CN111862237B - Camera calibration method for optical surface shape measurement and device for realizing method - Google Patents
Camera calibration method for optical surface shape measurement and device for realizing method Download PDFInfo
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- CN111862237B CN111862237B CN202010713454.9A CN202010713454A CN111862237B CN 111862237 B CN111862237 B CN 111862237B CN 202010713454 A CN202010713454 A CN 202010713454A CN 111862237 B CN111862237 B CN 111862237B
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- 238000000034 method Methods 0.000 title claims abstract description 49
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- 238000000354 decomposition reaction Methods 0.000 claims abstract description 8
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- 238000007476 Maximum Likelihood Methods 0.000 claims abstract description 6
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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
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformation in the plane of the image
- G06T3/40—Scaling the whole image or part thereof
- G06T3/4023—Decimation- or insertion-based scaling, e.g. pixel or line decimation
Abstract
The invention relates to the technical field of precision engineering, in particular to a camera calibration method in vision measurement and deflection operation. A camera calibration method for optical surface shape measurement, wherein the camera is arranged on a guide rail, and a calibration plate containing circular spot features can move along the guide rail, and the method comprises the following steps: respectively shooting corresponding position images at the focusing position and a plurality of front-back symmetrical positions; using pupil coordinates of feature points on the image at the focusing position as base points, and carrying out linear interpolation to represent pupil coordinates of feature points of other images by a triangular mesh method; constructing a corresponding equation between pixel points and actual object coordinates through affine transformation and distortion terms, and solving object image transformation matrix parameters through singular value decomposition; and reducing the re-projection error by a maximum likelihood estimation method to obtain an optimal solution, thereby obtaining the light direction. Compared with the existing camera calibration technology, the method has the advantages of high precision, wide applicability, convenience in operation and the like.
Description
Technical Field
The invention relates to the technical field of precision engineering, in particular to a small pupil camera calibration device and method in vision measurement and deflection operation.
Background
In modern precise measurement, a deflection operation measurement method is an optical surface shape high-precision measurement technology based on stripe reflection. The principle is that regular stripes are projected to a surface to be measured, the stripes are deformed after being reflected by the surface to be measured, a CCD camera is used for shooting deformation patterns, a geometric relationship between an object image point and the surface to be measured is obtained by a triangulation method, return correction of incident light rays and reflected light rays is obtained, gradient distribution of the surface to be measured is deduced according to angular bisectors, and surface shape height distribution [ Xu Xue ] is obtained by integration. The measuring method has the advantages of wide measuring range, large dynamic range, strong anti-interference capability, simple measuring equipment, low cost, non-contact measurement and the like, is widely focused in recent years, and has good application to large-caliber optical workpiece measurement and in-situ online measurement.
The accuracy of the deflection measurement depends on the accuracy of the calculation of the incident and reflected light rays. The traditional camera calibration method is to obtain an object image matching relation of characteristic points by using a calibration block with determined structural information, but the camera is described as a pinhole imaging model, the light passing through pixel points is considered to pass through an ideal camera pupil center, a mathematical model for object image point transformation is established by the characteristic of equal-ratio scaling of triangles, the parameter of the camera model is solved to obtain the object image point corresponding relation and the light direction [ Weng J, cohen P, herniou M.calibration of stereo cameras using a non-linear distortion model (CCD sensor) [ C ].10th International Conference on Pattern Recognition.IEEE,1990:246-253 ], the traditional camera model solving method is generally a Tasi two-step method [ Tsai R.A versatile camera calibration technique for high-accuracy 3-D machine vision metrology using off-the-shelf TV cameras and lenses [ J ]. IEEE Journal on Robotics Automation,1987,3 (4): 323-344 ], a Zhang Zhengyou plane calibration method [ Zhang Z.A flexible new technique for camera calibration [ J ]. IEEE Transactions on pattern analysis machine intelligence,2000,22 (11): 1330-1334 ], and the like.
