CN107133986B - A Camera Calibration Method Based on Two-Dimensional Calibration Object - Google Patents

Abstract

The present invention proposes a kind of camera calibration method based on two-dimensional calibrations object, camera calibration is realized on the basis of progress uncalibrated image is preferred, including preparing plane reference plate, with the image of each angle of camera acquisition plane scaling board, angle point grid is carried out to each image, calculate the corresponding homography matrix of each image, the parameter of consistency is randomly selected in initialization, homography matrix is randomly selected from all homography matrixes, calculate IAC, the distance between and judge the corresponding homography matrix of each image and IAC, the summation of interior point set and interior points is obtained according to judgement, and carry out local optimum；Finally according to all interior point estimation IAC, the corresponding image set of exterior point is removed, it is preferred to complete uncalibrated image；Calibration result is further obtained according to uncalibrated image preferred result.The present invention can promote the scaling method of Zhang Zhengyou two-dimensional surface, obtain more stable and reliable stated accuracy.

Description

A Camera Calibration Method Based on Two-Dimensional Calibration Object

technical field

The present invention relates to the technical field of camera calibration, in particular to a camera calibration technology based on a two-dimensional calibration object, and in particular to a camera calibration method based on calibration image optimization.

Background technique

Camera calibration techniques refer to finding the parameters of the camera model. The parameters generally include parameters from the scene to the image (internal parameters), and parameters from the reference coordinate system to the camera coordinate system (external parameters). In addition, it also includes nonlinear distortion parameters of the camera lens due to manufacturing errors. The accuracy of camera calibration directly affects the accuracy of 3D reconstruction, visual detection and visual navigation. Many scholars have conducted research on camera calibration, mainly divided into self-calibration and calibration based on calibration objects. Self-calibration does not need to calibrate the object, and directly calibrates the camera according to the corresponding points on the image of the collected static scene, but the extraction accuracy of its corresponding points is limited, and some scenes have no corresponding points, and it does not consider the distortion of the lens [2], Therefore, its calibration accuracy is limited [1]. Calibration methods based on calibrator are often used in occasions where high precision is required.

Calibration methods based on calibration objects are mainly divided into methods based on three-dimensional calibration objects and methods based on two-dimensional calibration objects. The method based on three-dimensional calibration objects requires three-dimensional calibration objects whose coordinates are precisely known, and the equipment it requires is very expensive. The most widely used is the calibration method based on two-dimensional calibration objects, and the most classic is Zhang Zhengyou’s two-dimensional planar template calibration method [3]. Zhang Zhengyou’s two-dimensional plane calibration method needs to collect multiple images of different viewing angles for calibration, and the calibration accuracy depends on the appropriate viewing angle [3] (when the angle of the calibration plate and the imaging plane of the camera is 45 degrees, the calibration The accuracy will be higher), the accuracy of corner point extraction, etc. Different image sets lead to different calibration accuracies. In order to deal with this problem, [2] proposed to use random extraction consistency [4] (RANSAC) to eliminate unreliable images to achieve better calibration results, but due to some shortcomings of standard RANSAC are as follows: (1) Standard RANSAC The running time is longer than theoretically predicted [5]. (2) It assumes that the model obtained from the interior points is consistent with all interior points. This assumption is usually not true, because interior points are sometimes affected by noise. Therefore, the number of interior points obtained by RANSAC has a certain degree of randomness, which is different from the theoretical interior points, and the obtained model is of course not the same as the theory.

Related references:

[1] S. Bougnoux, "From projective to euclidean space under any practical situation, a criticism of self-calibration," Proc.IEEE.International Conference on Computer Vision (ICCV 98), IEEE.CS Pess.Dec.1998, pp.790 –796, doi:10.1109/ICCV.1998.710808.

[2] Y.Lv, J.Feng, Z.Li, W.Li and J.Cao. "A New Robust 2D CameraCalibration Method using RANSAC," Optik-International Journal for Light and Electron Optics, vol.126, Dec.2015 , pp. 4910–4915.

