CN109522935B - Method for evaluating calibration result of binocular vision measurement system - Google Patents

Method for evaluating calibration result of binocular vision measurement system Download PDF

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CN109522935B
CN109522935B CN201811232049.4A CN201811232049A CN109522935B CN 109522935 B CN109522935 B CN 109522935B CN 201811232049 A CN201811232049 A CN 201811232049A CN 109522935 B CN109522935 B CN 109522935B
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CN109522935A (en
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邢威
张楠楠
郭磊
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Yi Si Si Hangzhou Technology Co ltd
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Isvision Hangzhou Technology Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
    • G06T7/85—Stereo camera calibration

Abstract

The invention discloses a method for evaluating a calibration result of a binocular vision measurement system, which comprises the steps of utilizing internal and external parameters obtained by calibration and image point coordinates of mark points on a calibration plate in left and right images, calculating a three-dimensional coordinate of the calibration point under a camera coordinate system, converting the three-dimensional coordinate into a world coordinate system to obtain a space coordinate measurement value of the mark point, calculating a Euclidean distance between the space coordinate measurement value and an actual coordinate value of the mark point, solving the mean value of the Euclidean distances of a plurality of mark points in the calibration plate under different calibration poses obtained by shooting, and judging whether the calibration result is correct or not; the method carries out calibration result precision evaluation on the binocular vision measurement system, and the evaluation mode is more reasonable; the method provided by the invention also evaluates the basic matrix, provides guarantee for the subsequent matching process of the binocular system, evaluates the calibration precision of the binocular vision detection system accurately, and has wide practicability.

Description

Method for evaluating calibration result of binocular vision measurement system
Technical Field
The invention relates to the field of machine vision detection, in particular to a method for evaluating a calibration result of a binocular vision measurement system.
Background
The binocular vision measurement system is used for photographing a target object from different angles by utilizing two cameras to acquire images, and reconstructing three-dimensional information of the target in a three-dimensional space so as to realize detection of object appearance, and is widely applied to the field of vision measurement.
The existing evaluation method is a back projection error analysis method, the method converts the three-dimensional coordinates of the marking points on the calibration plate into two-dimensional coordinates on an image plane through a conversion matrix obtained by calibration, and then calculates the distance between the measuring point and the ideal point.
Disclosure of Invention
The invention provides a novel calibration precision evaluation method aiming at a binocular vision measurement system, the method calculates the distance between a measurement point and an ideal point in a three-dimensional space, and the evaluation mode is more reasonable; meanwhile, for a measuring system with a binocular structure, most matching algorithms need to be restrained by means of an epipolar line, the calculation accuracy of a basic matrix determines whether the epipolar line calculation is accurate or not, and the method provided by the invention also evaluates the basic matrix and provides guarantee for the subsequent matching process of the binocular system. The method is more accurate in the evaluation of the calibration precision of the binocular vision detection system, and has wide practicability.
