CN103530880A - Camera calibration method based on projected Gaussian grid pattern - Google Patents

Abstract

A camera calibration method based on a projected Gaussian grid pattern, which is disclosed by the invention, belongs to the field of image processing and computer visual inspection, in particular to an on-site calibration method for the intrinsic and exterior parameters of cameras in a large forging dimension measurement system. By utilizing the characteristic of the Gaussian distribution of the widthwise grey scales of transverse and vertical light bars in the Gaussian grid pattern and fitting a Gaussian curve, the camera calibration method can accurately obtain the image coordinates of the points on the central lines of the light bars, so that a central line equation of the transverse and vertical light bars is fit out, the intersection points of the central lines of the transverse and vertical light bars are feature points for calibration, and according to the image coordinates of the feature points for calibration provided in the shot image of the Gaussian grid pattern, the intrinsic and exterior parameters of the cameras are acquired step by step. The camera calibration method has high real-timeness, robustness and high calibration precision, high-precision camera parameters can be obtained by step-by-step calibration, the problem of coupling in the simultaneous solution of all the camera parameters is avoided, and the camera calibration method is applicable to the on-line calibration of cameras on the forging site.

Description

Camera marking method based on projection Gaussian network pattern

Technical field

The invention belongs to image and process and Computer Vision Detection field, the field calibration method of the inside and outside parameter of video camera in particularly large forgings Size Measuring System.

Background technology

One of basic task that computer vision is processed is according to two-dimensional image information, to recover the three-dimensional geometric information of object.Realize task of utilizing picture point to ask for corresponding space object surface point, need to determine video camera imaging geometric model, the parameter of this geometric model is called camera parameters.Camera parameters is divided into inside and outside parameter, and intrinsic parameter is the parameter relevant with optical characteristics with how much of video camera self, and outer parameter is that video camera is with respect to three-dimensional position and the direction of a certain world coordinate system.The process of determining the inside and outside parameter of video camera is called camera calibration, and the precision of scaling method directly has influence on the precision of computer vision measurement.Therefore, video camera being carried out to research quick, simple and direct, accurate demarcation is significant undoubtedly.

Traditional camera marking method can be divided into based on 3D stereo target scaling method according to the difference of calibrated reference, based on 2D plane target drone scaling method (the gridiron pattern target scaling method that the Zhang Zhengyou of take proposes is representative) and the scaling method based on 1D target.These traditional scaling methods all need calibrated reference, and for the demarcation of large-field shooting machine, can the unique point of calibrated reference evenly be covered with in whole visual field, directly affects the precision of demarcation.On the one hand, make high-precision large scale demarcate target involve great expense, difficult in maintenance.On the other hand, also inapplicable for the occasion that is not suitable for online and impossible use calibrated reference.Under the hot environment of forging process for fuel workshop, the method for calibrating block, scaling board and stickup target spot all can not be applied.Therefore, traditional cameras scaling method can not meet the requirement that the online dimensional parameters of large forgings is measured.In addition, although self-calibrating method does not utilize any demarcation thing, the constraint that only utilizes camera intrinsic parameter self to exist, just can estimate camera intrinsic parameter according to the corresponding relation of inter-pictures point.Comparatively flexible in this class methods operation, but precision is not too high, and robustness is not enough.

By adopting projector projects target to address the above problem, the characteristic pattern of projection in theory edge should be step variation, but in fact due to diffusional effect, pattern edge is gradual change trend, and edge can move to black background one lateral deviation.The projector projects circular feature spot array of take is example, the center of circular light spot is the unique point for demarcating, because each hot spot can produce diffusion in various degree towards periphery, therefore be difficult to the accurate center that adopts centroid method to obtain round spot according to the image after binaryzation, utilize related algorithm to carry out circular feature Boundary Extraction and carry out circle (or oval) matching to obtain also not a duck soup of high-precision Yuan Ban center.In like manner, utilize the striation combination pattern that projector projection is general, extract the center of striation as characteristic curve, precision is also difficult to guarantee.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, for on-the-spot in forging, traditional scaling method exists precision low, non real-time, even can not apply and self-calibrating method exists precision not too high, the problems such as robustness deficiency, invent a kind of large-field shooting machine scaling method based on projection Gaussian network pattern, utilize in Gaussian network pattern horizontal, the gray scale of vertical striation on Width is the characteristic of Gaussian distribution, by fitted Gaussian curve, can obtain accurately the image coordinate of the point on light stripe centric line, and then simulate horizontal stroke, the center line equation of vertical striation, horizontal, the intersection point of vertical light stripe centric line is feature point for calibration, according to the image coordinate that the feature point for calibration providing in the image of the Gaussian network pattern obtaining is provided, substep obtain video camera in, outer parameter.

