CN107240133A - Stereoscopic vision mapping model building method - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 30
- 238000013507 mapping Methods 0.000 title claims abstract description 11
- 239000002245 particle Substances 0.000 claims abstract description 106
- 238000005457 optimization Methods 0.000 claims abstract description 16
- 238000012937 correction Methods 0.000 claims abstract description 8
- 238000005070 sampling Methods 0.000 claims description 23
- 239000011159 matrix material Substances 0.000 claims description 11
- 238000013508 migration Methods 0.000 claims description 11
- 230000005012 migration Effects 0.000 claims description 11
- 230000006870 function Effects 0.000 claims description 8
- 238000004364 calculation method Methods 0.000 claims description 5
- 230000003044 adaptive effect Effects 0.000 claims description 3
- 238000000205 computational method Methods 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 3
- 230000008447 perception Effects 0.000 claims description 3
- 230000000644 propagated effect Effects 0.000 claims description 3
- 238000002922 simulated annealing Methods 0.000 claims description 3
- 238000001914 filtration Methods 0.000 abstract 1
- 238000003384 imaging method Methods 0.000 description 8
- 238000011156 evaluation Methods 0.000 description 5
- 230000000007 visual effect Effects 0.000 description 4
- 238000004458 analytical method Methods 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 239000000284 extract Substances 0.000 description 2
- 238000000605 extraction Methods 0.000 description 2
- 238000012804 iterative process Methods 0.000 description 2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
- G06T7/85—Stereo camera calibration
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10004—Still image; Photographic image
- G06T2207/10012—Stereo images
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30204—Marker
- G06T2207/30208—Marker matrix
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Abstract
Compared with the prior art, the method for establishing the stereoscopic vision mapping model has the advantages that the Tsai-based improved algorithm is provided for calibrating the key distortion factor, the distortion correction is carried out on the image step by step, the increase of the calculated amount caused by the nonlinear mapping of the lens is avoided, the iteration times of the algorithm are reduced, and the method is efficient and simple. In order to further improve the calibration precision, a nonlinear optimization algorithm of particle swarm optimization particle filtering is adopted, and the particle set moves towards a region with a larger posterior probability density distribution value through particle swarm optimization, so that the problem of particle scarcity is solved, the number of particles required by accurate estimation is greatly reduced, and the estimation precision is improved. Meanwhile, projection pixel errors are used as constraint conditions during particle swarm optimization, the calibration precision and robustness are improved, and the method has a good application prospect in stereoscopic vision navigation.
Description
Technical field
The present invention relates to a kind of technical field of machine vision, more particularly to a kind of stereoscopic vision mapping model method for building up.
Background technology
Current vision system type mainly includes single camera vision system and stereo visual system, simple monocular vision system
System imaging mode be based on linear lens imaging, after the structure of vision system is considered, extend its be imaged onto space into
As coordinate system, and global coordinate system, camera coordinate system, imaging plane coordinate system and pixel coordinate system are constructed respectively.Mesh
The purpose of mark object space point conversion is the three dimensional space coordinate value that object is extracted from imaging picture, and stereo visual system exists
The depth of view information of target point is added on the basis of monocular image-forming principle, this causes mobile robot to can be good at recognizing target
Posture and dimensional orientation orientation information.But distortion factor during camera lens processing, it will inevitably influence vision
Judgement of the system to space coordinate point image space, therefore it is also to improve moving machine rationally to solve distortion factor using mathematical algorithm
The key of device human visual system's cognitive information precision.
The content of the invention
The purpose of the present invention is that provides a kind of stereoscopic vision mapping model method for building up to solve the above problems.