[3] Z. Zhang, "A Flexible New Technique for Camera Calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, Dec.2000, pp.1330–1334, doi:10.1109/34.888718.

[4] M.A.Fischler and R.C.Bolles, "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography," Communications of the ACM, vol.24, Dec.1981, pp.381–395.

[5] B.Tordoff and D.W.Murray, "Guided Sampling and Consensus for MotionEstimation," Proc. European Conference on Computer Vision (ECCV 02), Springer-Verlag Press, Dec.2002, pp.82–96.doi:10.1007/ 3-540-47969-4_6.

[6] O.Chum, J.Matas and J.Kittler, “Locally optimized RANSAC,” Lecture Notes in Computer Science, vol.2781, Dec.2003, pp.236–243.

[7] D.C. Brown, "Close-range Camera Calibration," Photogramm Eng, vol.37, Dec.2002, pp.855–866.

[8] J.Salvi, X.Armangue and J.Batlle, "A Comparative Review of Cam-era Calibrating Methods with Accuracy Evaluation," Pattern Recognition, vol.35, Dec.2002, pp.1617–1635.

[9]R.Hartley and A.Zisserman,Multiple View Geometry in ComputerVision,2nd ed.,vol.30.Cambridge University Press,2003,pp.1865–1872.

[10] http://www.vision.caltech.edu/bouguetj/calib_doc/.

Contents of the invention

In view of the fact that the traditional two-dimensional model-based calibration method needs to take images from different angles, and the calibration accuracy is affected by the acquisition angle, acquisition distance, and the location of feature points, the present invention provides a random extraction consistency using local optimization A method to improve the accuracy of Zhang Zhengyou's camera calibration method.

The technical solution of the present invention proposes a camera calibration method based on a two-dimensional calibration object, and realizes camera calibration on the basis of optimizing calibration images, including the following steps,

Step 1, prepare a plane calibration plate;

Step 2, use the camera to collect the images of each angle of the plane calibration plate, and obtain J images;

Step 3, extract the corner points of each image, and calculate the corresponding homography matrix of each image, denoted as Hj, where j is the image serial number, and the value is 1, 2, 3, ..., J;

Step 4, initialize the parameters of random extraction consistency, including taking the theoretical iteration number k as ∞, the initial actual iteration number as i=0, the best inlier set as bestSub=[], and the best inlier number as bestNin= 0; [] represents an empty set;

Step 5, randomly select s homography matrices from all homography matrices Hj obtained in step 3, calculate IAC, and judge the distance Dj between the homography matrix Hj corresponding to each image and IAC, according to the preset The corresponding threshold value thr judges whether Dj<thr, if it is, Hj is considered as an interior point, otherwise Hj is considered as an exterior point, and the sum Nin of the interior point set sub and the number of interior points is obtained; where s is the minimum number ^of sampling points; the IAC represents K- ^T K ^-1 , K is an internal parameter; i=i+1;

Step 6, judge whether Nin>bestNin, if yes, go to step 7 for local optimization, otherwise return to step 5;

Step 7, perform local optimization, including the following sub-steps,

Step 7.1, initialize the number of times of local optimization d=10, initialize the local maximum inlier number lobestNin=0 in the current iteration, and the local best inlier set lobestSub=[];

Step 7.2, set n=4, Nin=0, sub=[], randomly select slo interior points from the current interior point set sub to calculate IAC, slo is greater than the minimum number of sampling points s, and determine the corresponding homography of each image The distance Dj between matrix Hj and IAC;

Step 7.3, according to n times of the given threshold thr, judge the number of IAC internal points, including judging whether Dj<n*thr, if so, consider Hj as an internal point, otherwise consider Hj as an external point, and complete the judgment for each image Afterwards, the sum Nin of the current interior point set sub and the number of interior points is obtained, so that n=n-1;