The technical scheme that the present invention takes is a kind of camera marking method based on projection Gaussian network pattern, it is characterized in that, utilize in Gaussian network pattern horizontal, the gray scale of vertical striation on Width is the characteristic of Gaussian distribution, by fitted Gaussian curve, can obtain accurately the image coordinate of the point on light stripe centric line, and then simulate horizontal stroke, the center line equation of vertical striation, horizontal, the intersection point of vertical light stripe centric line is feature point for calibration, according to the image coordinate that the feature point for calibration providing in the image of the Gaussian network pattern obtaining is provided, substep obtain video camera in, outer parameter, concrete steps are as follows:

Step 1: build camera calibration systems.The four-dimensional automatically controlled platform 2a in left side, the four-dimensional automatically controlled platform 2b in right side and projector 3 are arranged on the table top of platform 1, left side camera 4a are fixed on to the four-dimensional automatically controlled platform 2a in left side upper, right side video camera 4b is fixed on the four-dimensional automatically controlled platform 2b in right side.

Step 2: projection Gaussian network pattern, take and obtain intersecting point coordinate.By projector 3, to projection on the flat board of polishing in factory building or metope 5, by many parallel horizontal striation vertical striations parallel with many, form Gaussian network pattern 6, the gray scale of each striation on Width is all Gaussian distribution, wherein horizontal, vertical striation intersection point A _i,jfor feature point for calibration, the numbering that i is horizontal striation, according to order from top to bottom, j is for the numbering of vertical striation, according to order from left to right.Due to the light intensity stack of horizontal, vertical striation intersection point place, left side camera 4a is carried out after binary conversion treatment to the speck at remaining grid intersection point place only in the image of acquisition, i.e. isolated UNICOM region one by one with the image that video camera 4b shooting in right side obtains.Utilize centroid method can obtain the center-of-mass coordinate (u0 in UNICOM region _i,j, v0 _i,j), as unique point A _i,jrough position.To take this rough position as the center of circle, and the border circular areas that the Δ pixel of usining is radius is as hunting zone, then at [u0 _i,j-Δ, u0 _i,j+ Δ] in scope every Δ/n broad ways search horizontal striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on horizontal light stripe centric line, therefore can obtain the some P on 2n+1 center line _{i, j, s}, subscript s is 1,2,3 ..., 2n+1, and then simulate straight line l _{h, i, j}.Similarly, at [v0 _i,j-Δ, v0 _i,j+ Δ] in scope every Δ/n broad ways search vertical striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on vertical light stripe centric line, can obtain the some Q on 2n+1 center line _{i, j, t}, subscript t is 1,2,3 ..., 2n+1, and then simulate straight line l _{v, i, j}.Finally, the intersection point by asking for two intersecting straight lines in same hunting zone is as feature point for calibration A _i,j, its coordinate is (u _i,j, v _i,j).

Step 3: the rough coordinates of obtaining principal point.Utilize left side camera 4a or right side video camera 4b under two kinds of different focal, to take the Gaussian network pattern 6 of same projection, unique point A _i,jimage coordinate be respectively (u1 _i,j, v1 _i,j) and (u2 _i,j, v2 _i,j), principal point coordinate is (u ₀, v ₀), have:

$\frac{{u2}_{i,j}-u_0}{{u1}_{i,j}-u_0}=\frac{{v2}_{i,j}-v_0}{{v1}_{i,j}{-v}_0}---\left(2\right)$

Can utilize above formula to obtain the coordinate (u of the rough position of principal point ₀, v ₀).