The present invention is achieved through the following technical solutions above-mentioned purpose：
1st, the present invention comprises the following steps：
Step 1：Particle sampler；The stereoscopic vision inside and outside parameter demarcated by improving Tsai algorithms is adopted for 28 totally
Sample, therefore sampling particle has 28 dimensions, carries out particle sampler using stochastical sampling method, the importance density function is Gaussian Profile,
Variance can be obtained by experience；Population H={ the h that scale is N are produced in space1, h2,…,hN, h is each particle
28 n dimensional vector ns in space, h=(αx1,αy1,u0l,v0l,k1l,k2l,p1l,p2l,αl,βl,γl,txl,tyl,tzl,αxr,αyr,
u0r,v0r,k1r,k2r,p1r,p2r,αr,βr,γr,txr tyr,tzr)
Step 2：Image is corrected using the distortion parameter for particle of sampling, generated using the other specification for particle of sampling
Projection matrix, so each particles spatial (28 n dimensional vector n) generates corresponding 2 width distortion correction image and 2 projection matrixes；
Step 3：Determine fitness function；
PiFor the pixel coordinate of the actual projection of k-space point,Represent that current particle h joins as stereoscopic vision nonlinear model
The pixel coordinate value of number estimation, the projection matrix generated using each particle is solved；
Step 4：Population updates；
In order to efficiently control particle migration speed, make algorithm that there is fine search ability, use for reference simulated annealing and think
Want to introduce inertial factor in population more new strategy；In each migration, each particle according to following criterion more new position and
Speed
In formula (2),For i-th of particle, in kth time migration, d ties up speed；c1For perception factor, c2For it is social because
Son, adjusts the step-length that particle is migrated to individual extreme value and global extremum direction respectively；r1And r2It is random for what is be distributed between (0,1)
Number；The individual extreme value place tieed up for i-th of particle in d,The global extremum position tieed up for population in d,WithIn an iterative process according to particle fitness real-time update；Inertial factor ω=b-k (b-a)/K, b=0.9, a=0.4, K
For maximum migration number of times；
Step 5：Population, which updates, to be terminated；
When population reaches that the cutoff number of times K or particle adaptive value of setting reach desired value ζ, population stops excellent
Change；Will update terminate after particle carry out particle filter, particle filter using the 3D coordinates of gridiron pattern characteristic point as optimal conditions,
It is also to meet stereoscopic vision practical application；
Step 6：Obtain characteristic point observation
Using first position of gridiron pattern as world coordinate system, the coordinate value of each characteristic point of gridiron pattern is asked for as observation
Value, the black and white grid for the 30cm*30cm that gridiron pattern is used, it is easy to obtain the observation of a characteristic point；
Step 7：Characteristic point predicted valueSolve；Pixel coordinate of the characteristic point in left and right cameras image is extracted, with current
Particle h calculates the predicted value of character pair point as the nonlinear parameter of stereoscopic vision；Computational methods are as follows；
Wherein, (XW, YW, ZW, 1) and it is homogeneous coordinates of the point P under world coordinate system, (u1, v1, 1) and (u2, v2, 1) point
Not Wei point P left and right camera image coordinate system project homogeneous coordinates；It can be obtained on X by formula (3) and (4)W, YW, ZW
Four linear equations：
Formula 4 equations of (5) 3 unknown numbers, are reduced influence of noise to improve computational accuracy, are asked using least square method
Solution；
Step 8：Granular Weights Computing, and do normalized；
Granular Weights Computing is exactly to calculate each particle hiProbability size；
Due to each feature point for calibration PiBetween error distribution be independent, the probability size of calibrating parameters sampling particle is calculated
Formula is as follows：
From formula (6), if it is possible to obtain each characteristic point PiInfluence to calibrating parameters sampling particle, namely obtain
p(Pi|hi), it is easy to ask for probability size of the calibrating parameters sampling particle under the influence of all characteristic points by formula (6)；If every
The observation of individual characteristic pointPredicted value isIt is simple in order to calculate, if p (Pi|hi) Gaussian distributed, wherein average u
ForWithDifference, variance be observed value varianceAnd predicted valueVariance sum；
Wherein observation is obtained by gridiron pattern, and error can be ignored, and predicted value is obtained by stereoscopic vision；
Road sign error calculation is as follows：
R in formula (8), c are projection coordinate of the characteristic point in left image, r0,c0It is centre coordinate variable c, the r of left image,
D is considered as the gaussian random distribution that average is zero, according to covariance propagated forward theorem,
J is the Jacobian matrix of formula (9),Respectively to the covariance of dependent variable, typically takeFormula (9) is calculated：
Normalized weight：
Step 9：Calibrating parameters fine estimation and its covariance are asked, calibrating parameters fine estimation is by every group of sampling grain
Son is multiplied by normalized weight and then summed such as formula (12), the covariance such as formula (13) of its calibrating parameters fine estimation：
The particle filter of use carries out stereoscopic vision calibration optimization algorithm, preferably combines the specific of stereoscopic vision navigation
Using carrying out global optimization to all parameters minimizes 3-dimensional coordinate re-projection error.
