CN103364012A - Multi-area array aerial camera platform calibration method with constraint condition - Google Patents

Abstract

The invention discloses a multi-area array aerial camera platform calibration method with a constraint condition. The method includes: employing a data acquisition strategy of multiple cross flying camera station exposure to acquire multiple groups of sub-images with an adjacent virtual image overlap degree of more than 80%; making use of the control point of a ground calibration field to calculate a photographing centre distance of sub-cameras and a sub-camera line element; during aerotriangulation, conducting bundle block adjustment, according to the control point coordinate, the connection points among matched sub-images, and the external orientation element initial value, establishing a model through a collinearity equation, adopting the photographing centre distance of the sub-cameras as a given value, i.e. taking the sub-camera line element constant as the constraint condition, and taking platform calibration parameters as a whole to perform calculation to solve the angle elements in the external orientation elements of the sub-images. According to the calibration method, a lot of uniformly distributed connection points are matched, precision of the platform calibration parameters is improved through the constraint condition, higher stitching precision of the generated virtual images can be guaranteed, and the mapping precision can be higher.

Description

A kind of multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions

Technical field

The present invention relates to the photogrammetric measurement technical field, relate in particular to a kind of multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions.

Background technology

Aerial camera in the world wide successful Application decades, two ten years in the past, photogrammetric data acquisition means are gradually to the future development of digital camera.Consider that from present manufacturing process and economic factors two aspects single digital camera also can't replace traditional film aerial camera.In order to adopt more economical means to satisfy the aerophotographic demand of large film size, some companies have adopted many camera lenses combination camera.At present many camera lenses combination aerial digital camera products of main flow mainly comprise the large film size aerial digital camera of UltraCam series in the world, the large film size aerial digital camera of DMC, and domestic then have SWDC-4 and a large film size aerial digital camera of TOPDC-4.

Multiaspect battle array aerial surveying camera is based on this principle, by the mode of four digital cameras being installed at platform, obtains and has the splicing image of ground coverage on a large scale.The platform calibration of multiaspect battle array aerial surveying camera is exactly the process of Obtaining Accurate camera and virtual projection face relative position relation, can generate high-precision virtual image from sub-image according to platform calibration parameter.The platform calibration is the committed step from sub-image generating virtual image.Only have and accurately known the relative elements of exterior orientation of sub-image with virtual image, could according to the projective transformation formula, generate spliced virtual image.If there is larger error in platform calibration parameter, the culture point in the virtual image can not correctly reflect the spatial relation of this point so.

The platform calibration can accurately calculate sub-image to the relative elements of exterior orientation of virtual image, makes the virtual image that generates after the splicing be equivalent to a high-precision central projection image, has guaranteed the precision of image data source.

In the prior art, adopt the mode platform calibration of cross overlay region more: four sub-images that this platform calibration method can adopt the synchronization exposure, in the cruciform overlay region, mate tie point, carry out bundle adjustment.The method utilizes the tie point of overlay region to calculate, and take 1 camera wherein as benchmark, calculates the relative elements of exterior orientation between all the other 3 cameras and the virtual image.

The shortcoming of prior art: the mode platform calibration of cross overlay region requires in the overlay region of four sub-images the tie point that is evenly distributed is arranged, and quantity is no less than 30～50.Group image overlap district scope is less, or the overlay region image texture is poor, can't match ideal quantity and during the tie point that is evenly distributed, the method can't accurately calculate platform calibration parameter.

Summary of the invention

The object of the present invention is to provide a kind of multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions, to address the above problem.

In order to achieve the above object, technical scheme of the present invention is achieved in that

A kind of multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions comprises the steps:

Adopt that cross flying is a plurality of to be taken the photograph the station exposure and obtain adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carry out the tie point coupling of many sub-images;

Utilize the reference mark of ground calibration field, calculate photo centre's distance and the sub-camera line element of sub-camera;

When carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and the elements of exterior orientation initial value of each sub-image is set up model by collinearity equation, with the photo centre of sub-camera distance as given value, be about to sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation;

Wherein, each is taken the photograph and is provided with four cameras on the station, and each takes the photograph four sub-images of station synchronization exposure.