The technical scheme is as follows:
a method for evaluating calibration results of a binocular vision measuring system, the calibration results comprising:
left camera intrinsic parameter matrix
Figure BDA0001837393510000021
Right camera intrinsic parameter matrix
Figure BDA0001837393510000022
Wherein f isxl，fylScale factors for the left camera x-axis and y-axis directions, (u)0l，v0l) Is a principal point coordinate; f. ofxr，fyrScale factors for the x-axis and y-axis directions of the right camera, (u)0r，v0r) Is a principal point coordinate;
rotation matrix from right camera coordinate system to left camera coordinate system
Figure BDA0001837393510000023
Translation matrix Tc＝ [t1t2 t3]T(ii) a Rotation matrix from left camera coordinate system to right camera coordinate system
Figure BDA0001837393510000024
Translation matrix
Figure BDA0001837393510000025
Coordinates (X) of each marking point in the calibration plate under the world coordinate system under different calibration posesij，Yij， Zij) I is 1, 2, 3 … m, and m is the number of the calibration poses; j is 1, 2, 3 … n, n is the number of marked points in the calibration board;
left or right camera coordinate system to world coordinate system transformation [ R ]wi Twi]，i＝1，2， 3…m；
The above calibration results were evaluated according to the following procedure:
step 1, calculating two-dimensional coordinates of each mark point in a calibration plate image under a left camera image coordinate system and a right camera image coordinate system respectively;
the two-dimensional coordinates of the single mark point under the left camera image coordinate system and the right camera image coordinate system are recorded as:
Figure BDA0001837393510000031
wherein: subscript l represents the image acquired by the left camera, subscript r represents the image acquired by the right camera, and subscript p represents the point p;
step 2, respectively calculating the three-dimensional coordinates of the single mark point in the left camera coordinate system
Figure BDA0001837393510000032
Figure BDA0001837393510000033
Figure BDA0001837393510000034
Wherein the content of the first and second substances,
Figure BDA0001837393510000035
step (ii) of3, three-dimensional coordinates of the mark points calculated in the step 2 in a left camera coordinate system
Figure BDA0001837393510000036
Converting into world coordinate system to obtain its space three-dimensional coordinate pj′＝ [xj yj zj]T：
Figure BDA0001837393510000037
Step 4, calculating the three-dimensional coordinate p of the marking point space obtained in the step 3j′＝[xj yj zj]TCoordinate (X) of corresponding mark point in the calibration result in world coordinate systemij，Yij，Zij) Has a Euclidean distance d betweenij；
Step 5, repeating the step 1 to the step 4 for the calibration plate image obtained based on different relative positions of the calibration plate and the camera, and calculating an evaluation parameter ep；
Figure BDA0001837393510000038
Wherein w is the sum of the number of marker points in all the calibration plate images used in the above calculation;
when e ispAnd when the value is smaller than the preset threshold value K, the calibration result is accurate, otherwise, the calibration result is inaccurate.
Further, when the relation between the right camera coordinate system and the world coordinate system is utilized, step 2 is replaced by step 2), and step 3 is replaced by step 3);
step 2), calculating the three-dimensional coordinates of the single mark point in the right camera coordinate system
Figure BDA0001837393510000041
Figure BDA0001837393510000042
Figure BDA0001837393510000043
Wherein the content of the first and second substances,
Figure BDA0001837393510000044
step 3), three-dimensional coordinates of the mark points calculated in the step 2) in a right camera coordinate system
Figure BDA0001837393510000045
Converting into world coordinate system to obtain its space three-dimensional coordinate pj′＝ [xj yj zj]T：
Figure BDA0001837393510000046
Further, the evaluation method of the basis matrix comprises the following steps:
according to the calibration result, calculating a basic matrix F:
F＝Ar -TEAl -1
coordinates for marker points in the left camera image coordinate system
Figure BDA0001837393510000047
Calculating the polar line I:
I＝Fpjl
where E is the eigenmatrix, E ═ Tc×Rc；
Calculating corresponding homonymy points in the right camera image
Figure BDA0001837393510000048
And when the distance h from the polar line I is smaller than a set threshold value s, the calculation of the basic matrix F is accurate, otherwise, the calculation of the basic matrix F is wrong.
The above evaluation method for the basis matrix may also include the following steps:
according to the calibration result, calculating a basic matrix F:
F＝Al -TEAr -1
coordinates for marker points in the right camera image coordinate system
Figure BDA0001837393510000051
Calculating the corresponding polar line I:
I＝Fpjr
wherein E is an intrinsic matrix of the matrix,
Figure BDA0001837393510000053
calculating corresponding homonymous points in the coordinate system of the left camera image
Figure BDA0001837393510000052
And when the distance h from the polar line I is smaller than a set threshold value s, the calculation of the basic matrix F is accurate, otherwise, the calculation of the basic matrix F is wrong.
The basic matrix reflects the geometric intrinsic projective relation of the two views, and only depends on the internal reference and the external reference of the camera;
the intrinsic matrix reflects the relation between camera coordinate systems of image points of space points under cameras with different view angles, and comprises rotation and translation information of the two cameras in a physical space.