Step 7.4, judge whether n>1, if not, go to step 7.5, if yes, calculate IAC from the current interior point set sub, and return to step 7.3;

Step 7.5, judge Nin>lobestNin, if so, lobestNin=Nin, lobestSub=sub, go to step 7.6, otherwise go to step 7.6;

Step 7.6, d=d-1, judge whether d<1, if otherwise return to step 7.2, if yes then return the final result lobestSub, lobestNin;

Step 8, according to the result returned in step 7, set bestNin=lobestNin, betSub=lobestsub, i=i+1; get interior point ratio ε=bestNin/J according to bestNin, update the number of theoretical iterations k, and judge whether i>k, If otherwise, go back to step 5, if yes, go to step 9;

Step 9: Estimate the IAC according to all inliers in bestSub, remove the image set corresponding to the outliers, and complete the calibration image optimization; further obtain the calibration result according to the calibration image optimization results.

And, the calculation IAC is carried out according to the following formula,

h ₁ ^T K ^-T K ^-1 h ₂ =0

h ₁ ^T K ^-T K ^-1 h ₁ ＝h ₂ ^T K ^-T K ^-1 h ₂

Among them, h ₁ , h ₂ are the column vectors of the homography matrix H.

Moreover, the determination of the distance Dj between the homography matrix Hj corresponding to each image and the IAC is performed according to the following formula,

Where, d is the distance, B=K ^-T K ^-1 , h ₃₀ =h ₁ -h ₂ , h ₄₀ =h ₁ +h ₂ , Bh _i is the product of B and h _i , i=1,2,30 ,40, Bh _i (1) represents the first element of Bh, and Bh _i (2) represents the second element of Bh.

Moreover, the update theoretical iteration number k is carried out according to the following formula,

where ε is the proportion of inliers and η is the given corresponding threshold.

Also, thr is preferably 2*10 ^-5 .

Also, J is 20.

Also, s is 2, and slo=min(4,Nin).

The present invention proposes to optimize the calibration image first before camera calibration, including proposing to define a distance between the homography matrix and the image of the absolute conic, and then use the locally optimized random sampling consistency (LO-RANSAC) to Eliminate unreliable images and eliminate the randomness of RANSAC, so that a stable and reliable image set can be obtained, and Zhang Zhengyou’s two-dimensional plane calibration method can be improved to obtain more stable and reliable calibration accuracy, and avoid being affected by acquisition angle, acquisition distance, and feature point positioning and other factors. From the simulation experiment and real experimental data, better calibration results can be obtained by applying the technical solution of the present invention. Since the unreliable images are accurately screened before calibration, the execution accuracy and efficiency of Zhang Zhengyou's two-dimensional plane calibration method are improved. The system resource consumption is low and has significant market value.

Description of drawings

Fig. 1 is a flow chart of an embodiment of the present invention.

FIG. 2 is a schematic diagram of a local optimization random extraction consistency process according to an embodiment of the present invention.

Detailed ways

The specific implementation manner of the present invention will be described in detail below in conjunction with the accompanying drawings and examples.

The camera model is divided into linear model and nonlinear model. The linear model based on the two-dimensional calibration plate is expressed as follows:

Where m is a scale factor, here K is an internal parameter, where f _x , f _y represent the focal length of the camera in pixel units; (u ₀ , v ₀ ) are the pixel coordinates of the image center; r ₁ , r ₂ are rotation matrices and t is the translation vector from the reference coordinate system to the camera coordinate system; (X, Y) is the world coordinate of the calibration board; (u, v) is the pixel coordinate of the imaging point corresponding to the calibration board. Suppose (X , Y) and (u, v) are known, the present invention can easily obtain the homography matrix H between the world coordinates of the calibration plate and the pixel coordinates, which is a 3*3 matrix, where h ₁₁ , h ₁₂ ..., h ₃₃ are elements of H respectively. Each image can get a homography matrix.