Compared with prior art, the advantage of the embodiment of the invention is:

The multiaspect battle array aerial surveying camera platform calibration method of a kind of Problem with Some Constrained Conditions provided by the invention, analyze its principle as can be known: at first, adopt and a plurality ofly take the photograph station exposure and obtain adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carry out the tie point coupling of many sub-images; Because taked the coupling between a large amount of sub-images, it is larger that four relatively traditional sub-images of the overlapping region that obvious many sub-images consist of consist of the cruciform overlay regions, degree of overlapping is higher, has enlarged like this matching range of tie point, and can match the tie point that is evenly distributed in a large number; Then utilize the reference mark of ground calibration field, calculate photo centre's distance and the sub-camera line element of sub-camera; Certainly, the data such as line element of obtaining between photo centre's distance and sub-camera are to realize first committed step of calibration method.Through above-mentioned pretreatment operation, can provide the data basis for setting up mathematical model;

Then, when carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and elements of exterior orientation initial value and the collinearity equation of each sub-image set up model, and photo centre's distance of sub-camera as given value, is about to described sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation; At this moment calculative unknown number is the setting angle of sub-camera, namely the angle element in the sub-image elements of exterior orientation (be about to sub-camera line element constant as constraint condition, find the solution angle element in the sub-image elements of exterior orientation).Like this, adjust each camera to virtual rotation angle according to 3 angle elements (correction) from camera, so that 4 sub-images are symmetrical to the anglec of rotation of virtual image, and then finish calibration operation, the elements of exterior orientation of each photo of finding the solution like this is more accurate, and calibration more meets the actual conditions that camera is settled.

Therefore, this platform calibration method is applicable to the multiaspect battle array aerial surveying camera of connecting method combination.Contrast traditional cross overlay region platform calibration method, group image overlap district scope is less, or the overlay region image texture is poor, can't match ideal quantity and during the tie point that is evenly distributed, can't accurately calculate the shortcoming of platform calibration parameter; The tie point that utilizes the method to match to be evenly distributed has in a large number also improved the precision of platform calibration parameter by constraint condition, ensures that the virtual image splicing precision that generates is higher, and plotting accuracy is higher.

Platform calibration method provided by the present invention its essence is, increased the line element restrictive condition for multiaspect battle array aerial surveying camera ad hoc structure on the basis that utilizes bundle adjustment, the platform calibration parameter of sub-camera is done as a whole resolving, thereby make platform calibration parameter more meet the actual placement situation of camera.

Description of drawings

The schematic flow sheet of the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that Fig. 1 provides for the embodiment of the invention;

The projection relation synoptic diagram of four sub-images and virtual image in the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that Fig. 2 provides for the embodiment of the invention;

The photo centre of four sub-images and virtual image photo centre concerns synoptic diagram in the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that Fig. 3 provides for the embodiment of the invention among Fig. 2;

The picture point error synoptic diagram that photo centre's vertical direction line element displacement causes in the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that Fig. 4 provides for the embodiment of the invention among Fig. 2;

The error synoptic diagram that sub-image angle element imbalance causes in the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that Fig. 5 provides for the embodiment of the invention.

Embodiment

Also by reference to the accompanying drawings the present invention is described in further detail below by specific embodiment.

Referring to Fig. 1, the embodiment of the invention provides a kind of multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions, comprises the steps:

Step S100, adopt that cross flying is a plurality of to be taken the photograph the station exposure and obtain adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carry out the tie point coupling of many sub-images;

Step S200, utilize the reference mark of ground calibration field, calculate photo centre's distance and the sub-camera line element of sub-camera;

Step S300, when carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and the elements of exterior orientation initial value of each sub-image is set up model by collinearity equation, with the photo centre of sub-camera distance as given value, be about to described sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation;

Wherein, each is taken the photograph and is provided with four cameras on the station, and each takes the photograph four sub-images of station synchronization exposure.