The beneficial effects of the present invention are：
The present invention is a kind of stereoscopic vision mapping model method for building up, compared with prior art, and the present invention is to key distortion
The demarcation of the factor is proposed based on Tsai innovatory algorithms.Describe the implementation method based on OpenCV in detail, algorithm takes into full account
The characteristics of OpenCV function library least square methods, carries out distortion correction, it is to avoid lens Nonlinear Mapping causes to image substep
Amount of calculation increase, reduce algorithm iteration number of times, be it is a kind of efficiently, easy algorithm.In order to further improve stated accuracy,
The nonlinear optimization algorithm of particle group optimizing particle filter is employed, particle collection is made towards posteriority probability density by particle group optimizing
The larger regional movement of value is distributed, so as to overcome the poor problem of particle, and the grain needed for accurate estimate is significantly reduced
Subnumber, improves estimated accuracy.Simultaneously using projected pixel error as constraints during particle group optimizing, and particle filter asks for grain
Calculated during sub- weight with tessellated characteristic point 3D error of coordinates, taken into full account that error is tieed up in 2 peacekeepings 3, greatly improved mark
Fixed precision and robustness.Experimental analysis has finally been carried out, using scaling board characteristic point 3D projection errors as precision evaluation index,
As a result show that this arithmetic accuracy height, robustness are good, have good application prospect in stereoscopic vision navigation.
Brief description of the drawings
Fig. 1 is the 3D road signs uncertainty figure of the present invention；
Fig. 2 is gridiron pattern plane reference mould of the present invention；
Fig. 3 is that the present invention successfully detects characteristic point comparison diagram；
Fig. 4 is distortion correction target of the present invention.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings：
The present invention comprises the following steps：
Step 1：Particle sampler；The stereoscopic vision inside and outside parameter demarcated by improving Tsai algorithms is adopted for 28 totally
Sample, therefore sampling particle has 28 dimensions, carries out particle sampler using stochastical sampling method, the importance density function is Gaussian Profile,
Variance can be obtained by experience；Population H={ the h that scale is N are produced in space1, h2,…,hN, h is each particle
28 n dimensional vector ns in space, h=(αx1,αy1,u0l,v0l,k1l,k2l,p1l,p2l,αl,βl,γl,txl,tyl,tzl,αxr,αyr,
u0r,v0r,k1r,k2r,p1r,p2r,αr,βr,γr,txr tyr,tzr)
Step 2：Image is corrected using the distortion parameter for particle of sampling, generated using the other specification for particle of sampling
Projection matrix, so each particles spatial (28 n dimensional vector n) generates corresponding 2 width distortion correction image and 2 projection matrixes；
Step 3：Determine fitness function；
PiFor the pixel coordinate of the actual projection of k-space point,Represent that current particle h joins as stereoscopic vision nonlinear model
The pixel coordinate value of number estimation, the projection matrix generated using each particle is solved；
Step 4：Population updates；
In order to efficiently control particle migration speed, make algorithm that there is fine search ability, use for reference simulated annealing and think
Want to introduce inertial factor in population more new strategy；In each migration, each particle according to following criterion more new position and
Speed
In formula (2),For i-th of particle, in kth time migration, d ties up speed；c1For perception factor, c2For it is social because
Son, adjusts the step-length that particle is migrated to individual extreme value and global extremum direction respectively；r1And r2It is random for what is be distributed between (0,1)
Number；The individual extreme value place tieed up for i-th of particle in d,The global extremum position tieed up for population in d,WithIn an iterative process according to particle fitness real-time update；Inertial factor ω=b-k (b-a)/K, b=0.9, a=0.4, K be
Maximum migration number of times；
Step 5：Population, which updates, to be terminated；
When population reaches that the cutoff number of times K or particle adaptive value of setting reach desired value ζ, population stops excellent
