CN1719477A - Calibration method of pick up camera or photographic camera geographic distortion - Google Patents

Abstract

The present invention relates to a calibration method of geometric distortion of pickup camera or photographic camera. Said method includes the following main steps: firstly, creating coordinate conversion relationship between ideal imaging plane and actual imaging plane and between actual imaging plane and pixel coordinate system, collecting calibration image, extracting image point on straight line, making coordinate conversion and adopting other measures, and utilizing optimization principle to obtain the geometric distortion parameter of pickup camera or photographic camera. Said method can be used for geometric calibration of pickup camera or photographic camera, standardization of pickup camera and their assembled quality inspection.

Description

The scaling method of video camera or camera geometric distortion

Technical field

The present invention relates to the scaling method of a kind of video camera or camera geometric distortion, can be applicable to geometric calibration, the camera calibration in the computer stereo vision and video camera or the camera lens processing and the assembly quality check of video camera or image that camera is taken the photograph.Belonging to advanced makes and automatic field.

Background technology

Because video camera or the camera various errors in element processing and assembling process, there is geometric distortion in the image of shooting.This geometric distortion not only influences the visual effect of image, and influences the camera calibration precision in the computer stereo vision.Therefore, the demarcation of video camera or camera geometric distortion is Flame Image Process, computer stereo vision, and the major issue in video camera or camera manufacturing and the check.

At present, the method for video camera or camera geometric distortion demarcation has two big classes.One class is based on the method for optical instrument, needs special instrument, cost height not only, and need the professional to demarcate, limited the popularization of using; The another kind of method that is based on image does not need special instrument, only need demarcate a few width of cloth images of target with video camera or camera, just can demarcate geometric distortion by calculating.This method is simple to operate, is convenient to popularization and application.

Existing method based on image all is based upon on the ideal image plane.Present more comprehensive a kind of scaling method (J.Weng.P.Cohen, and M.Herniou, Camera Calibration with Distortion Modelsand Accuracy Evaluation, IEEE Trans.Pattern Analysis and Machine Intelligence, vol.14, no.10, pp.965-980, Oct.1992) geometric distortion of video camera or camera is divided into three kinds of radial distortion, centrifugal distortion and thin prism distortion, represents by coefficient of radial distortion, centrifugal distortion coefficient and thin prism distortion factor respectively.Centrifugal distortion and the thin prism existing radial component that distorts has tangential component again.The weak point of this method is: 1, coefficient of radial distortion, centrifugal distortion coefficient and thin prism distortion factor are not independent mutually, and they are coupled mutually; 2, do not consider the concrete physics source of distortion, physical significance is indeterminate; 3, need the distortion parameter of demarcation many, computing cost is big, brings difficulty to demarcation.

(for example: Lili Ma also has certain methods, YangQuan Chen, and Kevin L.Moore, Flexiblecamera calibration using a new analytical radial undistortion formula withapplication to mobile robot localization, in IEEE International Symposium onIntelligent Control, Houston, USA, October 2003) think that radial distortion is a major part, thereby omit tangential distortion, only consider radial distortion, and utilize polynomial expression or other mathematical function match geometric distortion.These methods can be simplified calculating, have following deficiency: 1, because radial distortion and tangential distortion are couplings mutually, though tangential distortion is less important, but only come the whole distortion of match that stated accuracy is restricted with radial distortion; 2, mainly carry out match, the actual physics source of distortion can not be described from the angle of mathematics.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, propose a kind of new video camera or the scaling method of camera geometric distortion, with indefinite problem that solves that video camera or camera geometric distortion are difficult for demarcating and distortion physics is originated.

The present invention is to cause the physics origin cause of formation of geometric distortion in optical device processing and video camera or the camera assembling process, the video camera of proposition or camera geometric distortion scaling method are based upon on the actual imaging plane.