Step 4: the principal point coordinate of asking for distortion factor and optimization.According to distortion model, can release the intersection point A of actual photographed _i,jcoordinate p _i,j=(u _i,j, v _i,j, 1) ^twith desirable intersecting point coordinate q _i,j=(u' _i,j, v' _i,j, 1) ^ttransformational relation as follows:

Wherein,

k ₁with k ₂for coefficient of radial distortion, p ₁with p ₂for tangential distortion coefficient.

In addition, horizontal, the vertical the same number of lattice of striation of take is example, and intersection point adds up to num, on so every row, has

individual intersection point, linear according to the guarantor of straight line, i.e. the character of the some conllinear on same striation, in conjunction with the necessary and sufficient condition of three point on a straight line, can list optimization aim function as follows:

$\min \underset{i=1}{\overset{\sqrt{\mathrm{num}}}{\mathrm{\Σ}}}\left(\underset{j=\sqrt{\mathrm{num}}(i-1)+1}{\overset{\sqrt{\mathrm{num}}(i-1)+\sqrt{\mathrm{num}}-2}{\mathrm{\Σ}}}\right|q_{i,j+1}^T{\left[q_{i,j}\right]}_{\×}{q}_{i,j+2}\left|\right)---\left(4\right)$

Wherein,

be 3 A _i,j, A _{i, j+1}, A _{i, j+2}the necessary and sufficient condition of conllinear.[q _{i, j}] _*represent q _i,jantisymmetric matrix, that is:

${\left[q_{i,j}\right]}_{\×}=\left[\begin{array}{ccc}0& -1& {v^{\′}}_{i,j}\\ 1& 0& -{u^{\′}}_{i,j}\\ -{v^{\′}}_{i,j}& {u^{\′}}_{i,j}& 0\end{array}\right]---\left(5\right)$

By Levenberg-Marquardt nonlinear optimization algorithm, be optimized, make the value minimum of the objective function of formula (4), can obtain distortion factor k ₁, k ₂, p ₁with p ₂and the principal point coordinate (u' after optimizing ₀, v' ₀).Then utilize formula (3) that all intersecting point coordinates are modified to desirable coordinate.

Step 5: ask for remaining inner parameter of video camera.Utilize revised desirable intersection point as unique point, adopt active vision method, utilize the four-dimensional automatically controlled platform 2a in left side to drive left side camera 4a to do two groups of orthogonal motions, at three whole story of every group of orthogonal motion, on position, take respectively the image of the Gaussian network pattern 6 of a projection, final left side camera 4a takes and obtains 6 images.

Parallel lines and plane at infinity intersect at same infinity point, i.e. hidden disappearing a little.And one group of orthogonal motion contains twice translation, a translation motion the whole story position photographs two width images on the line of corresponding intersection point be one group of space parallel line, and twice translation be orthogonal, so we can obtain the hidden of one group of quadrature and disappear a little to e _i1(u _i1, v _i1) and e _i2(u _i2, v _i2), i=1 wherein, 2, represent the order of orthogonal motion, and have Oe _i1oe _i2=0, the principal point that wherein O is video camera.Utilize that two groups of quadratures are hidden to disappear a little rightly, can solve respectively by solving following system of equations the scale factor α in the Intrinsic Matrix K of left side camera 4a _xwith α _y:

$\left\{\begin{array}{c}(u_{11}-{u^{\&prime;}}_0)(u_{12}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{11}-{v^{\&prime;}}_0)(v_{12}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000396435270000011.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+1=0\\ (u_{21}-{u^{\&prime;}}_0)(u_{22}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{21}-{v^{\&prime;}}_0)(v_{22}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000396435270000011.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+1=0\end{array}\right.---\left(6\right)$

Similarly, can obtain the scale factor α in the Intrinsic Matrix K of right side video camera 4b _xwith α _y.

Step 6: the external parameter that obtains video camera.Left side camera 4a and right side video camera 4b take the Gaussian network pattern 6 of same projection, world coordinate system is based upon on the camera coordinate system of left side camera 4a, utilizes left and right video camera 4a, the revised match point of 4b photographic images to calculate fundamental matrix F.Utilize intrinsic parameter and the fundamental matrix asked for can in the situation that differing a scale factor s, calculate essential matrix E.After decomposing essential matrix E, can in the situation that differing a scale factor, determine external parameter (rotation matrix R' and translation vector t').