The lens distortion of camera can be divided into following three categories: radial distortion, eccentric distortion and thin prism distortion, wherein radial distortion accounts for the largest, and is mainly affected by the first item of radial distortion [7], so the present invention Only the first item of radial distortion is considered, and it is also applicable to other distortions. And more distortion considerations will not improve distortion accuracy [8]. The distortion model is as follows:

Here r=(x+y) ² , (x, y) are ideal image coordinates, and (u _d , v _d ) are distorted pixel coordinates. k ₁ is the coefficient of radial distortion, and the nonlinear model is to eliminate the lens distortion of the camera to obtain a correct linear model, and then use the linear model to restore the parameters of the camera.

In machine vision, RANSAC is widely used to estimate a model from a data set polluted by gross errors. First, a smallest subset of the data set is randomly selected to estimate the model parameters, and then the distance between the data points and the model is calculated, and those distances from the model are less than Points with a given threshold are considered inliers, and the model with more inliers considers it better. The process of random selection is repeated until the probability of finding more inliers than the current best model is less than a given threshold. That is, the probability of missing a sample with inlier set s in k samples is lower than the given corresponding threshold η.

where ε is the proportion of interior points.

It should be noted that the RANSAC method assumes that the model obtained from the interior point is consistent with all interior points. This assumption is incorrect, because the interior point will also be affected by noise, so the time for RANSAC to find the correct model is greater than k times [5]. Moreover, RANSAC selects the smallest sample to calculate the model, so the impact of noise will have a greater impact on the accuracy of the calculated model, which leads to the number of internal points found by RANSAC being smaller than the theoretical value and unstable.

In order to deal with this problem of RANSAC, the literature [6] proposes LO-RANSAC, which can eliminate the noise influence of internal points by locally optimizing the best model achieved in each step of RANSAC, and can obtain a stable and more accurate model. Therefore, the present invention proposes to use LO-RANSAC to eliminate unreliable images collected by the camera, so as to obtain a stable and high-precision calibration effect. In the present invention, when RANSAC reaches each current best model, a local optimization operation is performed.

Local optimization uses an internal RANSAC, plus an iteration, which is explained in the next two paragraphs.

Internal RANSAC: When RANSAC reaches the best model in the kth iteration, sampling is selected from the interior point set of the best model. Therefore, the sample size of this sampling may not be the minimum. Experiments show that the larger the sampling sample is Estimated model, the higher the accuracy of the model [6].

After the internal RANSAC, in order to get more reliable results, use an iterative framework: use all points smaller than a larger threshold n*thr to estimate the model by least squares, n is an integer, and then reduce n in turn And iterate until the threshold is thr. This iteration is because when using the least squares method, a data point with a coarse error will lead to an error in the estimated model. In the iteration, the distance of each sampling point is smaller than the given threshold, so there is no data point with a coarse error. .

The iteration of the internal RANSAC plus the least squares method will reduce the influence of the noise of the internal point, so a more accurate and stable model can be obtained.

In Zhang Zhengyou’s method based on plane calibration, the calibration results are limited by the quality of the collected images. It is shown in [3] that the best calibration results are when the angle between the image and the plane of the calibration plate is 45 degrees. When the angle When increasing, the perspective distortion will make the corner point extraction more imprecise, and different distances will also lead to the accuracy of corner point extraction. All of these can affect the quality of the sampled images, and different sets of sampled images will lead to inconsistent calibration accuracy. In order to eliminate these unreliable images and obtain an optimal image set, the present invention uses LO-RANSAC to remove unreliable images. As mentioned earlier, LO-RANSAC can reduce the randomness of RANSAC, and can get more and more reliable image sets, and then get more accurate calibration parameters.