Technical scheme of the present invention: at first set up between ideal image plane and the actual imaging plane, and the coordinate transform relation between actual imaging plane and the pixel coordinate system, gather uncalibrated image then, extract the picture point on the straight line, and by coordinate transform, the inverse transformation with radial distortion is found the solution in parsing, true picture point on the actual imaging plane is transformed to undistorted ideal image point on the ideal image plane, at last also should be positioned at principle on the straight line, utilize principle of optimality to obtain the geometric distortion parameter of video camera or camera according to the undistorted ideal image point of point on the ideal image plane on same straight line in the visual field.

The scaling method of video camera of the present invention or camera geometric distortion comprises following step:

1. set up the transformation relation between ideal image plane coordinate system and the actual imaging plane coordinate system: with the image coordinate system in the general pinhole camera modeling as the ideal image plane coordinate system, this ideal image plane coordinate system is rotated an angle around the x axle earlier, and then around an angle of y axle rotation and obtain the actual imaging plane coordinate system, an available above-mentioned rotation matrix of determining around the rotation angle of x axle and y axle is represented the transformation relation between actual imaging plane coordinate system and the ideal image plane coordinate system.

2. set up the transformation relation between actual imaging plane coordinate system and the pixel coordinate system: according to pixel coordinate is the coordinate of initial point in the actual imaging plane coordinate system, and pixel is in the size of both direction in length and breadth, and the transformation relation between actual imaging plane coordinate system and the pixel coordinate system is represented in an available linear transformation.

3. gather the calibration point image: a series of straight lines are set in the visual field, at the multiple image of different positions and these straight lines of angle shot, extract the point that belongs in the image on the straight line, these points are the true picture points on the actual imaging plane.

4. the transformation relation between actual imaging plane coordinate system of being set up and the pixel coordinate system coordinate of real image point in the actual imaging plane coordinate system of looking for the truth: according to step 2), the pixel coordinate of the true picture point that step 3) is extracted is converted to the coordinate in the actual imaging plane coordinate system.

5. the resonable coordinate that is thought of as in the photo coordinate system of the real image point of looking for the truth: the straight line and the ideal image Plane intersects that connect true picture point on perspective projection center and the actual imaging plane, intersection point is exactly the true picture point of point on the ideal image plane in the visual field, ideal image plane coordinate system of setting up according to step 1) and the transformation relation between the actual imaging plane coordinate system can be obtained the resonable coordinate that is thought of as in the photo coordinate system of this true picture point by analytic method.

6. correct distortion: the true picpointed coordinate on the ideal image plane is carried out inverse transformation by general radial distortion formula, obtain the undistorted ideal image point coordinate on the ideal image plane.

7. ask distortion parameter: also should be positioned at principle on the straight line according to the undistorted ideal image point of point on the ideal image plane on same straight line in the visual field, the utilization principle of optimality is obtained the parameter of expression geometric distortion, finishes the geometric distortion of video camera or camera and demarcates.

Compared with prior art, the parameter of these expression geometric distortions is separate among the present invention, thereby parameter is less, brings convenience to demarcation.On the other hand, these parameters have clear physical meaning: coefficient of radial distortion has illustrated the Main physical source of geometric distortion, be camera lens curvature deviation, coordinate conversion parameter represents that the actual imaging plane with respect to the off-centre on ideal image plane and crooked, is the principal element that causes tangential distortion.This not only can give correct the distortion provider to, and can be used for the crudy of optical device and the assembly quality of video camera or camera detects, instruct produce, to improve the quality.

Description of drawings

Fig. 1 is for adopting the imaging process synoptic diagram of video camera of the present invention or camera geometric distortion scaling method.

Embodiment

In order to understand technical scheme of the present invention better,, be described in further detail below in conjunction with drawings and Examples.

