CN104021543A - Lens distortion self-correction method based on planar chessboard template - Google Patents

Abstract

The invention relates to a lens distortion self-correction method based on a planar chessboard template. The method comprises the steps of establishing an image plane coordinate system and extracting image coordinates of index points from the planar template; establishing a constraint relation equation by utilizing the cross-ratio invariance contained in the index points in the same straight line in the planar template; establishing a constraint relation equation by utilizing geometric characteristics of the index points in the same straight line in the planar template; establishing a constraint relation equation by utilizing geometric characteristics of vanishing points of parallel straight lines in the planar template; and establishing an optimized objective function by combining the three constraint relation equations, carrying out overall least square optimization on all the extracted index points of the planar template, obtaining the coordinates of ideal index points which satisfy the geometrical constraints, and thus, completing distortion correction of the index points of the planar template. Compared with the prior art, the lens distortion self-correction method is high in correction precision, convenient and flexible.

Description

A kind of lens distortion automatic correcting method based on plane chessboard template

Technical field

The present invention relates to a kind of camera imaging bearing calibration, especially relate to a kind of lens distortion automatic correcting method based on plane chessboard template.

Background technology

Camera calibration is a very important job in photogrammetric, and its main task is to determine the mapping relations of camera two dimensional image plane and space three-dimensional scene.At present, because the monumented point quantity of plane chessboard template is more, monumented point easily extracts, and the camera calibration algorithm comparative maturity based on plane chessboard template, and therefore a lot of camera calibrations all can be selected plane template.

Meanwhile, due to the camera imaging distortion that the mismachining tolerance of the defect of camera lens spheric curvature when the imaging, CCD and camera lens rigging error etc. cause, the imaging process that makes desirable camera is impossible exist in actual measurement.When lens distortion be can not ignore, only with ideal model, demarcate the error obtaining often larger.

Therefore, when using plane template to carry out camera calibration, the monumented point extracting not is desirable picpointed coordinate, but the picpointed coordinate that contains distortion error.Picture point to these distortion is proofreaied and correct, and is conducive to improve stated accuracy.

At present, mostly the correction of the monumented point distortion that plane template is extracted is to set up camera distortion model, then in camera calibration process, proofreaies and correct.General this method adds some parameters in camera distortion model, then these distortion parameters and camera inside and outside parameter is optimized simultaneously and is finally obtained optimum solution, thereby obtaining more accurate camera distortion model.The parameter that the method is optimized due to needs is more, causes the speed of calibration optimization program slower.Owing to having increased some parameters, in optimizing process, between parameter, easily there is coupling phenomenon simultaneously, cause optimizing precision not high.And this distortion correction relies on camera imaging model, trimming process is complicated, and correcting image generally needs plurality of pictures, and the dirigibility of therefore proofreading and correct is not high yet.

The distortion correction of the plane template also having is the geometric properties that utilizes the upper monumented point of plane template, such as the rectilinearity of monumented point, cross ratio invariability etc.General these bearing calibrations, are also to take the imaging model of camera as basis, utilize these geometrical properties to join in computation process as new restriction relation, to improve stated accuracy, so that correcting distorted.This bearing calibration still needs to take several pictures, and the dirigibility of demarcation is still not high.

The above-mentioned distortion to plane checkerboard pattern is demarcated, and is all the imaging model based on camera substantially, utilizes at most the tessellated geometric properties of a small amount of plane to help solve as additional constraint, and often process more complicated, needs multiple image.And these methods can not be can be regarded as distortion automatic correcting method, dirigibility is also more limited.

Summary of the invention

Object of the present invention is exactly to provide a kind of correction accuracy high, the convenient, flexible lens distortion automatic correcting method based on plane chessboard template in order to overcome the defect of above-mentioned prior art existence.

Object of the present invention can be achieved through the following technical solutions:

A lens distortion automatic correcting method based on plane chessboard template, comprises the following steps:

Step 1: set up plane of delineation coordinate system, extract the image coordinate of monumented point in plane template;

Step 2: utilize the cross ratio invariability that in plane template, the monumented point on same straight line contains to set up restriction relation equation;

Step 3: utilize the geometric properties of the monumented point on same straight line in plane template to set up restriction relation equation;

Step 4: the geometric properties that utilizes parallel lines in plane template to intersect at vanishing point is set up restriction relation equation;

Step 5: comprehensive above-mentioned three kinds of restriction relation establishing equation optimization aim functions, the all plane template monumented points that extract are carried out to total least squares optimization, acquisition meets the desirable monumented point coordinate of above-mentioned geometrical constraint, completes the distortion correction of plane template monumented point.