The pupil of an actual camera lens has a certain size and thus pupil aberration occurs. The position and the direction of the obtained light rays have deviation, and the measurement accuracy is affected. Therefore, the camera calibration model needs to be optimized, and the camera calibration precision is improved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a camera calibration method for optical surface shape measurement, which can improve the calibration precision of a camera, thereby improving the precision of optical surface shape measurement by deflection operation.
The invention relates to a small pupil camera calibration method for optical surface shape measurement, wherein the camera is arranged on a guide rail, and a calibration plate with circular spot characteristics can move along the guide rail, and the method is characterized by comprising the following steps:
respectively shooting corresponding position images at the focusing position and a plurality of front-back symmetrical positions;
using pupil coordinates of feature points on the image at the focusing position as base points, and carrying out linear interpolation to represent pupil coordinates of feature points of other images by a triangular mesh method;
constructing a corresponding equation between pixel points and actual object coordinates through affine transformation and distortion terms, and solving object image transformation matrix parameters through singular value decomposition;
and reducing the re-projection error by a maximum likelihood estimation method to obtain an optimal solution, thereby obtaining the light direction.
The horizontal moving type calibration plate experimental device is adopted, the camera and the calibration plate are vertically fixed on the experiment table, the dot calibration plate is fixed on the guide rail, and the direction of the guide rail is parallel to the direction of the optical axis of the camera. The camera position, the lens f-number and the focal length are always kept fixed, the initial position of the calibration plate is positioned on the best clear imaging surface, the calibration plate is moved in parallel in the depth of field range of the camera through the guide rail, and the pupil offset (a) of the characteristic points of the image of the calibration plate at the most clear imaging position is used 0 ,b 0 ) As a base point, use (a) 0 ,b 0 ) And (5) representing pupil coordinates of other image feature points, and solving parameters through singular value decomposition. And setting respective corresponding pupil position offsets in the calibrated light rays. The invention breaks through the limitation that all light rays in the pinhole model must pass through the same optical center, breaks through the limitation of the traditional pinhole camera model, and improves the calibration accuracy of the camera.
Drawings
Fig. 1 to 2 are schematic structural views of the calibration device of the present invention.
FIG. 3 is a flow chart of the calibration process of the present invention.
Fig. 4 is a calibration plate image obtained by photographing.
Fig. 5 shows the reprojection error RMS obtained by the calibration method of translating the calibration plate.
Detailed Description
The invention will now be described in further detail with reference to the drawings and examples.
Fig. 1 and fig. 2 show structural schematic diagrams of the calibration device of the invention, from which the light path of the experimental equipment can be seen, the camera is a small pupil camera, and an image is shot after the calibration plate is moved in parallel, as shown in fig. 4; FIG. 3 is a flow chart of the calibration process of the present invention, comprising the steps of:
step 1, controlling a camera aperture, calculating the depth of field, and placing a calibration plate to enable the position of the calibration plate to be at the clearest imaging position;
step 2, moving the calibration plate and shooting images, wherein the images of the calibration plate are always clear, and the moving distance is recorded;
step 3, using pupil coordinates of feature points on the image at the clearest imaging position as base points, and representing pupil coordinates of other image feature points;
step 4, solving object-image transformation matrix parameters through singular value decomposition;
and 5, reducing the re-projection error by a maximum likelihood estimation method to obtain an optimal solution, thereby obtaining the light direction. According to the method provided by the invention, the actual object point position is compared with the object point position after the model is solved, and the reprojection error distribution is shown in figure 5. It can be shown that the re-projection error RMS of the method is 0.04 pixel, and very high accuracy can be achieved.