The imaging process that employing the inventive method is demarcated is specifically carried out as shown in Figure 1 as follows:

1. set up the transformation relation between ideal image plane coordinate system and the actual imaging plane coordinate system: with the image coordinate system in the general pinhole camera modeling as ideal image plane coordinate system oxyz, this ideal image plane coordinate system is rotated an angle θ around the x axle earlier, and then around an angle ψ of y axle rotation and obtain actual imaging plane coordinate system OUVW, an available above-mentioned rotation matrix R who determines around the rotation angle θ and the ψ of x axle and y axle _cTransformation relation between expression actual imaging plane coordinate system and the ideal image plane coordinate system:

$R_c=\left[\begin{array}{ccc}\cos \mathrm{\ψ}& 0& \sin \mathrm{\ψ}\\ \mathrm{son\θson\ψ}& \cos \mathrm{\θ}& -\sin \mathrm{\θ}\cos \mathrm{\ψ}\\ -\cos \mathrm{\θ}\sin \mathrm{\ψ}& \sin \mathrm{\θ}& \cos \mathrm{\θ}\cos \mathrm{\ψ}\end{array}\right]---\left(1\right)$

Because θ and ψ are very little, following formula can be reduced to:

$R_c=\left[\begin{array}{ccc}1& 0& \mathrm{\ψ}\\ 0& 1& -\mathrm{\θ}\\ -\mathrm{\ψ}& \mathrm{\θ}& 1\end{array}\right]---\left(2\right)$

2. set up the transformation relation between actual imaging plane coordinate system and the pixel coordinate system: according to pixel coordinate is the coordinate (u of initial point o ' in actual imaging plane coordinate system OUV of o ' uv ₀, v ₀), and pixel is at the size du and the dv of u and v both direction, can with the coordinate of picture point in the actual imaging plane coordinate system (U, V) with pixel coordinate system in coordinate (u, v) the relation between is expressed as with a linear transformation;

$\left[\begin{array}{c}U\\ V\end{array}\right]=\left[\begin{array}{cc}\mathrm{du}& 0\\ 0& \mathrm{dv}\end{array}\right]\left[\begin{array}{c}u\\ v\end{array}\right]+\left[\begin{array}{c}{u}_0\\ v_0\end{array}\right]---\left(3\right)$

3. gather the calibration point image: in this specific embodiments, adopt straight line on the gridiron pattern, take the multiple image of a gridiron pattern earlier, therefrom extract the some P on two groups of parallel lines of both direction in length and breadth in diverse location and attitude as demarcating object _Ij(u _Ij, v _Ij), i=1,2 ..., m represents different straight lines, j=1, and 2 ..., n, expression belongs to the different point of straight line i, and these points are the true picture points on the actual imaging plane;

4. real image point P looks for the truth _Ij(u _Ij, v _Ij) coordinate in the actual imaging plane coordinate system: actual imaging plane coordinate system of setting up according to step 2 and the transformation relation between the pixel coordinate system, the pixel coordinate (u of the true picture point that step 3 is extracted _Ij, v _Ij) be converted to the coordinate (U in the actual imaging plane coordinate system _Ij, V _Ij);

5. the resonable coordinate that is thought of as among the photo coordinate system oxyz of the real image point of looking for the truth: connect the perspective projection center O _cGo up true picture point P with actual imaging plane OUV _rStraight line and ideal image plane oxy intersect intersection point P _dBe exactly the some P in the visual field _cTrue picture point on the oxy of ideal image plane, ideal image plane coordinate system of setting up according to step 1 and the transformation relation between the actual imaging plane coordinate system can be obtained the resonable coordinate (x that is thought of as in the photo coordinate system of this true picture point by analytic method _d, y _d);

$x_d=\frac{U\·f}{\mathrm{\ψ}\·U-\mathrm{\θ}\·V+f};y_d=\frac{V\·f}{\mathrm{\ψ}\·U-\mathrm{\θ}\·V+f}---\left(4\right)$

6. correct distortion: with the true picpointed coordinate (x on the ideal image plane _d, y _d) carry out inverse transformation by general radial distortion formula, obtain the undistorted ideal image point P on the ideal image plane _iCoordinate (x, y);