In described step 2, cross ratio invariability refers to:

If same adjacent 4 P point-blank in plane template _i, i=1,2,3,4, through camera model, in plane of delineation imaging, its ideal image point is designated as P _ui, put P ₁(x _w1, y _w1), P ₂(x _w2, y _w2), P ₃(x _w3, y _w3), P ₄(x _w4, y _w4) double ratio and its ideal image point P of 4 _u1(u ₁, v ₁), P _u2(u ₂, v ₂), P _u3(u ₃, v ₃), P _u4(u ₄, v ₄) double ratio equate, that is:

$\mathrm{CR}(P_1,P_2,P_3,P_4)=\frac{d_{13}{d}_{24}}{d_{14}{d}_{23}}=\frac{s_{13}{s}_{24}}{s_{14}{s}_{23}}=\mathrm{CR}(P_{u1},P_{u2},P_{u3},P_{u4})=\mathrm{cr}$

In formula:

$d_{\mathrm{ij}}=\sqrt{{(x_{\mathrm{wi}}-x_{\mathrm{wj}})}^3+{(y_{\mathrm{wi}}-y_{\mathrm{wj}})}^2},$ Wherein i=1 or 2, j=3 or 4;

$s_{\mathrm{ij}}=\sqrt{{(u_i-u_j)}^2+{(v_i-v_j)}^2},$ Wherein i=1 or 2, j=3 or 4;

Cr is a definite value.

In described step 3, the geometric properties of the monumented point on same straight line refers to: the straight line in space is still straight line in picture plane imaging after pin-hole model imaging, and m monumented point on the straight line l after imaging meets following system of equations:

$\left\{\begin{array}{c}{a}_l{u}_1+b_l{v}_1+c_l=0\\ a_l{u}_2+b_l{v}_2+c_l=0\\ a_l{u}_3+b_l{v}_3+c_l=0\\ .\\ .\\ .\\ a_l{u}_m+b_l{v}_m+c_l=0\end{array}\right.$

According to above-mentioned system of equations, solve straight line parameter a _l, b _l, c _l, wherein, (u _i, v _i) be the coordinate of monumented point, i=1,2 ..., m.

In described step 4, if the total n bar straight line of plane template straight line group in one direction, and this group straight line is designated as V (u at the vanishing point as in plane _p, v _p), there is following system of equations:

$\left\{\begin{array}{c}{a}_1{u}_p+b_1{v}_p+c_1=0\\ a_2{u}_p+b_2{v}_p+c_2=0\\ a_3{u}_p+b_2{v}_p+c_3=0\\ .\\ .\\ .\\ a_n{u}_p+b_n{v}_p+c_n=0\end{array}\right.$

Straight line parameter in system of equations is tried to achieve by step 3, utilizes least square method, finally solves to obtain the coordinate of vanishing point, wherein, and a _i, b _i, c _ithe straight line parameter of each straight line on plane template, i=1,2 ..., n, n is the straight line number on plane template.

In described step 5, the optimization aim function of comprehensive three kinds of restriction relation establishing equations is:

$\begin{array}{c}F=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{m-3}{\mathrm{\Σ}}}\mathrm{CR}(P_{l,\mathrm{dk}},P_{l,\mathrm{dk}+1},P_{l,\mathrm{dk}+2},P_{l,\mathrm{dk}+3}){-\mathrm{cr})}^2+\\ \underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(a_l{u}_{\mathrm{di}}+b_l{v}_{\mathrm{di}}+c_l)}^2+\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{(a_l{u}_{p,d}+b_l{v}_{p,d}+c_l)}^2\end{array}$

Function F comprises three components altogether, first component CR (P _{l, dk}, P _{l, dk+1}, P _{l, dk+2}, P _{l, dk+3})-cr) ²represent the double ratio constraint of adjacent four monumented points on same straight line; Second component (a _lu _di+ b _lv _di+ c _l) ²represent the monumented point (u on same straight line _di, v _di) rectilinearity constraint; The 3rd component (a _lu _{p, d}+ b _lv _{p, d}+ c _l) ²represent two groups of parallel lines vanishing point (u _{p, d}, v _{p, d}) constraint that monumented point is applied; N is the straight line number on plane template, and m is the number that indicates point on every straight line.