Change；Will update terminate after particle carry out particle filter, particle filter using the 3D coordinates of gridiron pattern characteristic point as optimal conditions,
It is also to meet stereoscopic vision practical application；
Step 6：Obtain characteristic point observation
Using first position of gridiron pattern as world coordinate system, the coordinate value of each characteristic point of gridiron pattern is asked for as observation
Value, the black and white grid for the 30cm*30cm that gridiron pattern is used, it is easy to obtain the observation of a characteristic point；
Step 7：Characteristic point predicted valueSolve；Pixel coordinate of the characteristic point in left and right cameras image is extracted, with current
Particle h calculates the predicted value of character pair point as the nonlinear parameter of stereoscopic vision；Computational methods are as follows；
Wherein, (XW, YW, ZW, 1) and it is homogeneous coordinates of the point P under world coordinate system, (u1, v1, 1) and (u2, v2, 1) point
Not Wei point P left and right camera image coordinate system project homogeneous coordinates；It can be obtained on X by formula (3) and (4)W, YW, ZW
Four linear equations：
Formula 4 equations of (5) 3 unknown numbers, are reduced influence of noise to improve computational accuracy, are asked using least square method
Solution；
Step 8：Granular Weights Computing, and do normalized；
Granular Weights Computing is exactly to calculate each particle hiProbability size；
Due to each feature point for calibration PiBetween error distribution be independent, the probability size of calibrating parameters sampling particle is calculated
Formula is as follows：
From formula (6), if it is possible to obtain each characteristic point PiInfluence to calibrating parameters sampling particle, namely obtain
p(Pi|hi), it is easy to ask for probability size of the calibrating parameters sampling particle under the influence of all characteristic points by formula (6)；If every
The observation of individual characteristic pointPredicted value isIt is simple in order to calculate, if p (Pi|hi) Gaussian distributed, wherein average u
ForWithDifference, variance be observed value varianceAnd predicted valueVariance sum；
Wherein observation is obtained by gridiron pattern, and error can be ignored, and predicted value is obtained by stereoscopic vision；
Road sign error formation such as Fig. 1, is calculated as follows：
R in formula (8), c are projection coordinate of the characteristic point in left image, r0,c0It is centre coordinate variable c, the r of left image,
D is considered as the gaussian random distribution that average is zero, according to covariance propagated forward theorem,
J is the Jacobian matrix of formula (9),Respectively to the covariance of dependent variable, typically takeFormula (9) is calculated：
Normalized weight：
Step 9：Calibrating parameters fine estimation and its covariance are asked, calibrating parameters fine estimation is by every group of sampling grain
Son is multiplied by normalized weight and then summed such as formula (12), the covariance such as formula (13) of its calibrating parameters fine estimation：
The particle filter of use carries out stereoscopic vision calibration optimization algorithm, preferably combines the specific of stereoscopic vision navigation
Using carrying out global optimization to all parameters minimizes 3-dimensional coordinate re-projection error.
Experiment and interpretation of result
As shown in Figure 2：Because the 3D precision for demarcating thing is difficult to ensure that, here using the different black and white of multiple dimensional orientation angles
The gridiron pattern plane reference template being alternately arranged.Produced using Point Grey Research companies
Bumblebee2Camera is used as image capture device.Binocular vision system base length 120mm, ultimate resolution be 1024 ×
768, elemental area is 4.65um × 4.65um, and frame number is that the focal length under 30FPS, 70 ° of horizontal view angles is 3.8mm, 50 ° of levels
Focal length under visual angle is 6mm, and digital picture locating depth is set to 24bit by the data format supported, image signal noise ratio exists
Gain is more than 60dB when 0dB.
Target gridiron pattern demarcation board size 270mm × 210mm, each gridiron pattern size is 30mm × 30mm, centre-to-centre spacing
30mm, array 9 × 7, each image pixel ratio is 640 × 480, locating depth 8bit, demarcate face flatness error scope-
Within 0.05mm, the angle of lens imaging plane and demarcation target surface is maintained within 50 °.