The small pupil camera calibration device and method of the invention do not limit all light rays to pass through the same light center, and break a pinhole camera model by establishing a pupil coordinate system, in particular to a camera calibration method for optical surface shape measurement, which comprises the following elements and implementation steps:
1) The camera calibration system is constructed, and comprises a camera to be calibrated, a calibration plate with circular spot characteristics and a high-precision guide rail, wherein the calibration plate is fixed on the guide rail, is adjusted to the position of an optimal clear imaging surface, and images at the moment are recorded. Then, the calibration plate is moved in parallel, the movement distance is recorded, and the corresponding position images are respectively shot at the positions of 1/2 depth of field (or at the positions of 1/3 depth of field and at the positions of 2/3 depth of field) in front and back directions, and the positions of 1/2 depth of field in front and back directions are taken as examples. The lens can also symmetrically move a plurality of positions before and after the focusing position, and only the fact that the furthest distance does not exceed the depth of field is ensured;
2) Constructing a mathematical model between camera pixel points and feature points, and setting world coordinate system coordinates of the feature points as coordinatesj is represented as a calibration plate position number, j= -1,0,1, wherein the 0th position represents the best focus position, the-1 st position represents the forward 1/2 depth of field position, and the 1 st position represents the backward 1/2 depth of field position. i is expressed as a feature point number, n feature points are provided, and the coordinates of the pixel points of the corresponding feature points on the image plane are +.>Constructing an equation set according to the obtained object image point coordinates:
where Zc denotes the z-coordinate, t of the camera image plane j Indicating the z-direction offset at calibration plate position j. Wherein the method comprises the steps ofRepresenting the X-direction offset of the principal ray corresponding to the ith feature point at position j due to the difference in pupil coordinates +.>Indicating the corresponding Y-direction offset.
3) The above offsetAnd->By the offset of the reference position->And (5) interpolating the representation. Taking the image at position 0 as reference, pixel coordinates of all spots +.>Forming a triangulated mesh, and performing dot pixel coordinates on other images>Interpolation is performed on the triangulated mesh, corresponding offset is +.>Use->Is expressed by a linear combination of:
wherein the method comprises the steps ofIs composed of->And (5) determining interpolation coefficients.
4) Let dj denote the translation distance of the calibration plate from the 0th position to the j-position, it is possible to obtain:
coordinate data obtained by each feature pointCorresponding pixel coordinate data +.>The new equation set +.>Due to->All are all made up of->Indicating (I)>All are all made of->Representing, then formula (2) can be substituted into the system of equations +.>
Obtaining parameters (m) by singular value decomposition 11 ,m 12 ,m 13 ,m 21 ,m 22 ,m 23 ,m 31 ,m 32 ,m 33 ). Since the homogeneous system of equations has an infinite number of solutions, it is scaled here by a suitable coefficient such that zc=1, resulting in
5) By maximum likelihood estimation, a total of k graphs are provided,for the coordinate of the ith feature point on the calibration plate when the jth image is taken, use +.>Representing +.A. obtained by ray tracing Using the camera model described above>In correspondence with the image point,is the actual image point.
The best solution obtained using the Levenberg-Marquardt method minimizes the following equation.
The method of the invention is adopted to build a measuring system. The camera is manufactured by JAI company, the model is SP-2000C-PMCL, the focal length is 50mm, the F number is 11, the distance between the camera body and the calibration plate is about 400mm, the pixel size is 6.4 μm multiplied by 6.4 μm, the camera and the calibration plate are approximately in a vertical plane, and the depth of field is about 50mm. Since the equation set has 9M matrix unknowns, 2n pupil translationIn addition, each image has a t j The unknowns are translated. One image provides 2n equations, at least 6 feature points are needed if only 2 images are taken, and at least 3 feature points are needed if more than 3 images are taken. The number of feature points of the dot is 42×41, and the diameter of the dot is 3mm.
Then fixing the camera body position, the lens focal length, the f-number and the like, adjusting the position of the calibration plate to enable the calibration plate to be located on the best clear imaging surface as far as possible, and recording imaging at the moment. And then translating the calibration plate, always keeping imaging clear during translation, moving forward and backward by 20mm, and respectively recording corresponding position images.
Compared with the prior art, the invention has the following advantages:
the invention overcomes the limitation that all default light rays pass through the same pupil point in the traditional pinhole camera model, solves the object image point transformation matrix and the pupil offset by arranging the respective pupil offset for each calibration light ray and translating the calibration plate method, and compared with the traditional calibration method, the invention breaks model limitation, improves calibration precision, reduces image shooting times and can effectively improve calibration efficiency.