Compared with prior art, the present invention has the following advantages:

(1) distortion self-correcting, convenient, flexible; Only need a pictures to proofread and correct the plane template monumented point extracting;

(2) correction accuracy is higher; The geometrical constraint (cross ratio invariability, rectilinearity and vanishing point) that makes full use of the monumented point of plane template is proofreaied and correct;

Therefore (3) do not rely on camera imaging model, can before camera calibration, proofread and correct carrying out, be conducive to like this improve the precision of camera calibration.

Accompanying drawing explanation

Fig. 1 is for demarcating plane template schematic diagram used;

Fig. 2 is the plane template image of actual photographed;

Fig. 3 is the vanishing point schematic diagram of plane template;

Fig. 4 is the width standard uncalibrated image adopting in embodiment 1;

The grid schematic diagram that Fig. 5 directly utilizes spline interpolation to obtain for the monumented point being extracted by Fig. 4;

The grid schematic diagram that Fig. 6 utilizes spline interpolation to obtain for the monumented point after the present invention proofreaies and correct;

Fig. 7 is the width standard uncalibrated image adopting in embodiment 2;

Fig. 8 is the boxed area enlarged diagram of Fig. 7;

The grid schematic diagram of Fig. 9 for the monumented point coordinate extracting in Fig. 7 is carried out to spline interpolation acquisition;

Figure 10 is the grid schematic diagram that after utilizing the inventive method to proofread and correct, monumented point interpolation generates.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment be take technical solution of the present invention and is implemented as prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Embodiment 1

The lens distortion automatic correcting method based on plane chessboard template in the present invention mainly comprises the following steps:

Step 1: set up plane of delineation coordinate system, extract the image coordinate of monumented point in plane template;

Step 2: utilize the cross ratio invariability that in plane template, the monumented point on same straight line contains to set up restriction relation equation;

Step 3: utilize the geometric properties of the monumented point on same straight line in plane template to set up restriction relation equation;

Step 4: the geometric properties that utilizes parallel lines in plane template to intersect at vanishing point is set up restriction relation equation;

Step 5: comprehensive above-mentioned three kinds of restriction relation establishing equation optimization aim functions, the all plane template monumented points that extract are carried out to total least squares optimization, acquisition meets the desirable monumented point coordinate of above-mentioned geometrical constraint, completes the distortion correction of plane template monumented point.

1, cross ratio invariability restriction relation equation

As Figure 1-Figure 2, if in plane template with adjacent 4 P point-blank _i(wherein i=1,2,3,4), through camera model in plane of delineation imaging, its ideal image point is designated as P _ui, the actual picture point containing distortion is designated as P _di, by known some P of cross ratio invariability of projective transformation ₁(x _w1, y _w1), P ₂(x _w2, y _w2), P ₃(x _w3, y _w3), P ₄(x _w4, y _w4) double ratio and its ideal image point P of 4 _u1(u ₁, v ₁), P _u2(u ₂, v ₂), P _u3(u ₃, v ₃), P _u4(u ₄, v ₄) double ratio equate.From cross ratio invariability:

$\mathrm{CR}(P_1,P_2,P_3,P_4)=\frac{d_{13}{d}_{24}}{d_{14}{d}_{23}}=\frac{s_{13}{s}_{24}}{s_{14}{s}_{23}}=\mathrm{CR}(P_{u1},P_{u2},P_{u3},P_{u4})---\left(1\right)$

In formula:

$d_{\mathrm{ij}}=\sqrt{{(x_{\mathrm{wi}}-x_{\mathrm{wj}})}^3+{(y_{\mathrm{wi}}-y_{\mathrm{wj}})}^2},$ Wherein i=1 or 2, j=3 or 4;

$s_{\mathrm{ij}}=\sqrt{{(u_i-u_j)}^2+{(v_i-v_j)}^2},$ Wherein i=1 or 2, j=3 or 4;

Cr is a definite value.