Utilize the parallel Gauss's striation of projector 3 projections to physical length L ₀on the gauge block of accurately measuring, utilize the Gaussian characteristics of striation to simulate sub-pix light stripe centric line, utilize the point of gray scale cataclysm as the frontier point of gauge block, according to the length L of the above-mentioned inside and outside Reconstruction gauge block of asking for ' ₀, can obtain scale factor and be: s=L ₀/ L' ₀.Therefore, can obtain the external parameter (rotation matrix R=R' and translation vector t=s*t') of video camera reality.So far, completed the calibration process of video camera.

The invention has the beneficial effects as follows that the intersection point of the Gaussian network pattern that adopts projector projection, as feature point for calibration, avoided the use of calibrating block, scaling board and binding mark point, be convenient to realize the real-time calibration that carries out video camera under the complex environments such as the scene of forging.According to gray scale on striation Width, be Gaussian distribution characteristic and can determine accurately the positional information of feature point for calibration, there is high robustness, substep is demarcated can obtain high-precision camera parameters, coupling problem when the method can be avoided all camera parameters to solve simultaneously simultaneously.

Accompanying drawing explanation

Fig. 1 is calibration system schematic diagram of the present invention.Wherein: 1-shock insulation platform, the four-dimensional automatically controlled platform in 2a-left side, the four-dimensional automatically controlled platform in 2b-right side, 3-projector, 4a-left side camera, 4b-right side video camera, the flat board of 5-polishing or metope, 6-Gaussian network pattern.

Fig. 2 is that the present invention is taken the image of the lattice obtaining by video camera.

Fig. 3 is that the present invention carries out binary conversion treatment to the image of lattice and obtains the rough position of intersection point.

Fig. 4 is that Gauss light strip array reconstruction gauge block size of the present invention is asked for scale factor.

Embodiment

Below in conjunction with accompanying drawing and technical scheme, further describe the specific embodiment of the present invention.

Camera calibration adopts classical pinhole imaging system model conventionally, and the expression formula of this model is as follows:

Wherein, (X _w, Y _w, Z _w, 1) ^tfor the homogeneous coordinates of spatial point in world coordinate system, (u, v, 1) ^tfor corresponding image picture point pixel coordinate is o ₀homogeneous coordinates in uv, α _x=f/dx is o ₀scale factor in uv coordinate system on u axle, α _y=f/dy is o ₀scale factor in uv coordinate system on v axle, f is camera lens focal length, dx and dy are respectively the horizontal stroke of pixel, vertical physical size, (u ₀, v ₀) be principal point coordinate, ρ _cfor scale-up factor, K is intrinsic parameters of the camera matrix, the external parameter matrix that [R|t] is video camera, and wherein, R is rotation matrix, t is translation vector.

Intrinsic parameters of the camera comprises principal point coordinate (u ₀, v ₀), scale factor α _x, α _y, coefficient of radial distortion k ₁, k ₂with tangential distortion coefficient p ₁, p ₂.Video camera external parameter be camera coordinate system with respect to the orientation of world coordinate system, comprise rotation matrix R and translation vector t.

Step 1: build camera calibration systems.The four-dimensional automatically controlled platform 2a in left side, the four-dimensional automatically controlled platform 2b in right side and projector 3 are arranged on the table top of platform 1, left side camera 4a is fixed on the four-dimensional automatically controlled platform 2a in left side, right side video camera 4b is fixed on to the four-dimensional automatically controlled platform 2b in right side upper, as shown in Figure 1.