In embodiments of the present invention, at first, adopt and a plurality ofly take the photograph station exposure and obtain adjacent virtual image overlap degree greater than 80% many sub-images, and carry out the tie point coupling of many sub-images; Because taked the coupling of a large amount of many sub-images, it is larger that four relatively traditional sub-images of the overlapping region that obvious many sub-images consist of consist of the cruciform overlay regions, degree of overlapping is higher, has enlarged like this matching range of tie point, and can match the tie point that is evenly distributed in a large number; Then utilize the reference mark of ground calibration field, calculate photo centre's distance and the sub-camera line element of sub-camera; Certainly, the data such as line element of obtaining between photo centre's distance and sub-camera are to realize first committed step of calibration method.Through above-mentioned pretreatment operation, can provide the data basis for setting up mathematical model;

Then, when carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and elements of exterior orientation initial value and the collinearity equation of each sub-image set up model, and photo centre's distance of sub-camera as given value, is about to described sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation; At this moment calculative unknown number is the setting angle of sub-camera, namely the angle element in the sub-image elements of exterior orientation (be about to definite sub-camera line element constant as constraint condition, find the solution angle element in the sub-image elements of exterior orientation).Like this, adjust each camera to virtual rotation angle according to 3 angle elements (correction) from camera, so that 4 sub-images are symmetrical to the anglec of rotation of virtual image, and then finish calibration operation, the elements of exterior orientation of each photo of finding the solution like this is more accurate, and calibration more meets the actual conditions that camera is settled.

Therefore, owing to increased sub-camera line element directly calculates sub-image as restrictive condition elements of exterior orientation, the platform calibration parameter that goes out in prediction on such basis is more accurate, can truly reflect the actual positional relationship between sub-camera, and then ensureing that the virtual image splicing precision that generates is higher, plotting accuracy is higher.

Simultaneously, the multiaspect battle array aerial surveying camera platform calibration method of the Problem with Some Constrained Conditions that the embodiment of the invention provides is less to the calibration field area requirement, can carry out at the ground calibration field, has reduced the required cost of flight calibration.

The below is elaborated to embodiment of the invention above steps in the specific implementation:

Further, before step 100 (be that described employing cross flying is a plurality of take the photograph station exposure and obtain adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carry out before the tie point coupling of many sub-images), also comprise the steps:

Step R100, each is taken the photograph station sub-cameras of upper four of arranging adopt high strength supports to be fastened on the platform, the distance between four sub-cameras is fixed, and does four sub-cameras as a whole.

Preferably, in step S200, photo centre distance and the sub-camera line element of sub-camera are calculated in the described reference mark that utilizes the ground calibration field, comprise the steps:

Step S201, utilize the reference mark of ground calibration field, calculate photo centre's distance of sub-camera and the line element mean value between sub-camera by space resection's method;

Line element mean value between step S202, the sub-camera that will repeatedly calculate is as sub-camera line element.

Bundle block adjustment is with the light shafts of the width of cloth aerial map picture block aerial triangulation method as the adjustment unit; Aerotriangulation utilizes the space geometry relation between aerophoto and the photographing object, according to a small amount of picture control point, calculates the elements of exterior orientation of unknown point;

Need to prove: the data such as line element of obtaining between photo centre's distance and sub-camera are to realize first committed step of calibration method.Through above-mentioned pretreatment operation, can and set up mathematical model for subsequent optical bundle method adjustment the data basis is provided.

Need to prove: adopt the high strength support fastening when being installed to platform owing to sub-camera, the distance between sub-camera can change hardly, can regard an integral body as, referring to Fig. 2.Photo centre's distance of sub-camera can be utilized the reference mark of ground calibration field, calculates by space resection's method.