Further, the calibration plate image in step 1 is an image obtained in the calibration process or an image obtained by using the calibrated left and right cameras.
Further, the calibration pose comprises the position and the angle of a binocular vision system shooting calibration plate;
preferably, the number of the calibration images obtained in the step 5 based on different relative positions of the calibration plate and the camera is 10-30.
Further, the calibration result is obtained by the Zhang calibration method, and the calibration plate is a plane calibration plate characterized by concentric circles.
Compared with the traditional method for evaluating the calibration result by back projection, the method for evaluating the calibration result by the binocular vision measurement system can evaluate the internal and external parameters and the basic matrix calibrated by the binocular vision measurement system, calculate the deviation between the measured value and the theoretical value of the marker point in the three-dimensional space, and evaluate more accurately.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the specific embodiments.
Fixing the position of a binocular vision measuring system, setting a plurality of calibration poses according to the focal length of a camera, shooting and storing plane calibration plate images which are characterized by circles at different calibration poses; 695 circle features are contained in a single calibration plate;
in one embodiment of the invention, the focal length of the left camera and the focal length of the right camera are 40mm, and different calibration poses are set as follows:
Figure BDA0001837393510000061
at a working distance of 900mm, calibration plates facing the binocular vision measuring system are respectively: the posture is taken as 8-11, and the inclination angle is 30 degrees upwards, 30 degrees downwards, 30 degrees leftwards and 30 degrees rightwards; correspondingly shooting calibration plate images of the four groups of calibration poses with different inclination angles by the binocular vision measurement system;
at the working distance of 900mm, rotating a calibration plate which is right opposite to the binocular vision measuring system clockwise by 90 degrees, then respectively inclining upwards by 30 degrees, inclining downwards by 30 degrees, inclining leftwards by 30 degrees and inclining rightwards by 30 degrees to be used as poses 12-15;
the calibration results obtained by the Zhang calibration method are as follows:
left camera intrinsic parameter matrix
Figure BDA0001837393510000071
Right camera intrinsic parametersMatrix array
Figure BDA0001837393510000072
Rotation matrix from right camera coordinate system to left camera coordinate system
Figure BDA0001837393510000073
Translation matrix Tc＝ [t1t2 t3]T；
Coordinates (X) of each marking point in the calibration plate under the world coordinate system under different calibration posesij，Yij， Zij) I is 1, 2, 3 … m, and m is the number of the calibration poses; j is 1, 2, 3 … n, n is the number of marked points in the calibration board;
left or right camera coordinate system to world coordinate system transformation [ R ]wiTwi]，i＝1，2， 3…m；
The above calibration results were evaluated according to the following procedure:
step 1, calculating two-dimensional coordinates of each mark point in a calibration plate image of the pose 1 under a left camera image coordinate system and a right camera image coordinate system respectively;
the two-dimensional coordinates of the single mark point under the left camera image coordinate system and the right camera image coordinate system are recorded as:
Figure BDA0001837393510000074
wherein: subscript l represents the image acquired by the left camera, subscript r represents the image acquired by the right camera, and subscript p represents the point p;
step 2, respectively calculating the three-dimensional coordinates of the single mark point in the left camera coordinate system
Figure BDA0001837393510000081
Figure BDA0001837393510000082
Figure BDA0001837393510000083
Wherein the content of the first and second substances,
Figure BDA0001837393510000084
step 3, three-dimensional coordinates of the mark points calculated in the step 2 in a left camera coordinate system
Figure BDA0001837393510000085
Converting into world coordinate system to obtain its space three-dimensional coordinate pj′＝ [xj yj zj]T：
Figure BDA0001837393510000086
In the steps 2 and 3, the three-dimensional coordinates of the mark points in the right camera coordinate system can be calculated
Figure BDA0001837393510000087
Figure BDA0001837393510000088
And p isjConverting to a world coordinate system;
step 4, calculating the three-dimensional coordinate p of the marking point space obtained in the step 3j′＝[xj yj zj]TCoordinate (X) of corresponding mark point in the calibration result in world coordinate systemij，Yij，Zij) Has a Euclidean distance d betweenij；
Step 5, for the calibration plate images stored under each pose 2-13, repeating the step 1-4 in sequence, and calculating an evaluation parameter ep；
Figure BDA0001837393510000089
Wherein w is the sum of the number of marker points in all the calibration plate images used in the above calculation;
when e ispAnd when the value is smaller than the preset threshold value K, the calibration result is accurate, otherwise, the calibration result is inaccurate.