Step 2: projection Gaussian network pattern, take and obtain intersecting point coordinate.By projector 3 to projection Gaussian network pattern 6 on the flat board of polishing in factory building or metope 5, Gaussian network pattern 6 is comprised of many parallel horizontal striation vertical striations parallel with many, the gray scale of each striation is all Gaussian distribution on Width, wherein horizontal, vertical striation intersection point A _i,jfor feature point for calibration, the numbering that i is horizontal striation, according to order from top to bottom, j is for the numbering of vertical striation, according to order from left to right.The image of the projection Gaussian network pattern being obtained by left side camera 4a or right side video camera 4b shooting as shown in Figure 2.Due to the light intensity stack of horizontal, vertical striation intersection point place, left side camera 4a is carried out after binary conversion treatment with the image that video camera 4b shooting in right side obtains, the speck at remaining grid intersection point place only in the image of acquisition, i.e. isolated UNICOM region one by one, as shown in Figure 3.Utilize centroid method can obtain the center-of-mass coordinate (u0 in UNICOM region _i,j, v0 _i,j), as unique point A _i,jrough position.To take this rough position as the center of circle, and the border circular areas that the Δ pixel of usining is radius is as hunting zone, then at [u0 _i,j-Δ, u0 _i,j+ Δ] in scope every Δ/n broad ways search horizontal striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on horizontal light stripe centric line, therefore can obtain the some P on 2n+1 center line _{i, j, s}, subscript s is 1,2,3 ..., 2n+1, and then simulate straight line l _{h, i, j}.Similarly, at [v0 _i,j-Δ, v0 _i,j+ Δ] in scope every Δ/n broad ways search vertical striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on vertical light stripe centric line, can obtain the some Q on 2n+1 center line _{i, j, t}, subscript t is 1,2,3 ..., 2n+1, and then simulate straight line l _{v, i, j}.Finally, the intersection point by asking for two intersecting straight lines in same hunting zone is as feature point for calibration A _i,j, its coordinate is (u _i,j, v _i,j).

Step 3: the rough coordinates of obtaining principal point.Utilize varifocal method to ask for principal point, left side camera 4a or right side video camera 4b take same projection Gaussian network pattern 6, unique point A under two kinds of different focal _i,jimage coordinate be respectively (u1 _i,j, v1 _i,j) and (u2 _i,j, v2 _i,j), principal point coordinate is (u ₀, v ₀), have:

$\frac{{u2}_{i,j}-u_0}{{u1}_{i,j}-u_0}=\frac{{v2}_{i,j}-v_0}{{v1}_{i,j}-v_0}---\left(2\right)$

For the time being lens zoom center is considered as to principal point, can utilizes above formula to obtain the coordinate (u of the rough position of principal point ₀, v ₀).

Step 4: the principal point coordinate of asking for distortion factor and optimization.According to distortion model, can release the intersection point A of actual photographed _i,jcoordinate p _i,j=(u _i,j, v _i,j, 1) ^twith desirable intersecting point coordinate q _i,j=(u' _i,j, v' _i,j, 1) ^ttransformational relation as follows:

Wherein, k ₁with k ₂for coefficient of radial distortion, p ₁with p ₂for tangential distortion coefficient.

In addition, horizontal, the vertical the same number of lattice of striation of take is example, and intersection point adds up to num, on so every row, has

individual intersection point, linear according to the guarantor of straight line, i.e. the character of the some conllinear on same striation, in conjunction with the necessary and sufficient condition of three point on a straight line, can list optimization aim function as follows:

$\min \underset{i=1}{\overset{\sqrt{\mathrm{num}}}{\mathrm{\&Sigma;}}}\left(\underset{j=\sqrt{\mathrm{num}}(i-1)+1}{\overset{\sqrt{\mathrm{num}}(i-1)+\sqrt{\mathrm{num}}-2}{\mathrm{\&Sigma;}}}\right|q_{i,j+1}^T{\left[q_{i,j}\right]}_{\&times;}{q}_{i,j+2}\left|\right)---\left(4\right)$

Wherein,

be 3 A _i,j, A _{i, j+1}, A _{i, j+2}the necessary and sufficient condition of conllinear.[q _{i, j}] _*represent q _i,jantisymmetric matrix, that is:

${\left[q_{i,j}\right]}_{\&times;}=\left[\begin{array}{ccc}0& -1& {v^{\&prime;}}_{i,j}\\ 1& 0& -{u^{\&prime;}}_{i,j}\\ -{v^{\&prime;}}_{i,j}& {u^{\&prime;}}_{i,j}& 0\end{array}\right]---\left(5\right)$

By Levenberg-Marquardt nonlinear optimization algorithm, be optimized, make the value minimum of the objective function of formula (4), can obtain distortion factor k ₁, k ₂, p ₁with p ₂and the principal point coordinate (u' after optimizing ₀, v' ₀).Then utilize formula (3) that all intersecting point coordinates are modified to desirable coordinate.