Because plane template is uniform gridiron pattern pattern, on the same straight line of Gu Qishang, the double ratio of adjacent 4 is certain value, i.e. cr=CR (P ₁, P ₂, P ₃, P ₄), and cr is a definite value.And the actual imaging of plane template point is containing distortion, therefore above-mentioned 4 corresponding actual imaging point P _d1(u _d1, v _d1), P _d2(u _d2, v _d2), P _d3(u _d3, v _d3), P _d4(u _d4, v _d4) double ratio can not meet formula (1) completely.But the monumented point coordinate of actual extracting of can take is initial value, usings cross ratio invariability as constraint, utilize non-linear search method to find ideal image point here.If total n bar straight line, has m point on plane template on every straight line, the target equation of nonlinear optimization is:

$F_{\mathrm{CR}}=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{m-3}{\mathrm{\Σ}}}(\mathrm{CR}(P_{l,\mathrm{dk}},P_{l,\mathrm{dk}+1},P_{l,\mathrm{dk}+2},P_{l,\mathrm{dk}+3})-\mathrm{cr})---\left(2\right)$

In formula:

P _{l, dk+i}---k+i monumented point on real image on l bar straight line, i=0,1,2,3.

Because the gridiron pattern pattern of plane template is to consist of orthogonal two groups of straight lines, this just means that each monumented point belongs to two orthogonal straight lines simultaneously.Therefore, F in above formula _cRneed on both direction, be optimized to minimum, guarantee monumented point fully meets cross ratio invariability constraint simultaneously.

2, the restriction relation equation of the geometric properties of the monumented point on same straight line

From the geometric invariance of projective transformation, the straight line in space is still straight line in picture plane imaging after pin-hole model imaging.Still suppose on plane template that, by n bar straight line, every straight line has m point, if wherein the straight line of straight line after linear model imaging represents with l, and P _ui(u _i, v _i) be ideal image point corresponding to a monumented point, P on straight line _uimeet

a _lu _i+v _lv _i+c _l＝0 (3)

In formula:

A _l, b _l, c _l---three parameters of straight line l.

Because projective transformation is one to one, therefore upper total m the point of straight line l can obtain system of equations:

$\left\{\begin{array}{c}{a}_l{u}_1+b_l{v}_1+c_l=0\\ a_l{u}_2+b_l{v}_2+c_l=0\\ a_l{u}_3+b_l{v}_3+c_l=0\\ .\\ .\\ .\\ a_l{u}_m+b_l{v}_m+c_l=0\end{array}\right.---\left(4\right)$

Utilize the principle of least square to obtain:

$\left[\begin{array}{ccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{v}_i& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{v}_i& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i& m\end{array}\right]\left[\begin{array}{c}{a}_l\\ b_l\\ c_l\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]---\left(5\right)$

In order to obtain a _lwith b _l, abbreviation above formula can obtain

$\left[\begin{array}{cc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i^2-\frac{{\left({\mathrm{\Σ}}_{i=1}^m{u}_i\right)}^2}{m}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{v}_i-\frac{\left({\mathrm{\Σ}}_{i=1}^m{u}_i\right)\left({\mathrm{\Σ}}_{i=1}^m{v}_i\right)}{m}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i{v}_i-\frac{\left({\mathrm{\Σ}}_{i=1}^m{u}_i\right)\left({\mathrm{\Σ}}_{i=1}^m{v}_i\right)}{m}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i^2-\frac{{\left({\mathrm{\Σ}}_{i=1}^m{v}_i\right)}^2}{m}\end{array}\right]\left[\begin{array}{c}{a}_l\\ b_l\end{array}\right]=\left[\begin{array}{c}0\\ 0\end{array}\right]---\left(6\right)$

By calculating the proper vector of above formula matrix of coefficients, just can solve a _lwith b _l.Obtaining a _lwith b _lafter just can utilize following formula to calculate c _l.

$c_l=-(a_l\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{u}_i+b_l\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i)/m---\left(7\right)$

For monumented point on straight line on plane template, we cannot directly obtain its ideal image point P _ui, and can only directly from image, extract the actual image point P that it becomes _di(u _di, v _di), and P _dicontain distortion, can not meet the constraint of formula (3) completely.Therefore, using formula (3) as constraint condition, the monumented point extracting is carried out to nonlinear optimization to find desirable monumented point coordinate here, the objective function of optimization is

$F_{\mathrm{LS}}=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(a_l{u}_{\mathrm{di}}+b_l{v}_{\mathrm{di}}+c_l)}^2---\left(8\right)$

Equally, because the gridiron pattern pattern of plane template is by orthogonal two groups of rectilinear(-al)s, in order to guarantee the rectilinearity of two straight lines at each monumented point place, need to guarantee F _lSon above-mentioned both direction, optimize simultaneously and reach minimum.

