω=100 that number of particles, which is arranged, and search space dimension is D
=28, the sum of corresponding calibration inside and outside parameter to be optimized；
Second step, the fitness value f (θ) for calculating each particle, bring each particle into formula (27) and acquire optimization object function
Value utilizes the calibration point three-dimensional coordinate of actual measurement that is, by constructing three-dimensional re-projection error function as optimization object function
(Xwi Ywi Zwi)TWith the three-dimensional coordinate (X' being calculated by modelwi Y'wi Z'wi)TBetween residual error indicate:
Third step is updated the speed of particle and position using formula (28)~(30)；
vi,d(t+1)=ω (t) vi,d(t)+c1r1(t)[Pbesti,d(t)-xi,d(t)]+c2r2(t)[Gbestd(t)-xi,d(t)]
(28)
xi,d(t+1)=xi,d(t)+vi,d(t+1) (29)
Wherein, vi,d(t+1) the particle i position corresponding speed that d is tieed up in the t+1 times iteration, ν in group are indicatedi,d(t) it indicates
The particle i position corresponding speed that d is tieed up in the t times iteration, x in groupi,d(t) indicate that particle i is in the t times iteration in group
In d dimension position；c1、c2For acceleration constant；r1(t)、r2It (t) is [0,1] equally distributed random number；Pbesti,d(t)
Element, Gbest are tieed up for the d of particle i personal best particle vectordIt (t) is the d of entire population global optimum position vector
Tie up element；ω (t) is inertia weight, ωmaxFor inertia weight maximum value, ωminFor inertia weight minimum value；T is current iteration
Number, tmaxFor total the number of iterations；
Faster more accurately to find global extreme point, so that the precision that camera interior and exterior parameter optimizes in binocular calibration is improved,
Global adaptive dynamic inertia weight (GAIW) is introduced, as shown in formula (31)；
Wherein, Gbest (t+1) is the t+1 times iteration global optimum position vector, and Gbest (t) is the t times iteration global optimum
Position vector, f (Gbest (t+1)) and f (Gbest (t)) respectively correspond the global optimum of Gbest (t+1) and the position Gbest (t)
Fitness value；
The value of ω (t) is updated according to global optimum's fitness value of history iteration and current iteration, if the search of particle
Cheng Zhongwei finds more preferably global fitness value position, then ω (t) is set 0, if being for the value of ω (t) continuous K times 0, basisω (t) value is updated, so that particle is attached in the corresponding position of current global optimum's fitness value
Nearly search；
4th step calculates particle i desired positions Pbest experiencedi(t) namely particle lived through have adaptive optimal control degree
The position of value, as shown in formula (32):
Wherein, xiIt (t+1) is the t+1 times iteration optimal location vector of particle i, f (xiIt (t+1)) is the fitness value of corresponding position；
All particles live through desired positions in 5th step, calculating group, that is, have the corresponding overall situation of global optimum's fitness value
Optimal location Gbest (t) is easily trapped into local optimum, using particle due to the particle swarm algorithm fast convergence rate of global version
The local optimum position Gbest of all particles in i neighborhoodi(t) global optimum position Gbest (t) is replaced；It is opened up by Dynamic Annular
The distribution of structure construction particle is flutterred, the neighborhood of particle is determined in iterative optimization procedure in the way of linear increment, for the t times
Iteration, the corresponding Size of Neighborhood of particle i is 2t, until extending to entire particle group；
To prevent certain particles to stagnate in iteration, to the local optimum position Gbest in above-mentioned particle i neighborhoodi(t) root
Chaos optimization is carried out according to chaotic maps equation, using the ergodic of Chaos Variable, with the local optimum searched in particle i neighborhood
Position is that basic iteration generates a chaos sequence, then replaces current particle i adjacent at random the optimum particle position in sequence
The position of a certain particle in domain is iterated, to solve algorithm premature convergence problem caused by particle is stagnated, specific steps are such as
Under:
I. pass through formula (33) for Gbesti(t) it is mapped in the domain [0,1] of chaotic maps equation (34), and remembers Gbesti(t)
=[Gbesti,1(t),Gbesti,2(t),...,Gbesti,d(t),...,Gbesti,D(t)], d=1,2 ..., D；
Ii. rightQ iteration is carried out by chaotic maps equation (34), obtains the chaos sequence as shown in formula (35)；
Iii. chaos sequence is returned into former solution space by formula (36) inverse mapping, obtains the feasible solution sequence of Chaos VariableAs shown in formula (37)；
Iv. feasible solution sequence is calculatedIn each feasible solution vectorFitness value, and retain fitness value
Feasible solution vector when optimal, is denoted as Gbesti'(t)；
V. a particle is randomly choosed from current particle i neighborhood, and uses Gbesti' (t) position vector replace the particle position
Set vector；
6th step judges termination condition, if the fitness value of objective function evolves to preset precision ε, terminates optimization
And the inside and outside parameter of left and right cameras is exported as a result, otherwise returning to second step.
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