Step 5: ask for remaining inner parameter of video camera.Utilize revised desirable intersection point as unique point, adopt active vision method, utilize the four-dimensional automatically controlled platform 2a in left side to drive left side camera 4a to do two groups of orthogonal motions, at three whole story of every group of orthogonal motion, on position, take respectively the image of a projection Gaussian network pattern 6, final left side camera 4a takes and obtains 6 images.Idiographic flow is as follows: (1) regulates the four-dimensional automatically controlled platform 2a in left side to suitable position, starts first group of orthogonal motion, takes respectively the image of a projection Gaussian network pattern 6 at three whole story of orthogonal motion on position; (2) utilize the four-dimensional automatically controlled platform 2a in left side to make left side camera 4a overlook certain angle, start second group of orthogonal motion, at three whole story of orthogonal motion, on position, take respectively the image of a projection Gaussian network pattern 6.

On straight line, the image of infinity point is called the hidden of this straight line and disappears a little.Because parallel lines and plane at infinity intersect at same infinity point, i.e. hidden disappearing a little.One group of orthogonal motion contains twice translation, a translation motion the whole story position photographs two width images on the line of corresponding intersection point be one group of space parallel line, and twice translation be orthogonal, so we can obtain the hidden of one group of quadrature and disappear a little to e _i1(u _i1, v _i1) and e _i2(u _i2, v _i2), subscript i=1,2, represent the order of orthogonal motion, and have Oe _i1oe _i2=0, the principal point that wherein O is video camera.Utilize that two groups of quadratures are hidden to disappear a little rightly, can solve respectively by solving following system of equations the scale factor α in the Intrinsic Matrix K of left side camera 4a _xwith α _y:

$\left\{\begin{array}{c}(u_{11}-{u^{\&prime;}}_0)(u_{12}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{11}-{v^{\&prime;}}_0)(v_{12}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000396435270000011.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+1=0\\ (u_{21}-{u^{\&prime;}}_0)(u_{22}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{21}-{v^{\&prime;}}_0)(v_{22}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000396435270000011.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+1=0\end{array}\right.---\left(6\right)$

Similarly, can obtain the scale factor α in the Intrinsic Matrix K of right side video camera 4b _xwith α _y.

Step 6: obtain external parameter.Left side camera 4a and right side video camera 4b take same projection Gaussian network pattern 6, world coordinate system are based upon on the camera coordinate system of left side camera 4a, utilize left and right video camera 4a, the revised match point of 4b photographic images to calculate fundamental matrix F.Utilize intrinsic parameter and fundamental matrix can in the situation that differing a scale factor s, calculate essential matrix E.After decomposing essential matrix E, can in the situation that differing a scale factor, determine external parameter (rotation matrix R' and translation vector t').

As shown in Figure 4, utilize the parallel Gauss's striation of projector 3 projections to physical length L ₀on the gauge block of accurately measuring, utilize the Gaussian characteristics of striation to simulate sub-pix light stripe centric line, utilize the point of gray scale cataclysm as the frontier point of gauge block, according to the length L of the above-mentioned inside and outside Reconstruction gauge block of asking for ' ₀, can obtain scale factor and be: s=L ₀/ L' ₀.Therefore, can obtain the external parameter (rotation matrix R=R' and translation vector t=s*t') of video camera reality.So far, completed the calibration process of video camera.

The camera marking method that the present invention proposes has good real-time, robustness and higher stated accuracy, can be used under the complex environments such as the scene of forging large-field shooting machine is carried out to on-line proving.