During experiment, binocular camera has the image in 3 groups of collection totally 10 secondary different spaces orientation altogether, should ensure that the chessboard of acquisition
Lattice occupy the most of region of imaging plane.When algorithm carries out feature point extraction, drawn in the picture in heart point regional extent first
Feature dot image is two straight in circle in characteristic point position figure to avoid image border from crossing demarcation actual error caused by distortion
The intersection point in footpath is represented, then demarcates the ranks number of characteristic point on flat board.Extract successful image, last feature of previous row
Point is connected with first characteristic point of rear a line by colored straight line, to judge whether to find all characteristic points, per a line characteristic point
All distinguished with the circle of different colours.Three width chessboard table images of the first row are that left camera feature point extracts result in figure, the
Three width images of two rows are the feature point extraction results of right video camera under same space imaging mapping.
As shown in Figure 3：In order to verify the feasibility of this paper scaling methods, by set forth herein particle group optimizing particle filter
The stereoscopic vision two-stage calibration method that optimized algorithm (method 1) is demarcated with genetic algorithm nonlinear optimization respectively[81](method 2) and only
The stereoscopic vision two-stage calibration method demarcated using particle cluster algorithm nonlinear optimization[77](method 3) is compared, in method 1
Heredity cut-off evolutionary generation is population cut-off in 10000, method 3 in particle numerical digit 500, cutoff number of times 500, method 2
It is 3000 to migrate number of times, and design parameter is as shown in table 3.2 after optimization.
The parameter comparison of table 3.2
By after particle group optimizing particle filter optimized algorithm closer to actual value, it is excellent for further evaluation algorithms
It is bad, with reference to stereoscopic vision navigation application environment, the root mean square of corresponding coordinate value after employing space true coordinate point and rebuilding
As evaluation index, such as formula (3-30), its parameter such as table 3.3.
The Evaluation results of table 3.3
The mutual alignment parameter such as table 3.4 of the stereoscopic vision of three kinds of algorithm demarcation, the parameter of particle group optimizing particle filter
The parameter dispatched from the factory closer to producer.
The camera mutual alignment parameter of table 3.4 or so compares
Distortion correction is finally carried out to image with the distortion parameter of demarcation, Fig. 3 chessboard calibrations table images are rectified by distortion
Result such as Fig. 4 after just, it can be seen that when algorithm can significantly correct lens imaging generation image border radial distortion and cut
To distortion.
Brief summary
Present invention describes stereoscopic vision demarcation, passes through the scaling method to several vision systems conventional at present
Analysis, it is proposed that a kind of multinomial distortion model stereo camera scaling method based on 2D plane target drones, algorithm linear solution
Ten video cameras ginseng including the yardstick focal length factor, pixel planes center point coordinate, spin matrix parameter, translation matrix parameter
Number.Demarcation to crucial distortion factor is proposed based on Tsai innovatory algorithms.Describe the implementation method based on OpenCV in detail,
Algorithm has taken into full account the characteristic of OpenCV function library least square methods, carries out distortion correction to image substep, it is to avoid lens are non-
Amount of calculation increase, reduces algorithm iteration number of times caused by Linear Mapping, is a kind of efficient, easy algorithm.In order to further
Stated accuracy is improved, the nonlinear optimization algorithm of particle group optimizing particle filter is employed, particle collection is made by particle group optimizing
Towards the regional movement that posteriority probability density distribution value is larger, so as to overcome the poor problem of particle, and essence is significantly reduced
Required population is really estimated, estimated accuracy is improved.Simultaneously using projected pixel error as constraints during particle group optimizing, and
Calculated when particle filter asks for particle weights with tessellated characteristic point 3D error of coordinates, taken into full account that 2 peacekeeping 3-dimensionals are missed
Difference, greatly improves the precision and robustness of demarcation.Finally carried out experimental analysis, using scaling board characteristic point 3D projection errors as
Precision evaluation index, as a result shows that this arithmetic accuracy height, robustness are good, has good application prospect in stereoscopic vision navigation.
