CN101149836B - Three-dimensional reconfiguration double pick-up camera calibration method - Google Patents

Abstract

The 3-D reconstitution demarcating method for two pick-up cameras includes: (1) turn on the two pick-up cameras to obtain at same time a series of images about demarcating object points and adopts traditional single-pick-up-camera demarcation method to respectively demarcate the two pick-up cameras; (2) use the central point of the common perpendicular of the two pick-up-cameras' sight lines as the space object point of 3-D reconstitution to build a 3-D reconstitution algebra expression and use the minimum 3-D reconstitution error of the object point as aim function and use the internal and the external parameters obtained from the previous step as primary value to resolve through interation to demarcate the relative positions of the two pick-up cameras. Numerically resolve the solid demarcation model set up by the step 2 to complete the demarcation course of the two pick-up cameras. Advantage: accurate demarcation and minimum error.

Description

A kind of double-camera calibrating method of three-dimensionalreconstruction

Technical field

The present invention relates to a kind of double-camera calibrating method of three-dimensionalreconstruction, be a kind of be the double-camera calibrating method of application background with the three-dimensionalreconstruction.Belong to the vision detection technology field.

Background technology

In the vision detection system,, need carry out camera calibration for the picture element from image calculates the three-dimensional coordinate of space object point.Camera calibration is exactly according to selected camera model, finds the solution the geometry and the optical characteristics of video camera inside, i.e. the pose of the relative world coordinate system of intrinsic parameter, and camera coordinate system changes, promptly outer parameter.

All adopt non-linear camera model for the field that accuracy requirement is higher, document " J.Weng; P.Cohen and M.Herniou.Calibration of stereo camerasusing a non-linear distortion model.Proc.Int.Confer.onPattern Recognition; p246～253,1990. " has carried out comparatively perfect description to the lens distortion of non-linear video camera.Numerous scholars has launched research at non-linear Camera calibration, for example document " Roger Y.Tsai.A versatile cameracalibration technique for high-accuracy 3d machine visionmetrology using off-the-shelf TV cameras and lenses.IEEEjournal of Robotics and Automation; 1,987 3 (4); 323～343. " under the radially geometric distortion situation of only considering camera lens, has proposed famous two-step approach; Document " G.Q.Wei and S.D.Ma.Implicit and explicit cameracalibration:theory and experiment.PRMI; 1994; 16 (5). " proposes a kind of biplane camera model, this method is combined into intermediate parameters with linear dimensions and nonlinear parameter, carry out linear solution then, simplified computation process; Document " Zhengyou Zhang.A flexible new technique for camera calibration.TechnicalReport MSR-TR-98-71. " proposes a kind of plane template scaling method, carries out the demarcation of camera interior and exterior parameter by obtaining the plane reference plate at a few width of cloth images of any different azimuth.

These methods have solved the Camera calibration problem to a certain extent, but they mainly are at single camera calibration, are objective function (the straight line p as shown in fig. 1 of calibrated and calculated with the error minimum of spatial point re-projection ₁q ₁), or objective function does not have tangible geometric meaning.Because the existence of calibrated error, when carrying out the stereoscopic vision measurement, the calibrated error of its outer parameter will inevitably cause bigger measuring error with two video cameras of demarcating separately.

Summary of the invention

Purpose of the present invention is to measure and demarcate the shortcoming that has bigger measuring error carrying out stereoscopic vision with the video cameras of demarcating separately with two in order to overcome prior art, and a kind of double-camera calibrating method of three-dimensionalreconstruction error minimum is provided.

Purpose of the present invention can reach by taking following measure:

A kind of double-camera calibrating method of three-dimensionalreconstruction is characterized in: the three-dimensional reconstruction error minimum with the space calibration point is an objective function, and the relative pose of twin camera is demarcated, and comprises the steps:

1) initial value of acquisition camera intrinsic parameter and outer parameter

Open two video cameras, obtain simultaneously, adopt traditional single camera calibration method, respectively two video cameras are demarcated about demarcating a series of images of object point;

2) set up the three-dimensional peg model of twin camera

Mid point with the common vertical line of twin camera sight line is the space object point of three-dimensionalreconstruction, set up the algebraic expression of three-dimensionalreconstruction, three-dimensionalreconstruction error minimum with object point is an objective function, the inside and outside parameter that obtains with previous step is an initial value, by iterative, the relative pose of twin camera is demarcated;

3) to the 2nd) the three-dimensional peg model set up of step quantizes and finds the solution, and finishes the double-camera calibrating process.