Claims (1)

1. the camera marking method based on projection Gaussian network pattern, it is characterized in that, camera marking method utilizes in Gaussian network pattern horizontal, the gray scale of vertical striation on Width is the characteristic of Gaussian distribution, by fitted Gaussian curve, can obtain accurately the image coordinate of the point on light stripe centric line, and then simulate horizontal stroke, the center line equation of vertical striation, horizontal, the intersection point of vertical light stripe centric line is feature point for calibration, according to the image coordinate that the feature point for calibration providing in the image of the Gaussian network pattern obtaining is provided, substep obtain video camera in, outer parameter, concrete steps are as follows:

Step 1: build camera calibration systems; The four-dimensional automatically controlled platform (2a) in left side, the four-dimensional automatically controlled platform (2b) in right side and projector (3) are arranged on the table top of platform (1), left side camera (4a) is fixed on to the four-dimensional automatically controlled platform in left side (2a) upper, right side video camera (4b) is fixed on the four-dimensional automatically controlled platform in right side (2b);

Step 2: projection Gaussian network pattern, take and obtain intersecting point coordinate; By projector (3), to flat board or the upper projection of metope (5) of polishing in factory building, by many parallel horizontal striation vertical striations parallel with many, form Gaussian network pattern (6), the gray scale of each striation on Width is all Gaussian distribution, wherein horizontal, vertical striation intersection point A _i,jfor feature point for calibration, the numbering that i is horizontal striation, according to order from top to bottom, j is for the numbering of vertical striation, according to order from left to right; Due to the light intensity stack of horizontal, vertical striation intersection point place, left side camera (4a) and right side video camera (4b) are taken to the image obtaining and carry out after binary conversion treatment, the speck at remaining grid intersection point place only in the image of acquisition, i.e. isolated UNICOM region one by one; Utilize centroid method can obtain the center-of-mass coordinate (u0 in UNICOM region _i,j, v0 _i,j), as unique point A _i,jrough position; To take this rough position as the center of circle, and the border circular areas that the Δ pixel of usining is radius is as hunting zone, then at [u0 _i,j-Δ, u0 _i,j+ Δ] in scope every Δ/n broad ways search horizontal striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on horizontal light stripe centric line, therefore can obtain the some P on 2n+1 center line _{i, j, s}, subscript s is 1,2,3 ..., 2n+1, and then simulate straight line l _{h, i, j}; Similarly, at [v0 _i,j-Δ, v0 _i,j+ Δ] in scope every Δ/n broad ways search vertical striation once, according to Gaussian distribution characteristic, carry out matching, the point using Gaussian distribution peak point on vertical light stripe centric line, can obtain the some Q on 2n+1 center line _{i, j, t}, subscript t is 1,2,3 ..., 2n+1, and then simulate straight line l _{v, i, j}; Finally, the intersection point by asking for two intersecting straight lines in same hunting zone is as feature point for calibration A _i,j, its coordinate is (u _i,j, v _i,j);

Step 3: the rough coordinates of obtaining principal point; Utilize left side camera (4a) or right side video camera (4b) under two kinds of different focal, to take the Gaussian network pattern (6) of same projection, unique point A _i,jimage coordinate be respectively (u1 _i,j, v1 _i,j) and (u2 _i,j, v2 _i,j), principal point coordinate is (u ₀, v ₀), have:

$\frac{{u2}_{i,j}-u_0}{{u1}_{i,j}-u_0}=\frac{{v2}_{i,j}-v_0}{{v1}_{i,j}-v_0}---\left(2\right)$

Can utilize above formula to obtain the coordinate (u of the rough position of principal point ₀, v ₀);

Step 4: the principal point coordinate of asking for distortion factor and optimization; According to distortion model, can release the intersection point A of actual photographed _i,jcoordinate p _i,j=(u _i,j, v _i,j, 1) ^twith desirable intersecting point coordinate q _i,j=(u' _i,j, v' _i,j, 1) ^ttransformational relation as follows:

Wherein,

k ₁with k ₂for coefficient of radial distortion, p ₁with p ₂for tangential distortion coefficient;

In addition, horizontal, the vertical the same number of lattice of striation of take is example, and intersection point adds up to num, on so every row, has individual intersection point, linear according to the guarantor of straight line, i.e. the character of the some conllinear on same striation, in conjunction with the necessary and sufficient condition of three point on a straight line, can list optimization aim function as follows:

$\min \underset{i=1}{\overset{\sqrt{\mathrm{num}}}{\mathrm{\&Sigma;}}}\left(\underset{j=\sqrt{\mathrm{num}}(i-1)+1}{\overset{\sqrt{\mathrm{num}}(i-1)+\sqrt{\mathrm{num}}-2}{\mathrm{\&Sigma;}}}\right|q_{i,j+1}^T{\left[q_{i,j}\right]}_{\&times;}{q}_{i,j+2}\left|\right)---\left(4\right)$