According to the Euclidean distance d of each mark point under a single pose obtained by calculationijIs calculated, a fold line graph is drawn, dijThe results of the mean calculation are given in the following table:
position 1 Position 2 Position 3 Position 4 Position 5 Position 6 Position 7 Position 8
dijMean value of 0.014 0.016 0.016 0.016 0.015 0.018 0.018 0.014
Position 9 Position 10 Position 11 Position 12 Position 13 Position 14 Position 15
dijMean value of 0.013 0.014 0.016 0.018 0.019 0.016 0.015
Meanwhile, the basic matrix in the matching process of the binocular vision measuring system is evaluated, and the method comprises the following steps:
according to the calibration result, calculating a basic matrix F:
F＝Ａr -TEＡl -1
coordinates for marker points in the left camera image coordinate system
Figure BDA0001837393510000091
Calculating an polar line I:
I＝Fpjl
wherein E is an intrinsic matrix, E ═ T 'xr';
calculating corresponding homonymous points in the coordinate system of the right camera image
Figure BDA0001837393510000092
And when the distance h from the polar line I is smaller than a set threshold value s, the calculation of the basic matrix F is accurate, otherwise, the calculation of the basic matrix F is wrong.
Drawing a line graph according to h values obtained by calculation of all mark points under a single pose, wherein the h calculation result is as follows:
position 1 Position 2 Position 3 Position 4 Position 5 Position 6 Position 7 Position 8
h value 0.033 0.039 0.034 0.031 0.039 0.022 0.030 0.028
Position 9 Position 10 Position 11 Position 12 Position 13 Position 14 Position 15
h value 0.028 0.038 0.033 0.038 0.033 0.052 0.030
For convenience in explanation and accurate definition in the appended claims, the terms "upper", "lower", "left" and "right" are used in describing exemplary embodiments in the particular locations.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. The foregoing description is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable others skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications thereof. It is intended that the scope of the invention be defined by the following claims and their equivalents.

Claims (5)

1. A method for evaluating calibration results of a binocular vision measuring system, the calibration results comprising:
left camera intrinsic parameter matrix
Figure FDA0003020371070000011
Right camera intrinsic parameter matrix
Figure FDA0003020371070000012
Wherein f isxl，fylScale factors for the left camera x-axis and y-axis directions, (u)0l，v0l) Is a principal point coordinate; f. ofxr，fyrScale factors for the x-axis and y-axis directions of the right camera, (u)0r，v0r) Is a principal point coordinate;
rotation matrix from right camera coordinate system to left camera coordinate system
Figure FDA0003020371070000013
Translation matrix Tc＝[t1 t2 t3]T(ii) a Rotation matrix from left camera coordinate system to right camera coordinate system
Figure FDA0003020371070000014
Translation matrix Tc＝[t`1t`2 t`3]T；
Under different calibration poses, each of the calibration platesCoordinates (X) of the marked point in world coordinate systemij，Yij，Zij) I is 1, 2, 3 … m, and m is the number of the calibration poses; j is 1, 2, 3 … n, n is the number of marked points in the calibration board;
left or right camera coordinate system to world coordinate system transformation [ R ]wi Twi]，i＝1，2，3…m；
The method is characterized in that the calibration result is evaluated according to the following steps:
step 1, calculating two-dimensional coordinates of each mark point in a calibration plate image under a left camera image coordinate system and a right camera image coordinate system respectively;
the two-dimensional coordinates of the single mark point under the left camera image coordinate system and the right camera image coordinate system are recorded as:
Figure FDA0003020371070000015
Figure FDA0003020371070000016
wherein: subscript l represents the image acquired by the left camera, subscript r represents the image acquired by the right camera, and subscript p represents the point p;
step 2, respectively calculating the three-dimensional coordinates of the single mark point in the left camera coordinate system