3, parallel lines intersects at the restriction relation equation of the geometric properties of vanishing point

In space, one group of parallel lines can meet at a bit as plane imaging after projective transformation, and this point is the vanishing point of these group parallel lines.Obviously, the plane template being comprised of two groups of parallel lines also has this character.

As shown in Figure 3, four limit points establishing plane template gridiron pattern pattern are designated as A, B, C, D, and they are designated as A ', B ', C ', D ' at the ideal image point as plane.From the characteristic of parallel lines vanishing point, with parallel straight line group will meet at their some V on as plane ₁, with parallel straight line group will meet at a V ₂, put V ₁with a V ₂be respectively the vanishing point of above two groups of straight lines.It should be noted is that vanishing point V ₁with V ₂line be plane template at the hachure that goes out as in plane.

If plane template straight line group in one direction has n bar straight line, and this group straight line is designated as V (u at the vanishing point as in plane _p, v _p),, for any straight line l in this group straight line, there is a V on l, so there is following restriction relation:

a _lu _p+b _lv _p+c _l＝0 (9)

In formula:

A _l, b _l, c _l---the parameter of straight line l, can utilize formula (6) and formula (7) to solve.

The computing method of vanishing point coordinate are discussed below,, there is following system of equations in the vanishing point V for n bar straight line:

$\left\{\begin{array}{c}{a}_1{u}_p+b_1{v}_p+c_1=0\\ a_2{u}_p+b_2{v}_p+c_2=0\\ a_3{u}_p+b_2{v}_p+c_3=0\\ .\\ .\\ .\\ a_n{u}_p+b_n{v}_p+c_n=0\end{array}\right.---\left(10\right)$

Utilize least square method to obtain

$\left[\begin{array}{cc}\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l^2& \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{b}_l\\ \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{b}_l& \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{b}_l^2\end{array}\right]\left[\begin{array}{c}{u}_p\\ v_p\end{array}\right]=\left[\begin{array}{c}-\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{c}_l\\ -\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{b}_l{c}_l\end{array}\right]---\left(11\right)$

Finally can solve to such an extent that the coordinate of vanishing point is:

$\left[\begin{array}{c}{u}_p\\ v_p\end{array}\right]={\left[\begin{array}{cc}\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l^2& \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{b}_l\\ \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{b}_l& \underset{l=1}{\overset{n}{\mathrm{\Σ}}}{b}_l^2\end{array}\right]}^{-1}\left[\begin{array}{c}-\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{a}_l{c}_l\\ -\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{b}_l{c}_l\end{array}\right]----\left(12\right)$

Owing to can only extracting the monumented point coordinate that contains distortion the image from plane template, at the vanishing point coordinate that utilizes formula (12) to calculate, be therefore also the constraint that can not meet formula (9) completely.Therefore, can utilize vanishing point constraint to carry out nonlinear optimization to the monumented point coordinate of actual extracting here, the target equation of optimization is:

$F_{\mathrm{VP}}=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{(a_l{u}_{p,d}+b_l{v}_{p,d}+c_l)}^2---\left(13\right)$

In formula:

(u _{p, d}, v _{p, d})---the vanishing point coordinate being estimated by actual tag point coordinate.

Two groups of parallel lines on plane template can produce respectively a vanishing point, therefore need to formula (13), be optimized respectively at these two vanishing point places, make F _vPreach minimum.

4, comprehensive above-mentioned three kinds of restriction relation establishing equation optimization aim functions

Up to the present discussed respectively and utilized cross ratio invariability, straight line and vanishing point constraint to proofread and correct logos point.In fact, desirable monumented point coordinate is to meet above-mentioned three kinds of constraints simultaneously, therefore, in order to make full use of the geometrical constraint of plane template, above-mentioned three kinds of constraints can be acted on to monumented point coordinate simultaneously, and the objective function of optimization is:

$\begin{array}{c}F=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{m-3}{\mathrm{\Σ}}}\mathrm{CR}(P_{l,\mathrm{dk}},P_{l,\mathrm{dk}+1},P_{l,\mathrm{dk}+2},P_{l,\mathrm{dk}+3}){-\mathrm{cr})}^2+\\ \underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(a_l{u}_{\mathrm{di}}+b_l{v}_{\mathrm{di}}+c_l)}^2+\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{(a_l{u}_{p,d}+b_l{v}_{p,d}+c_l)}^2\end{array}---\left(14\right)$