Claims (4)
1. The small pupil camera calibration method for optical surface shape measurement is characterized by comprising the following steps that a camera is arranged on a guide rail, and a calibration plate containing circular spot characteristics can move along the guide rail within the depth of field of the camera:
at the focusing position and at a plurality of front-back symmetrical positions, respectively shooting images of the calibration plate by using cameras;
using pupil coordinates of feature points on the image at the focusing position as base points, and carrying out linear interpolation to represent pupil coordinates of feature points of other images by a triangular mesh method;
constructing a corresponding equation between pixel points and actual object coordinates through affine transformation and distortion terms, and solving object image transformation matrix parameters through singular value decomposition;
constructing a mathematical model between camera pixel points and feature points, and setting world coordinate system coordinates of the feature points as coordinatesj is represented as a calibration plate position number, j= -1,0,1, wherein the 0th position represents the best focusing position, the-1 st position represents the forward 1/2 depth of field position, and the 1 st position represents the backward 1/2 depth of field position; i is expressed as a feature point number, n feature points are provided, and the coordinates of the pixel points of the corresponding feature points on the image plane are +.>Constructing an equation set according to the obtained object image point coordinates:
where Zc denotes the z-coordinate, t of the camera image plane j Indicating the z-direction offset at the calibration plate position j; wherein the method comprises the steps ofRepresenting the X-direction offset of the principal ray corresponding to the ith feature point at position j due to the difference in pupil coordinates +.>Representing the corresponding Y-direction offset;
the above offsetAnd->By the offset of the reference position->Interpolation representation; taking the image at position 0 as reference, pixel coordinates of all spots +.>Forming a triangulated mesh, and performing dot pixel coordinates on other images>Interpolation is performed on the triangulated mesh, corresponding offset is +.>Use->Is expressed by a linear combination of:
wherein the method comprises the steps ofIs composed of->The interpolation coefficient determined;
let dj denote the translation distance of the calibration plate from the 0th position to the j-position, it is possible to obtain:
coordinate data obtained by each feature pointCorresponding pixel coordinate data +.>Substituting formula (3) to obtain new equation set +.>Due to->All are all made up of->Indicating (I)>All are all made of->Representing, then formula (2) can be substituted into the system of equations +.>
Obtaining parameters (m) by singular value decomposition 11 ,m 12 ,m 13 ,m 21 ,m 22 ,m 23 ,m 31 ,m 32 ,m 33 ) The method comprises the steps of carrying out a first treatment on the surface of the Since the homogeneous system of equations has an infinite number of solutions, it is scaled here by a suitable coefficient such that zc=1, resulting in
And reducing the re-projection error by a maximum likelihood estimation method to obtain an optimal solution, thereby obtaining the light direction.
2. The small pupil camera calibration method for optical surface shape measurement according to claim 1, characterized in that: the front-back symmetrical positions are positions which are respectively moved by 1/2 depth of field.
3. The small pupil camera calibration method for optical surface shape measurement according to claim 1, characterized in that: the front-back symmetrical positions are positions of 1/3 depth of field of each front-back movement and positions of 2/3 depth of field of each front-back movement.
4. An apparatus for implementing the small pupil camera calibration method as defined in claim 1, characterized by an imaging system comprising a camera, a guide rail and a calibration plate with circular spot features, and a program module comprising the steps of:
at the focusing position and at a plurality of front-back symmetrical positions, respectively shooting images of the calibration plate by using cameras;
using pupil coordinates of feature points on the image at the focusing position as base points, and carrying out linear interpolation to represent pupil coordinates of feature points of other images by a triangular mesh method;
constructing a corresponding equation between pixel points and actual object coordinates through affine transformation and distortion terms, and solving object image transformation matrix parameters through singular value decomposition;
and reducing the re-projection error by a maximum likelihood estimation method to obtain an optimal solution, thereby obtaining the light direction.
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| CN108489421A (en) * | 2018-03-12 | 2018-09-04 | 四川大学 | A kind of fringe projection detection plane component face shape method and device |
| CN109325981A (en) * | 2018-09-13 | 2019-02-12 | 北京信息科技大学 | Based on the microlens array type optical field camera geometrical parameter calibration method for focusing picture point |
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