Figure FDA0003020371070000021
Figure FDA0003020371070000022
Figure FDA0003020371070000023
Figure FDA0003020371070000024
Wherein the content of the first and second substances,
Figure FDA0003020371070000025
step 3, three-dimensional coordinates of the mark points calculated in the step 2 in a left camera coordinate system
Figure FDA0003020371070000026
Figure FDA0003020371070000027
Converting into world coordinate system to obtain its space three-dimensional coordinate pj′＝[xj yj zj]T：
Figure FDA0003020371070000028
Step 4, calculating the three-dimensional coordinate p of the marking point space obtained in the step 3j′＝[xj yj zj]TCoordinates (X) of corresponding mark points in the calibration result in the world coordinate systemij，Yij，Zij) Has a Euclidean distance d betweenij；
Step 5, repeating the step 1 to the step 4 for the calibration plate image obtained based on different relative positions of the calibration plate and the camera, and calculating an evaluation parameter ep；
Figure FDA0003020371070000029
Wherein w is the sum of the number of marker points in all the calibration plate images used in the above calculation;
when e ispWhen the value is smaller than a preset threshold value K, the calibration result is accurate, otherwise, the calibration result is inaccurate;
according to the calibration result, calculating a basic matrix F:
F＝Ar -TEAl -1
for markers in the left camera image coordinate systemCoordinates of points
Figure FDA00030203710700000210
Calculating the polar line I:
I＝Fpjl
where E is the eigenmatrix, E ═ Tc×Rc；
Calculating corresponding homonymous points in the coordinate system of the right camera image
Figure FDA0003020371070000031
The distance h from the polar line I is smaller than a set threshold value s, the calculation of the basic matrix F is accurate, and otherwise, the calculation of the basic matrix F is wrong;
or, according to the calibration result, calculating a basis matrix F:
F＝Al -TEAr -1
coordinates for marker points in the right camera image coordinate system
Figure FDA0003020371070000032
Calculating the corresponding polar line I:
I＝Fpjr
where E is an intrinsic matrix, and E ═ T ″c×R`c；
Calculating corresponding homonymous points in the coordinate system of the left camera image
Figure FDA0003020371070000033
And when the distance h from the polar line I is smaller than a set threshold value s, the calculation of the basic matrix F is accurate, otherwise, the calculation of the basic matrix F is wrong.
2. The method of evaluating the calibration results of a binocular vision measuring system of claim 1, wherein: step 2 is replaced by step 2), step 3 is replaced by step 3),
step 2), calculating the three-dimensional coordinates of the single mark point in the right camera coordinate system
Figure FDA0003020371070000034
Figure FDA0003020371070000035
Figure FDA0003020371070000036
Wherein the content of the first and second substances,
Figure FDA0003020371070000037
step 3), three-dimensional coordinates of the mark points calculated in the step 2) in a right camera coordinate system
Figure FDA0003020371070000038
Figure FDA0003020371070000039
Converting into world coordinate system to obtain its space three-dimensional coordinate pj′＝[xj yj zj]T：
Figure FDA0003020371070000041
3. The method of evaluating calibration results of a binocular vision measuring system according to claim 1 or 2, wherein: in step 1, the calibration plate image is an image obtained in the calibration process or an image obtained by using the calibrated left and right cameras.
4. The method of evaluating calibration results of a binocular vision measuring system according to claim 1 or 2, wherein: and 5, the number of the calibration images obtained at different relative positions of the calibration plate and the camera is 10-30.
5. The method of evaluating calibration results of a binocular vision measuring system according to claim 1 or 2, wherein: the calibration result is obtained by a Zhang calibration method, and the calibration plate is a plane calibration plate which is characterized by concentric circles.
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