The general principle and principal character and advantages of the present invention of the present invention has been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the simply explanation described in above-described embodiment and specification is originally
The principle of invention, without departing from the spirit and scope of the present invention, various changes and modifications of the present invention are possible, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (1)
1. a kind of stereoscopic vision mapping model method for building up, it is characterised in that：Comprise the following steps：
Step 1：Particle sampler；The stereoscopic vision inside and outside parameter demarcated by improving Tsai algorithms is sampled for 28 totally, because
This sampling particle has 28 dimensions, carries out particle sampler using stochastical sampling method, the importance density function is Gaussian Profile, and variance can
To be obtained by experience；Population H={ the h that scale is N are produced in space1,h2,…,hN, h is each particle in space
28 n dimensional vector ns,
H=(αx1,αy1,u0l,v0l,k1l,k2l,p1l,p2l,αl,βl,γl,txl,tyl,tzl,αxr,αyr,u0r,v0r,k1r,k2r,p1r,
p2r,αr,βr,γr,txr tyr,tzr)
Step 2：Image is corrected using the distortion parameter for particle of sampling, is generated and projected using the other specification for particle of sampling
Matrix, so each particles spatial (28 n dimensional vector n) generates corresponding 2 width distortion correction image and 2 projection matrixes；
Step 3：Determine fitness function；
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The pixel coordinate value of meter, the projection matrix generated using each particle is solved；
Step 4：Population updates；
In order to efficiently control particle migration speed, make algorithm that there is fine search ability, use for reference simulated annealing thought and exist
Inertial factor is introduced in population more new strategy；In each migration, each particle is according to following criterion more new position and speed
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<mi>i</mi>
<mi>d</mi>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (2),For i-th of particle, in kth time migration, d ties up speed；c1For perception factor, c2For the social factor, divide
Tiao Jie not the step-length that is migrated to individual extreme value and global extremum direction of particle；r1And r2For the random number being distributed between (0,1)；
The individual extreme value place tieed up for i-th of particle in d,The global extremum position tieed up for population in d,WithRepeatedly
According to particle fitness real-time update during generation；Inertial factor ω=b-k (b-a)/K, b=0.9, a=0.4, K move for maximum
Move number of times；
Step 5：Population, which updates, to be terminated；
When population reaches that the cutoff number of times K or particle adaptive value of setting reach desired value ζ, population stops optimization；Will
Update the particle after terminating and carry out particle filter, particle filter is also using the 3D coordinates of gridiron pattern characteristic point as optimal conditions
Meet stereoscopic vision practical application；
Step 6：Obtain characteristic point observation
Using first position of gridiron pattern as world coordinate system, the coordinate value of each characteristic point of gridiron pattern is asked for as observation, chess
The black and white grid for the 30cm*30cm that disk lattice are used, it is easy to obtain the observation of a characteristic point；
Step 7：Characteristic point predicted valueSolve；Pixel coordinate of the characteristic point in left and right cameras image is extracted, with current particle h
The predicted value of character pair point is calculated as the nonlinear parameter of stereoscopic vision；Computational methods are as follows；
<mrow>
<msub>
<mi>Z</mi>
<mrow>
<mi>C</mi>
<mn>1</mn>
</mrow>
</msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
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<mtable>
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</mrow>
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</mfenced>
<mfenced open = "[" close = "]">
<mtable>
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<mi>X</mi>
<mi>W</mi>
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<mtr>
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<mi>Y</mi>
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</mtr>
<mtr>
<mtd>
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<mi>Z</mi>
<mi>W</mi>
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</mtable>
</mfenced>
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<mo>-</mo>
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<mrow>
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<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
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<msub>
<mi>v</mi>
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</msub>
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<mtr>
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<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
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<msub>
<mi>m</mi>
<mn>11</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
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<msub>
<mi>m</mi>
<mn>12</mn>
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</msup>
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<mi>m</mi>
<mn>13</mn>
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<mi>m</mi>
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<mi>m</mi>
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<msub>
<mi>m</mi>
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<mtr>
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<mrow>
<msup>
<msub>
<mi>m</mi>
<mn>31</mn>
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<mi>m</mi>
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<mi>m</mi>
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</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
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<mi>X</mi>
<mi>W</mi>
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<mtd>
<msub>
<mi>Y</mi>
<mi>W</mi>
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<mtr>
<mtd>
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<mi>Z</mi>
<mi>W</mi>
</msub>
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<mtr>
<mtd>
<mn>1</mn>
</mtd>
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</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, (XW, YW, ZW, 1) and it is homogeneous coordinates of the point P under world coordinate system, (u1, v1, 1) and (u2, v2, 1) and it is respectively point P