Wherein,

be 3 A _i,j, A _{i, j+1}, A _{i, j+2}the necessary and sufficient condition of conllinear; [q _{i, j}] _*represent q _i,jantisymmetric matrix, that is:

${\left[q_{i,j}\right]}_{\&times;}=\left[\begin{array}{ccc}0& -1& {v^{\&prime;}}_{i,j}\\ 1& 0& -{u^{\&prime;}}_{i,j}\\ -{v^{\&prime;}}_{i,j}& {u^{\&prime;}}_{i,j}& 0\end{array}\right]---\left(5\right)$

By Levenberg-Marquardt nonlinear optimization algorithm, be optimized, make the value minimum of the objective function of formula (4), can obtain distortion factor k ₁, k ₂, p ₁with p ₂and the principal point coordinate (u' after optimizing ₀, v' ₀); Then utilize formula (3) that all intersecting point coordinates are modified to desirable coordinate;

Step 5: ask for remaining inner parameter of video camera; Utilize revised desirable intersection point as unique point, adopt active vision method, utilize the four-dimensional automatically controlled platform in left side (2a) to drive left side camera (4a) to do two groups of orthogonal motions, at three whole story of every group of orthogonal motion, on position, take respectively the image of the Gaussian network pattern 6 of a projection, final left side camera (4a) is taken and is obtained 6 images;

Parallel lines and plane at infinity intersect at same infinity point, i.e. hidden disappearing a little; And one group of orthogonal motion contains twice translation, a translation motion the whole story position photographs two width images on the line of corresponding intersection point be one group of space parallel line, and twice translation be orthogonal, so we can obtain the hidden of one group of quadrature and disappear a little to e _i1(u _i1, v _i1) and e _i2(u _i2, v _i2), subscript i=1,2, represent the order of orthogonal motion, and have Oe _i1oe _i2=0, O=(u' wherein ₀, v' ₀) be the principal point of video camera; Utilize that two groups of quadratures are hidden to disappear a little rightly, can solve respectively by solving following system of equations the scale factor α in the Intrinsic Matrix K of left side camera (4a) _xwith α _y:

$\left\{\begin{array}{c}(u_{11}-{u^{\&prime;}}_0)(u_{12}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{11}-{v^{\&prime;}}_0)(v_{12}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_y^2+1=0\\ (u_{21}-{u^{\&prime;}}_0)(u_{22}-{u^{\&prime;}}_0)/{\mathrm{\&alpha;}}_x^2+(v_{21}-{v^{\&prime;}}_0)(v_{22}-{v^{\&prime;}}_0)/{\mathrm{\&alpha;}}_y^2+1=0\end{array}\right.---\left(6\right)$

Equally, can obtain the scale factor α in the Intrinsic Matrix K of right side video camera (4b) _xwith α _y;

Step 6: the external parameter that obtains video camera; Left side camera (4a) is taken the Gaussian network pattern (6) of same projection with right side video camera (4b), world coordinate system is based upon on the camera coordinate system of left side camera (4a), utilizes left and right video camera (4a) and (4b) the revised match point of photographic images to calculate fundamental matrix F; Utilize intrinsic parameter and the fundamental matrix asked for can in the situation that differing a scale factor s, calculate essential matrix E; After decomposing essential matrix E, can in the situation that differing a scale factor, determine external parameter (rotation matrix R' and translation vector t');

Utilize the parallel Gauss's striation of projector (3) projection to physical length L ₀on the gauge block of accurately measuring, utilize the Gaussian characteristics of striation to simulate sub-pix light stripe centric line, utilize the point of gray scale cataclysm as the frontier point of gauge block, according to the length L of the above-mentioned inside and outside Reconstruction gauge block of asking for ' ₀, can obtain scale factor and be: s=L ₀/ L' ₀; Therefore, can obtain the external parameter (rotation matrix R=R' and translation vector t=s*t') of video camera reality; So far, completed the calibration process of video camera.

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