Function F in formula (14) comprises three components altogether, first component CR (P _{l, dk}, P _{l, dk+1}, P _{l, dk+2}, P _{l, dk+3})-cr) ²represent the double ratio constraint of adjacent four monumented points on same straight line; Second component (a _lu _di+ b _lv _di+ c _l) ²represent the rectilinearity constraint of the monumented point on same straight line; The 3rd component (a _lu _{p, d}+ b _lv _{p, d}+ c _l) ²represent the constraint that two groups of parallel lines vanishing points apply monumented point.When F is optimized, be to using the monumented point coordinate that extracts on image as initial value, above-mentioned three components are optimized simultaneously, guarantee like this monumented point coordinate maximizing that obtains after optimizing and meet above-mentioned three kinds of constraints.The a of every straight line after optimizing _l, b _l, c _lalso be improved with two vanishing point coordinates.

After utilizing formula (14) to be optimized monumented point coordinate, the monumented point coordinate obtaining can meet double ratio constraint, line constraint and vanishing point constraint substantially, thereby realizes the preliminary correction of the monumented point coordinate to extracting.

The standard uncalibrated image that obtains from OpenCV machine vision storehouse of take is below proofreaied and correct experiment as example.As shown in Figure 4, Fig. 4 is a width standard uncalibrated image, and referred to herein as image 1, the monumented point extracting on image 1 represents with "+"; Figure 5 shows that the grid that the monumented point that extracts directly utilizes spline interpolation to obtain from image 1; Figure 6 shows that the grid that the monumented point after correction utilizes spline interpolation to obtain.Comparison diagram 5 and Fig. 6 can find out, rectilinearity and the homogeneity of the grid after correction all make moderate progress.

Embodiment 2

Get again now a width standard uncalibrated image, referred to herein as image 2, image 2 is extracted to monumented point as shown in Figure 7.

Fig. 7 represents that image 2 is carried out to monumented point extracts schematic diagram, and the monumented point extracting uses "+" to be marked equally.Fig. 8 is the enlarged drawing of boxed area in Fig. 7, has as can be seen from Figure part monumented point coordinate to extract and has obvious mistake.Fig. 9 obtains monumented point grid for the monumented point coordinate that image 2 is extracted carries out spline interpolation, can find out that there is obvious uncontinuity in meshing region, and this causes because monumented point extracts unsuccessfully.Figure 10 is the grid that after utilizing method described in embodiment 1 to proofread and correct, monumented point interpolation generates.By relatively finding out, because monumented point extracts, the wrong uncontinuity causing disappears grid substantially, and homogeneity, the rectilinearity of grid are also improved.

Final experimental result shows: not only this bearing calibration has corrective action to the distortion of image, and extracts wrong certain corrective action that also has for the monumented point being caused by monumented point extraction algorithm defect.

Claims (5)

1. the lens distortion automatic correcting method based on plane chessboard template, is characterized in that, comprises the following steps:

Step 1: set up plane of delineation coordinate system, extract the image coordinate of monumented point in plane template;

Step 2: utilize the cross ratio invariability that in plane template, the monumented point on same straight line contains to set up restriction relation equation;

Step 3: utilize the geometric properties of the monumented point on same straight line in plane template to set up restriction relation equation;

Step 4: the geometric properties that utilizes parallel lines in plane template to intersect at vanishing point is set up restriction relation equation;

Step 5: comprehensive above-mentioned three kinds of restriction relation establishing equation optimization aim functions, the all plane template monumented points that extract are carried out to total least squares optimization, acquisition meets the desirable monumented point coordinate of above-mentioned geometrical constraint, completes the distortion correction of plane template monumented point.