In Zhang Zhengyou's calibration, the two constraints are as follows:

Where h ₁ , h ₂ are the column vectors of the homography matrix H, that is, h ₁ =(h ₁₁ h ₂₁ h ₃₁ ) ^T , h ₂ =(h ₁₂ h ₂₂ h ₃₂ ) ^T Therefore, at least two equations ( 5) To calculate K ^-T K ^-1 , in literature [9], K ^-T K ^-1 is called the image of the absolute conic (IAC, imageof the absolute conic), the present invention does not need to know the specific meaning of IAC , the present invention only needs to know that it represents K ^{- T} K ^-1 , after solving it, the closed solution of equation (1) can be obtained. In the end, this closed solution is used as the initial value, and lens distortion is considered, and the Lewenberg algorithm is used for nonlinear optimization. Therefore, the solution of this IAC has a great influence on the initial value, and an unreasonable initial value can easily lead to unrestricted optimization. Stuck in a local optimum. Literature [2] defines the distance between an IAC and the homography matrix as follows:

Where, d is the distance, B=K ^-T K ^-1 , h ₃₀ =h ₁ -h ₂ , h ₄₀ =h ₁ +h ₂ , Bh _i is the product of B and h _i , i=1,2,30 ,40. And Bh _i (1) represents the first element of Bh, Bh _i (2) represents the second element of Bh, the threshold value can be given according to the simulation during specific implementation, thr is preferably 2* in the embodiment of the present invention ^10-5 . In order to eliminate unreliable images, the present invention proposes to use this distance for screening.

The present invention is designed further, and the realization scheme principle that proposes is as follows:

1. Collect enough photos of the calibration board from different angles, preferably more than 20;

2. Extract the corner points for each image, and calculate the homography matrix of each image;

3. Setting parameters: s=2, ε=0, k=∞, thr=2*10 ^-5 , i=1;

4. Randomly select s images and calculate IAC:K ^-T K ^-1 ;

5. Calculate and judge the distance between the homography matrix corresponding to each image and IAC according to the given threshold thr according to formula (6), determine the number of interior points Nin of IAC, that is, the image set consistent with IAC, and update the proportion of interior points ε.

6. If a larger number of internal points is found, perform local optimization.

7. if i>k, go to the 8th step by the required number of samplings of formula (4) renewal; Otherwise i=i+1, go to the 4th step;

8. After RANSAC ends, the subset of images used for calibration is determined. Then use Zhang Zhengyou's method to calibrate the parameters of the camera.

Referring to Figure 1, the implementation of the specific process of the embodiment is described as follows:

1. First prepare a plane calibration board, the embodiment uses 12*13 checkerboards, the size of each checkerboard is 30mm, then the world coordinates (X, Y) of each checkerboard are known accordingly.

2. Place the checkerboard at different angles, and use the camera to collect images from each angle. Assuming that J images are obtained, in the embodiment, 20 images are collected.

3. Extract the corner points of each image to obtain the pixel coordinates (u, v) of the corner points of the checkerboard, according to the pixel coordinates (u, v) and world coordinates (X, Y) corresponding to the checkerboard of each image , calculate the homography matrix corresponding to each image according to formula (2), denoted as Hj (j=1,2,3,...,20), where j is the image number, the value is 1,2,3,... ,J.

4. Initialize the parameters of random extraction consistency, including taking the theoretical iteration number k as ∞, the initial actual iteration number as i=0, the best inlier set as bestSub=[], and the best inlier number as bestNin=0 . [ ] represents an empty set.

5. Carry out iterations of random extraction consistency, randomly select s=2 homography matrices Hj (s is Minimum number of sampling points, note here j=r1, r2 in the embodiment, 1<=r1<=20, 1<=r2<=20, r1!=r2), calculate IAC according to formula (5), and according to formula ( 6) Judging the distance Dj (j=1, 2, 3, . If yes, consider Hj to be an interior point, otherwise consider Hj to be an exterior point. The interior point set is sub=(Hj|Hj is the interior point), and the sum Nin of interior points is calculated. And i=i+1.

The IAC mentioned in this process represents K ^-T K ^-1 , and K is an internal parameter.