Purpose of the present invention can also reach by taking following measure:

One embodiment of the present invention are: adopt following two kinds of scaling methods to obtain camera intrinsic parameter and outer parameter initial value;

1) adopts the two-step approach of Tsai, require all calibration points can not coplane;

2) the plane template scaling method of employing Zhang, the amount of images that requires to be in different poses can not be less than 3 width of cloth.

One embodiment of the present invention are: in the process that entire image is gathered, the relative pose between the twin camera can not change; Gather in each process to image at twin camera, the pose of demarcating object point can not change.

The image that obtains is carried out feature extraction and feature identification, set up the corresponding relation between space object point and the image pixel point, calculate according to the scaling method of selecting then, obtain the initial value of the inside and outside parameter of video camera; The intrinsic parameter that utilizes camera calibration to obtain carries out geometric distortion correction to uncalibrated image.

One embodiment of the present invention are: the three-dimensional peg model of the twin camera of being set up is expressed by following equation:

$\stackrel{\→}{O_1{P}_1}=z_1\stackrel{\→}{O_1{p}_1}=\stackrel{\→}{O_1{O}_2}+z_2\stackrel{\→}{O_2{p}_2}+\mathrm{\λ}(\stackrel{\→}{O_1{p}_1}\×\stackrel{\→}{O_2{p}_2})---\left(1\right)$

$\stackrel{\→}{P_1}=T+R\stackrel{\→}{P_2}+\mathrm{\λ}\·(\stackrel{\→}{P_1}\×R\stackrel{\→}{P_2})---\left(2\right)$

One embodiment of the present invention are: the three-dimensional peg model method for solving that quantizes is to take following strategy to carry out numerical solution:

1) directly goes out linear iterative formula based on the matrix algebra equation inference;

2) utilize all information of matrix equation in the linearization procedure, construct the contradiction system of linear equations, take the solution technique of inconsistent equation group to find the solution then.

Adopt the present invention and have following beneficial effect:

The present invention is that to utilize twin camera be application background with the three-dimensionalreconstruction, and adopting a kind of is the double-camera calibrating method that error is passed judgment on criterion with three-dimensionalreconstruction error minimum.The present invention at first utilizes traditional camera marking method, as Tsai method, Zhang method etc., single camera is demarcated, and obtains the initial value of camera interior and exterior parameter; Mid point with the common vertical line of twin camera sight line is the space object point of three-dimensionalreconstruction then, is that error is passed judgment on criterion with the three-dimensionalreconstruction error minimum of object point, and the relative position of twin camera is demarcated.The present invention overcomes prior art and measures and demarcate the shortcoming that has bigger measuring error carrying out stereoscopic vision with the video cameras of demarcating separately with two, have demarcate accurately, outstanding beneficial effect that error is minimum.

Description of drawings

Fig. 1 is an objective function to demarcate object point re-projection error minimum during to single camera calibration.

Fig. 2 is during to double-camera calibrating, and the present invention is an objective function with the error minimum of spatial point three-dimensionalreconstruction.

Fig. 3 is during to double-camera calibrating, and the present invention is the space calibration point of correspondence with the mid point of twin camera sight line vertical line.

Embodiment

Describe the present invention below in conjunction with example:

(1) image acquisition and video camera initial value obtain

As previously mentioned, can adopt different scaling methods to obtain camera intrinsic parameter and outer parameter initial value.According to the difference of selected method, the space distribution of calibration point, amount of images etc. there is different requirements, for example: adopt the two-step approach of Tsai, require all calibration points can not coplane; The amount of images that the plane template scaling method of Zhang requires to be in different poses can not be less than 3 width of cloth etc.For this part concrete requirement, according to the difference of selecting method, can be with reference to relevant list of references.

In the process that entire image is gathered, the relative pose between the twin camera can not change; Gather in each process to image at twin camera, the pose of demarcating object point can not change.

The image that obtains is carried out feature extraction and feature identification, set up the corresponding relation between space object point and the image pixel point, calculate according to the scaling method of selecting then, obtain the initial value of the inside and outside parameter of video camera; The intrinsic parameter that utilizes camera calibration to obtain carries out geometric distortion correction to uncalibrated image.