2. a kind of lens distortion automatic correcting method based on plane chessboard template according to claim 1, is characterized in that, in described step 2, cross ratio invariability refers to:

If same adjacent 4 P point-blank in plane template _i, i=1,2,3,4, through camera model, in plane of delineation imaging, its ideal image point is designated as P _ui, put P ₁(x _w1, y _w1), P ₂(x _w2, y _w2), P ₃(x _w3, y _w3), P ₄(x _w4, y _w4) double ratio and its ideal image point P of 4 _u1(u ₁, v ₁), P _u2(u ₂, v ₂), P _u3(u ₃, v ₃), P _u4(u ₄, v ₄) double ratio equate, that is:

$\mathrm{CR}(P_1,P_2,P_3,P_4)=\frac{d_{13}{d}_{24}}{d_{14}{d}_{23}}=\frac{s_{13}{s}_{24}}{s_{14}{s}_{23}}=\mathrm{CR}(P_{u1},P_{u2},P_{u3},P_{u4})=\mathrm{cr}$

In formula:

$d_{\mathrm{ij}}=\sqrt{{(x_{\mathrm{wi}}-x_{\mathrm{wj}})}^3+{(y_{\mathrm{wi}}-y_{\mathrm{wj}})}^2},$ Wherein i=1 or 2, j=3 or 4;

$s_{\mathrm{ij}}=\sqrt{{(u_i-u_j)}^2+{(v_i-v_j)}^2},$ Wherein i=1 or 2, j=3 or 4;

Cr is a definite value.

3. a kind of lens distortion automatic correcting method based on plane chessboard template according to claim 2, it is characterized in that, in described step 3, the geometric properties of the monumented point on same straight line refers to: the straight line in space is still straight line in picture plane imaging after pin-hole model imaging, m monumented point on the straight line l after imaging, meets following system of equations:

$\left\{\begin{array}{c}{a}_l{u}_1+b_l{v}_1+c_l=0\\ a_l{u}_2+b_l{v}_2+c_l=0\\ a_l{u}_3+b_l{v}_3+c_l=0\\ .\\ .\\ .\\ a_l{u}_m+b_l{v}_m+c_l=0\end{array}\right.$

According to above-mentioned system of equations, solve straight line parameter a _l, b _l, c _l, wherein, (u _i, v _i) be the coordinate of monumented point, i=1,2 ..., m.

4. a kind of lens distortion automatic correcting method based on plane chessboard template according to claim 3, it is characterized in that, in described step 4, if the total n bar straight line of plane template straight line group in one direction, and this group straight line is designated as V (u at the vanishing point as in plane _p, v _p), there is following system of equations:

$\left\{\begin{array}{c}{a}_1{u}_p+b_1{v}_p+c_1=0\\ a_2{u}_p+b_2{v}_p+c_2=0\\ a_3{u}_p+b_2{v}_p+c_3=0\\ .\\ .\\ .\\ a_n{u}_p+b_n{v}_p+c_n=0\end{array}\right.$

Straight line parameter in system of equations is tried to achieve by step 3, utilizes least square method, finally solves to obtain the coordinate of vanishing point, wherein, and a _i, b _i, c _ithe straight line parameter of each straight line on plane template, i=1,2 ..., n, n is the straight line number on plane template.

5. a kind of lens distortion automatic correcting method based on plane chessboard template according to claim 4, is characterized in that, in described step 5, the optimization aim function of comprehensive three kinds of restriction relation establishing equations is:

$\begin{array}{c}F=\underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{m-3}{\mathrm{\Σ}}}\mathrm{CR}(P_{l,\mathrm{dk}},P_{l,\mathrm{dk}+1},P_{l,\mathrm{dk}+2},P_{l,\mathrm{dk}+3}){-\mathrm{cr})}^2+\\ \underset{l=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(a_l{u}_{\mathrm{di}}+b_l{v}_{\mathrm{di}}+c_l)}^2+\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{(a_l{u}_{p,d}+b_l{v}_{p,d}+c_l)}^2\end{array}$

Function F comprises three components altogether, first component CR (P _{l, dk}, P _{l, dk+1}, P _{l, dk+2}, P _{l, dk+3})-cr) ²represent the double ratio constraint of adjacent four monumented points on same straight line, P _{l, dk+i}for k+i monumented point on l bar straight line on real image, i=0,1,2,3; Second component (a _lu _di+ b _lv _di+ c _l) ²represent the monumented point (u on same straight line _di, v _di) rectilinearity constraint; The 3rd component (a _lu _{p, d}+ b _lv _{p, d}+ c _l) ²represent two groups of parallel lines vanishing point (u _{p, d}, v _{p, d}) constraint that monumented point is applied; N is the straight line number on plane template, and m is the number that indicates point on every straight line.