The homogeneous coordinates of the image coordinate system projection of camera in left and right；It can be obtained on X by formula (3) and (4)W, YW, ZWFour lines
Property equation：
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<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
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<mn>1</mn>
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<mi>m</mi>
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</mrow>
</mtd>
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<mo>-</mo>
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<mrow>
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</mrow>
</mrow>
Formula 4 equations of (5) 3 unknown numbers, are reduced influence of noise to improve computational accuracy, are solved using least square method；
Step 8：Granular Weights Computing, and do normalized；
Granular Weights Computing is exactly to calculate each particle hiProbability size；
Due to each feature point for calibration PiBetween error distribution be independent, calibrating parameters are sampled the probability size calculation formula of particle
It is as follows：
<mrow>
<mi>p</mi>
<mrow>
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<mi>P</mi>
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<mi>h</mi>
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</msub>
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</mrow>
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<munder>
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<mi>i</mi>
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<mi>p</mi>
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</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
From formula (6), if it is possible to obtain each characteristic point PiInfluence to calibrating parameters sampling particle, namely obtain p (Pi|
hi), it is easy to ask for probability size of the calibrating parameters sampling particle under the influence of all characteristic points by formula (6)；If each special
Levy observation a littlePredicted value isIt is simple in order to calculate, if p (Pi|hi) Gaussian distributed, wherein average u isWithDifference, variance be observed value varianceAnd predicted valueVariance sum；
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<mtd>
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<mn>2</mn>
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<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
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<mo>&times;</mo>
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<msub>
<mover>
<mi>m</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>P</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>m</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein observation is obtained by gridiron pattern, and error can be ignored, and predicted value is obtained by stereoscopic vision；
Road sign error calculation is as follows：
<mrow>
<mi>X</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mfrac>
<mi>b</mi>
<mi>d</mi>
</mfrac>
<mo>;</mo>
<mi>Y</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mfrac>
<mi>b</mi>
<mi>d</mi>
</mfrac>
<mo>;</mo>
<mi>Z</mi>
<mo>=</mo>
<mi>f</mi>
<mfrac>
<mi>b</mi>
<mi>d</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
R in formula (8), c are projection coordinate of the characteristic point in left image, r0,c0It is that centre coordinate the variables c, r, d of left image is recognized
The gaussian random distribution for being zero for average, according to covariance propagated forward theorem,
<mrow>
<msub>
<mi>&Sigma;</mi>
<mi>X</mi>
</msub>
<mo>&ap;</mo>
<mi>J</mi>
<mi>d</mi>
<mi>i</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&sigma;</mi>
<mi>c</mi>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>&sigma;</mi>
<mi>r</mi>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<msup>
<mi>J</mi>
<mi>T</mi>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
2
J is the Jacobian matrix of formula (9),Respectively to the covariance of dependent variable, typically take Formula (9) is calculated：
<mrow>
<msub>
<mo>&Sigma;</mo>
<mi>X</mi>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>b</mi>
<mi>d</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>&times;</mo>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>c</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
</mtd>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>f</mi>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>r</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>r</mi>
<mn>2</mn>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
</mtd>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>f</mi>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>f</mi>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
<mtd>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>d</mi>
<mn>2</mn>
</msubsup>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mfrac>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Normalized weight：
<mrow>
<msup>
<mover>
<mi>&omega;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msup>
<mo>=</mo>
<mfrac>
<msup>
<mi>&omega;</mi>
<mi>i</mi>
</msup>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
</munder>
<msup>
<mi>&omega;</mi>
<mi>i</mi>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Step 9：Calibrating parameters fine estimation and its covariance are asked, calibrating parameters fine estimation is to multiply every group of sampling particle
With normalized weight and then summation such as formula (12), the covariance such as formula (13) of its calibrating parameters fine estimation：
<mrow>
<mi>P</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mover>
<mi>h</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mover>
<mi>h</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
The particle filter of use carries out stereoscopic vision calibration optimization algorithm, preferably combines specifically should for stereoscopic vision navigation
With carrying out global optimization to all parameters minimizes 3-dimensional coordinate re-projection error.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109726853A (en) * | 2018-12-04 | 2019-05-07 | 东莞理工学院 | Industrial collaboration Robot Path Planning Algorithm based on machine vision |
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| CN112465918B (en) * | 2020-12-06 | 2024-04-02 | 西安交通大学 | Microscopic vision calibration method based on Tsai calibration |
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