The specific judgment process can be designed as, initializing j=1, sub=[], then judge whether Dj<thr, if otherwise Hj is an out-point, j=j+1, if so then Nin=Nin+1, sub=(sub+ Hj), Hj is the interior point, j=j+1, then judge whether j>20, if not, return to judge whether Dj<thr for the current j, if so, go to step 6.

6. Determine whether Nin>bestNin, if yes, go to step 7 for local optimization, otherwise return to step 5, and perform random extraction and other processing again.

7. Local optimization is implemented by LO-RANSAC, including the following sub-steps, see Figure 2:

7.1, initialize the number of times of local optimization d=10, initialize the local maximum inlier number lobestNin=0 in the current iteration, and the local best inlier set lobestSub=[];

7.2, let n=4, Nin=0, sub=[], n is the multiple of the threshold; from the current interior point set sub, randomly select the interior points of the interior point set slo greater than the minimum number of sampling points s to estimate the IAC, this The embodiment selects Hj corresponding to slo=min (4, Nin) images, calculates IAC according to formula (5), and judges the distance Dj between the homography matrix Hj corresponding to each image and IAC according to formula (6), j = 1, 2, 3, . . . , 20.

7.3. Judging the number of internal points in IAC according to n times the given threshold value thr, including judging whether Dj<n*thr, * means multiplying, if yes, consider Hj as an internal point, otherwise consider Hj as an external point. The initial value of n is a preset multiple, and gradually decreases in subsequent iterations. After the judgment of each image is completed, the current inlier set sub is obtained, and the sum Nin of inlier numbers is calculated, and n=n-1 is set, and the next step 7.4 is entered.

The process can be designed as follows: initialize j=1, judge whether Dj<n*thr, if not, Hj is an outpoint, j=j+1, if so, then Nin=Nin+1, Hj is an inpoint, and then set j=j+ 1, sub=sub+Hj; then judge whether j>20, if yes, n=n-1, enter the next step 7.4, otherwise return to continue to judge whether Dj<n*thr for the current j.

7.4, judge whether n>1, if not, enter step 7.5, if yes, calculate IAC according to formula (5) from the current interior point set, return to step 7.3;

7.5. Determine whether Nin>lobestNin, if yes, lobestNin=Nin, lobestSub=sub, go to step 7.6, if not go to step 7.6.

7.6, d=d-1, judge whether d<1, if not, return to step 7.2, if yes, return the final results lobestSub, lobestNin.

8. According to the result returned in step 7, set bestNin=lobestNin, betSub=lobestsub, obtain the interior point ratio εbestNin/20 according to bestNin, update the theoretical iteration number k according to formula (4), and judge whether i>k, if not, then Return to step 5, if yes, go to step 9.

9. Use all the internal points in bestSub to estimate IAC, remove the image set corresponding to the external points, and complete the calibration image optimization. According to the optimization results of the calibration image, the calibration results are further obtained, including further obtaining the linear solution, which is used as the initial value of the camera model, considering the first-order radial distortion, and optimized by maximum likelihood to obtain the final camera model calibration parameters. At the end of the process, the calibration result and the back-projection error will be returned.

During specific implementation, the above technical solutions can use computer software technology to realize the automatic operation process.

In order to verify the technical effect of the embodiment of the present invention, a simulation experiment has been carried out:

If the camera parameters are randomly selected for the simulation experiment, the impact of noise is great, which may lead to non-real parameter solutions. Therefore, the experiment of the present invention uses the calibration results obtained from the actual experimental data in the literature [10] as the camera parameters. The internal parameters are as follows:

f _x = 657.384416175761;

f _y =658.058046335663;

u ₀ =303.625818604402;

_v0 = 244.843359357986.

The external parameters are the rotation matrix r and the translation vector t, where the rotation matrix r is represented by a Rodrigues matrix, which is a 3-dimensional vector. 20 different rotation matrices and translation vectors are represented by Table 1 and Table 2. In the experiment of the present invention, the lens distortion is set to 0, and the synthetic chess calibration board has 12*13=144 corner points, and the size of the checkerboard is 30mm*30mm. Using these parameters, the experiment of the present invention can generate the image coordinates of the corner points of the synthetic calibration plate. Finally, the image coordinates and world coordinates synthesized by the experiment of the present invention are used to simulate the calibration algorithm.