(2) the three-dimensional peg model of twin camera

Since the existence of various errors, straight line R ₁, R ₂Can not really intersect, its geometric relationship is the space line of antarafacial.Can set up the simultaneously vertical R of a line segment ₁, R ₂, and hand over two straight lines respectively in a P ₁, P ₂, the mid point P of this line segment is the most close straight line R ₁, R ₂Point can be it as picture point p ₁, p ₂Corresponding calibration point, as shown in Figure 3.Point P ₁, P ₂, O ₁, O ₂Between relation can be expressed as:

$\stackrel{\→}{O_1{P}_1}=z_1\stackrel{\→}{O_1{p}_1}=\stackrel{\→}{O_1{O}_2}+z_2\stackrel{\→}{O_2{p}_2}+\mathrm{\λ}(\stackrel{\→}{O_1{p}_1}\×\stackrel{\→}{O_2{p}_2})---\left(1\right)$

Inside and outside parameter with single camera calibration is an initial value, and formula (1) is rewritten as equation in first camera coordinate system:

$\stackrel{\→}{P_1}=T+R\stackrel{\→}{P_2}+\mathrm{\λ}\·(\stackrel{\→}{P_1}\×R\stackrel{\→}{P_2})---\left(2\right)$

Wherein

Be the coordinate vector of spatial point P in first camera coordinate system,

Be the coordinate vector of spatial point P in second camera coordinate system, the result that these two coordinate figures can be used single camera calibration obtains by changes in coordinates as initial value.R, T represent second video camera rotation, the translation matrix of first video camera relatively, and λ is the unknown quantity of corresponding spatial point P.Formula (2) be one about rotating vector (α, beta, gamma), translation vector (t _x, t _y, t _z) and the nonlinear equation of λ, be expressed as with matrix form:

$\left[\begin{array}{c}{x}_1\\ y_1\\ z_1\end{array}\right]=\begin{array}{c}\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]\end{array}+\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ z_2\end{array}\right]+\mathrm{\λ}\·\left[\begin{array}{c}{x}_1\\ y_1\\ z_1\end{array}\right]\×\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ z_2\end{array}\right]---\left(3\right)$

Wherein, (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂) respectively expression demarcate the coordinate of object point in first, second camera coordinate system.By the third line of equation, can obtain the expression formula of λ:

$\mathrm{\λ}=(z_1-t_z-r_3\·\stackrel{\→}{p_2})/(x_1{r}_2\·\stackrel{\→}{p_2}-y_1{r}_1\·\stackrel{\→}{p_2})$ (4)

Brief note is: λ=λ (α, β, λ, t _x, t _y, t _z)

Bring following formula (4) into formula (3), can get:

$\left[\begin{array}{c}{x}_1\\ y_1\\ z_1\end{array}\right]=\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]+\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ z_2\end{array}\right]+\mathrm{\λ}(\mathrm{\α},\mathrm{\β},\mathrm{\λ},t_x,t_y,t_z)\·\left[\begin{array}{c}{x}_1\\ y_1\\ z_1\end{array}\right]\×\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ z_2\end{array}\right]---\left(5\right)$

For a given n spatial point, form Nonlinear System of Equations:

X ⁽ⁱ⁾＝A ⁽ⁱ⁾

(6)

i＝1，...，n

Wherein, X ⁽ⁱ⁾Be the left-hand component of i some corresponding (5), A ⁽ⁱ⁾It is the right-hand component of i some corresponding (5).

(3) quantizing of model found the solution

Formula (6) is the luxuriant and rich with fragrance system of linear equations of a matrix form, is difficult to directly search out effective algebraic equation by this equation, therefore, takes following strategy to carry out numerical solution: 1) directly to go out linear iterative formula based on the matrix algebra equation inference; 2) utilize all information of matrix equation in the linearization procedure, construct the contradiction system of linear equations, take the solution technique of inconsistent equation group to find the solution then.

For discussing conveniently, with rotating vector (α, beta, gamma), translation vector (t _x, t _y, t _z) in the variable unification be designated as x, to make the single order Taylor expansion:

$X^{\left(i\right)}\≅{\tilde{A}}^{\left(i\right)}+\underset{k=1}{\overset{6}{\mathrm{\Σ}}}\frac{\∂{\tilde{A}}_i}{{\∂x}_k}{\mathrm{dx}}_k---\left(7\right)$

By Gauss-Seidel iteration (Li Qingyang. wait numerical analysis. publishing house of HUST, 1986.) find the solution following formula, obtain whole rotating vector (α, beta, gamma), translation vector (t _x, t _y, t _z).In theory, the three-dimensional demarcation can be finished, in reality is demarcated, the number of the number of equation should be made, to reduce the influence that error causes considerably beyond error when n 〉=3.

In demarcating practice, for two video cameras of demarcating separately, in the process of demarcating, only considered the inside and outside parameter of single camera relative Calibration object point, the result of demarcation is the optimum to the inside and outside parameter of single camera.And stereoscopic vision is measured the inside and outside parameter that need use two video cameras, and the inside and outside parameter optimum of single camera can not guarantee the last result optimal of measuring, and reason is as follows:

For two video cameras of demarcating separately, the relative pose between two video cameras is by demarcating how much a kind of indirect position orientation relations that object point is set up, because there is error in single camera calibration, also there is error in how much position orientation relations therefore being set up.And the calibrated error of stereoscopic vision measurement process, particularly outer parameter that to be error amplify is particularly evident to the influence of measuring accuracy, and therefore, two video cameras of demarcating separately will inevitably bigger together measuring error when carrying out the stereoscopic vision measurement.