$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{1+k_1({x_d}^2+{y_d}^2)}\left[\begin{array}{c}{x}_d\\ y_d\end{array}\right]---\left(5\right)$

7. ask distortion parameter: also should be positioned at principle on the straight line according to the undistorted ideal image point of point on the ideal image plane on same straight line in the visual field, the utilization principle of optimality is obtained the parameter [u of expression geometric distortion ₀v ₀k ₁θ ψ], to finish the geometric distortion of video camera or camera is demarcated, detailed process can be described below:

Supposing that captured cross-hatch pattern looks like to add up to the num width of cloth, is the image of k for a width of cloth sequence number wherein, k=1, and 2 ..., num supposes the undistorted ideal image point P on the ideal image plane _Ij(x _j, y _j), j=1,2 ..., n is from the straight line L on the gridiron pattern _i, i=1,2 ..., m is from these undistorted ideal image point P _Ij(x _j, y _j), j=1,2 ..., n utilizes least square method can simulate straight line l _i: a _iX+b _iY+c _i=0.Postulated point P _Ij(x _j, y _j) to straight line l _iDistance be d _Ij, the line correspondence of having a few apart from sum so $\underset{k=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left(\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}\right)\right)$ Can be used as the tolerance of linear correction degree.By making $\underset{k=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left(\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}\right)\right)$ Minimize, can calibrate distortion parameter [u ₀v ₀k ₁θ ψ], finish the geometric distortion of video camera or camera and demarcate.

Claims (1)

1. video camera or camera geometric distortion scaling method is characterized in that comprising following concrete steps:

1) set up transformation relation between ideal image plane coordinate system and the actual imaging plane coordinate system: with the image coordinate system in the general pinhole camera modeling as the ideal image plane coordinate system, this ideal image plane coordinate system is rotated an angle around the x axle earlier, and then around an angle of y axle rotation and obtain the actual imaging plane coordinate system, represent transformation relation between actual imaging plane coordinate system and the ideal image plane coordinate system around a definite rotation matrix of the rotation angle of x axle and y axle with above-mentioned;

2) set up actual imaging plane coordinate system and pixel coordinate the system between transformation relation: according to pixel coordinate is the coordinate of initial point in the actual imaging plane coordinate system, and pixel is in the size of both direction in length and breadth, represents transformation relation between actual imaging plane coordinate system and the pixel coordinate system with a linear transformation;

3) gather the calibration point image: a series of straight lines are set in the visual field, at the multiple image of different positions and these straight lines of angle shot, extract the point that belongs in the image on the straight line, these points are the true picture points on the actual imaging plane;

4) transformation relation between actual imaging plane coordinate system of being set up and the pixel coordinate system coordinate of real image point in the actual imaging plane coordinate system of looking for the truth: according to step 2), the pixel coordinate of the true picture point that step 3) is extracted is converted to the coordinate in the actual imaging plane coordinate system;

5) the resonable coordinate that is thought of as in the photo coordinate system of real image point of looking for the truth: the straight line and the ideal image Plane intersects that connect true picture point on perspective projection center and the actual imaging plane, intersection point is exactly the true picture point of point on the ideal image plane in the visual field, ideal image plane coordinate system of setting up according to step 1) and the transformation relation between the actual imaging plane coordinate system are obtained the resonable coordinate that is thought of as in the photo coordinate system of this true picture point by analytic method;

6) correct distortion: the true picpointed coordinate on the ideal image plane is carried out inverse transformation by general radial distortion formula, obtain the undistorted ideal image point coordinate on the ideal image plane;

7) ask distortion parameter: also should be positioned at principle on the straight line according to the undistorted ideal image point of point on the ideal image plane on same straight line in the visual field, the utilization principle of optimality is obtained the parameter of expression geometric distortion, finishes the geometric distortion of video camera or camera and demarcates.