Table 1 Rotation vector R

The image coordinates of the corner points are added with a mean of 0 and a variance of pixel noise from 0 to 1 that increases with a pixel value of 0.1 per step. The distance between the IAC and the homography matrix was calculated. The actual noise is 0.2 pixels, so the experiment of the present invention sets thr as 2*10 ^-5 . Next, in the experiment of the present invention, the noise that increases from 0 to 4 pixels with a variance of 0.2 pixels per step is added to the image coordinates. At each noise level, RANSAC and the method of the present invention were performed 100 times each. The average error of the calibration result includes the average relative error of f _x and f _y , and the absolute error of u ₀ and v ₀ . It can be seen through experiments that the average error obtained by the method of the present invention is smaller than that obtained by RANSAC, especially u ₀ , v ₀ . This shows that the method of the present invention can obtain a more accurate calibration effect. The standard deviation of the calibration results includes the standard deviation of the relative errors of f _x and f _y , and the standard deviation of the errors of u ₀ and v ₀ . It can be seen through experiments that the standard deviation obtained by the method of the present invention is smaller than that obtained by RANSAC, especially u ₀ , v ₀ . This shows that the method of the present invention can obtain a more stable calibration effect.

Table 2 Translation vector T

In order to verify the technical effect of the embodiment of the present invention, a real experiment was carried out:

In this part, the present invention uses 20 images from [10] for calibration. Since the real experimental data is not known, the present invention uses the average back-projection error (the world coordinate point is back-projected to the pixel coordinate of the image with the camera parameters obtained by calibration, and the error between it and the extracted corner point is calculated) to represent Calibrated accuracy. The results obtained by RANSAC and the method of the present invention were run 100 times. The average backprojection error and the variance of the error are shown in Table 3. It can be seen from Table 3 that the average error and variance of LO-RANSAC are smaller than RANSAC, so the method of the present invention can obtain a more accurate and stable calibration result than RANSAC.

Table 3 real experimental results

Calibration method Mean reprojection error Standard deviation of the error RANSAC 0.159679252519579 0.004770649100921 The method of the invention 0.156598456968103 1.952678215459548*10^-16

Camera calibration is a fundamental problem in computer vision, especially in vision measurement. The accuracy of measurement depends largely on the accuracy of calibration, which is limited by experimental conditions and calibration methods. Here, the present invention uses locally optimized RANSAC to reject unreliable images. The result obtained by the method of the present invention defines the distance between an IAC and the homography matrix, and performs local optimization when RANSAC reaches the best model. The local optimization can eliminate the randomness that RANSAC is affected by interior point noise, and then the optimal model can be obtained. The best image set can get the best calibration results. Simulation experiments and real experiments prove that the method of the present invention is more accurate and more stable than traditional methods.

All the above are preferred embodiments of the present invention, and are not limited to this embodiment. All modifications, replacements, improvements, etc. made within the spirit and principles of this embodiment should be included in the scope of protection of this patent within.

Claims (7)

1. a kind of camera calibration method based on two-dimensional calibrations object, it is characterised in that: on the basis of progress uncalibrated image is preferred It realizes camera calibration, includes the following steps,

Step 1, prepare plane reference plate；

Step 2, with the image of each angle of camera acquisition plane scaling board, if obtaining J width image；

Step 3, angle point grid is carried out to each image, calculates the corresponding homography matrix of each image, is denoted as Hj, wherein j is Picture numbers, value 1,2,3 ..., J；

Step 4, the parameter of consistency is randomly selected in initialization, including taking theoretical the number of iterations k is ∞, initial practical iteration time Number is i=0, and best interior point set is bestSub=[], and best interior points are bestNin=0；[] shows empty set；