Three-dimensional reconstruction is exactly at a concrete mock-up, adopts someway, obtains a large amount of point data about the model geometric profile, then according to these point data, sets up a digital model in computing machine.

Stereoscopic vision scaling method proposed by the invention, the error minimum with three-dimensionalreconstruction in calibration process is the objective function of camera calibration, by external Parameter Optimization, effectively reduces the error that stereoscopic vision is measured.

The present invention utilizes to demarcate object point, simultaneously two video cameras is demarcated.

Camera intrinsic parameter mainly comprises: the scale factor of focal length, center position and pixel etc., outer parameter mainly are meant pose conversion such as the rotation, translation of camera coordinate system relative reference coordinate system.

Claims (6)

1. the double-camera calibrating method of a three-dimensionalreconstruction, it is characterized in that: the three-dimensional reconstruction error minimum with the space calibration point is an objective function, and the relative pose of twin camera is demarcated, and comprises the steps:

1) initial value of acquisition camera intrinsic parameter and outer parameter

Open two video cameras, obtain simultaneously, adopt traditional single camera calibration method, respectively two video cameras are demarcated about demarcating a series of images of object point;

2) set up the three-dimensional peg model of twin camera

Mid point with the common vertical line of two video camera sight lines is the space object point of three-dimensionalreconstruction, set up the algebraic expression of three-dimensionalreconstruction, three-dimensionalreconstruction error minimum with object point is an objective function, with the 1st) the inside and outside parameter that obtains of step is initial value, by iterative, the relative pose of two video cameras is demarcated;

3) to the 2nd) the three-dimensional peg model set up of step quantizes and finds the solution, and finishes two camera calibration processes.

2. according to the double-camera calibrating method of the described a kind of three-dimensionalreconstruction of claim 1, it is characterized in that: adopt the two-step approach of Tsai to obtain camera intrinsic parameter and outer parameter initial value, require all demarcation object points can not coplane; Perhaps adopt the plane template scaling method of Zhang to obtain camera intrinsic parameter and outer parameter initial value, the amount of images that requires to be in different poses can not be less than 3 width of cloth.

3. according to the double-camera calibrating method of the described a kind of three-dimensionalreconstruction of claim 1, it is characterized in that: in the process that entire image is gathered, the relative pose between two video cameras can not change; In each process to image of two camera acquisitions, the pose of demarcating object point can not change.

4. according to the double-camera calibrating method of the described a kind of three-dimensionalreconstruction of claim 1, it is characterized in that: the image that obtains is carried out feature extraction and feature identification, set up the corresponding relation between space object point and the image pixel point, calculate according to the scaling method of selecting then, obtain the initial value of the inside and outside parameter of video camera; Utilize the 1st) go on foot the intrinsic parameter that camera calibration obtains, uncalibrated image is carried out geometric distortion correction.

5. according to the double-camera calibrating method of the described a kind of three-dimensionalreconstruction of claim 1, it is characterized in that: the three-dimensional peg model of the twin camera of being set up is expressed by following equation:

$1)\stackrel{\→}{O_1{P}_1}=z_1\stackrel{\→}{O_1{p}_1}=\stackrel{\→}{O_1{O}_2}+z_2\stackrel{\→}{O_2{p}_2}+\mathrm{\λ}(\stackrel{\→}{O_1{p}_1}\×\stackrel{\→}{O_2{p}_2})$

$2)\stackrel{\→}{P_1}=T+R\stackrel{\→}{P_2}+\mathrm{\λ}\·(\stackrel{\→}{P_1}\×R\stackrel{\→}{P_2})$

Wherein,

Be the coordinate vector of spatial point P in first camera coordinate system,

Be the coordinate vector of spatial point P in second camera coordinate system, R, T represent second video camera rotation, the translation matrix of first video camera relatively, and λ is the unknown quantity of corresponding spatial point P.

6. according to the double-camera calibrating method of the described a kind of three-dimensionalreconstruction of claim 1, it is characterized in that: the three-dimensional peg model method for solving that quantizes is to take following strategy to carry out numerical solution:

1) directly goes out linear iterative formula based on the matrix algebra equation inference;

2) utilize all information of matrix equation in the linearization procedure, construct the contradiction system of linear equations, take the solution technique of inconsistent equation group to find the solution then.

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