Step 5, s homography matrix is randomly selected from homography matrix Hj all obtained by step 3, calculates IAC, and judge The distance between each image corresponding homography matrix Hj and IAC Dj, according to preset respective threshold thr judge whether Dj < Thr is to think that Hj for interior point, otherwise it is assumed that Hj is exterior point, obtains the summation Nin of interior point set sub and interior points；Wherein s is Minimum sampling number；The IAC represents K^-TK^-1, K is intrinsic parameter；I=i+1；

Step 6, judge whether Nin > bestNin, if so, enter step 7 carry out local optimums, otherwise return step 5；

Step 7, local optimum, including following sub-step are carried out,

Step 7.1, the number d=10 of local optimum is initialized, the at most interior points in part in current iteration are initialized LobestNin=0, the preferably interior point set lobestSub=[] in part；

Step 7.2, n=4, Nin=0 are enabled, point in slo is randomly selected from current interior point set sub, it is corresponding to select slo width The corresponding homography matrix Hj of image, calculates IAC, and slo is greater than minimum sampling number s, judges the corresponding homography of each image The distance between matrix H j and IAC Dj；

Step 7.3, the judgement counted in IAC is carried out according to n times of preset respective threshold thr, comprises determining whether Dj < n* Thr if it is thinks that Hj is interior point, otherwise it is assumed that Hj is exterior point, after the completion of each image judgement, obtains current interior point The summation Nin for collecting sub and interior points, enables n=n-1；

Step 7.4, judge whether n > 1, if otherwise entering step 7.5, IAC if it is calculated by current interior point set sub, Return step 7.3；

Step 7.5, judge Nin > lobestNin, if so, lobestNin=Nin, lobestSub=sub, enter step 7.6, If otherwise entering step 7.6；

Step 7.6, d=d-1 judges whether d < 1, if otherwise return step 7.2, if it is return to final result lobestSub,lobestNin；

Step 8, according to step 7 return as a result, enable bestNin=lobestNin, betSub=lobestsub, according to BestNin show that interior point ratio ε=bestNin/J, renewal theory the number of iterations k judge whether i > k, if otherwise returning to step 5, it is to enter step 9；

Step 9, according to all interior point estimation IAC in bestSub, the corresponding image set of exterior point is removed, it is excellent to complete uncalibrated image Choosing；Calibration result is further obtained according to uncalibrated image preferred result.

2. according to claim 1 based on the camera calibration method of two-dimensional calibrations object, it is characterised in that: the calculating IAC is pressed It is carried out according to following formula,

h₁ ^TK^-TK^-1h₂=0

h₁ ^TK^-TK^-1h₁=h₂ ^TK^-TK^-1h₂

Wherein, h₁,h₂It is the column vector of homography matrix H.

3. according to claim 2 based on the camera calibration method of two-dimensional calibrations object, it is characterised in that: the every width figure of judgement As the distance between corresponding homography matrix Hj and IAC Dj is carried out according to the following formula,

Wherein, d is distance, B=K^-TK^-1, h₃₀=h₁-h₂, h₄₀=h₁+h₂, Bh_iIt is B and h_iProduct, i=1,2,30,40, Bh_i (1) first element of Bh, Bh are represented_i(2) second element of Bh is represented.

4. according to claim 1 based on the camera calibration method of two-dimensional calibrations object, it is characterised in that: the renewal theory changes Generation number k is carried out according to the following formula,

Wherein, ε is the ratio of interior point, and η is given respective threshold.

5. the according to claim 1 or 2 or 3 or described camera calibration methods based on two-dimensional calibrations object, it is characterised in that: thr is 2*10^-5。

6. the according to claim 1 or 2 or 3 or described camera calibration methods based on two-dimensional calibrations object, it is characterised in that: J 20.

7. the according to claim 1 or 2 or 3 or described camera calibration methods based on two-dimensional calibrations object, it is characterised in that: s 2, Slo=min (4, Nin).