When calculating the elements of exterior orientation of sub-camera by ground calibration field resection, the stable not phenomenon of angle element solution can be occurred, the seam of image can be found in the splicing image that directly generates.But because the distance that ground control point distance is taken the photograph the station about 40m only, for the flying height of aerophotography 700m, the same ground photography base-height ratio of standing between sub-camera of taking the photograph becomes aerophotographic about 17.5 times.Analyze from experimental data, the line element difference between sub-camera is tending towards relatively stable, and near design load, gets the mean value of repeatedly measurement as sub-camera line element.

Because there were correlativity in line element and angle element when sky three resolved, the little deviation of line element can compensate by the angle element, consider the physical arrangement of camera, can be with the photo centre of sub-camera distance as given value, platform calibration parameter is done as a whole resolving, more meet the actual conditions that camera is settled.At this moment calculative unknown number is the setting angle of sub-camera, namely the angle element in the sub-image elements of exterior orientation.

Particularly, as shown in Figure 3, physical arrangement according to the camera arrangement, cross a plane M of photo centre's match (referring to Fig. 3) of four sub-images, the center of gravity O of four photo centres can be used as the photo centre of virtual image, because the camera shooting center is relatively stable, be parallel to S1S3 line direction as Y-axis to cross the O point, be parallel to S4S3 line direction as X-axis to cross the O point, setting up rectangular coordinate system in space O-XYZ(is right-handed coordinate system O-XYZ), O-XYZ is an auxiliary coordinates setting up four sub-camera shooting center line element relations.Four planimetric coordinatess of photo centre in O-XYZ are given value (Da _i, Db _i).

4 estrade camera synchronization exposure during photography, and photo centre's spacing is very little, can think that the Z coordinate of four photo centres in O-XYZ equates.In fact, because the impact of mechanical erection and hardware self structure, there is the maximum distance that is no more than 10mm in the photo centre of sub-camera to plane M.Be horizontal image with the inclination image rectification, can not produce rectification error in theory.

The below comes analytical photography center Z direction to get the impact that approximate value is brought take horizontal image as example.

Illustrate, as shown in Figure 4, camera focus is f, and flying height is H, and photo centre is S, and A is ground point.Length is that the ground line segment MA of P is l in the projected length as the plane ₁, as S vertically during translation dS to S ', above-ground route MA becomes l in the projected length as the plane ₂, can calculate the picture point error dl that dS causes _V

${\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00003533046300031.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=P\frac{f}{H}---\left(1\right)$

$l_2=P\frac{f}{H+\mathrm{dS}}---\left(2\right)$

${\mathrm{dl}}_V=l_1-l_2=\mathrm{Pf}\frac{\mathrm{dS}}{H+\mathrm{dS}}---\left(3\right)$

P be the A point to the distance of photo centre at ground projection M, four piece together the viewing field of camera angles is about 74 ° of 96 ° of *, then the maximal value along long side direction P is 1.11H, is 0.75H along the maximal value of broadside P.

Work as f=47mm, during H=700m, the error of the vertical direction 10mm of photo centre is about 0.52um in the picture point error that long side direction causes, the picture point error that causes in broadside is about 0.35um, four jiaos picture point max value of error is about 0.63um, be 0.1 pixel of maximum picture point error less than, and less the closer to this value of image center.Therefore, sub-camera shooting center is very little on result's impact of splicing image to the deviation of M, can ignore, and can think that the Z coordinate of four photo centres in O-XYZ equates, i.e. Dz1=Dz2=Dz3=Dz4=0.

So by above-mentioned analysis as can be known, sub-camera shooting center is very little on result's impact of splicing image to the deviation of M.Therefore, as given value, although there is deviation, this deviation is very little on result's impact of splicing image, can ignore, and like this platform calibration parameter is done as a whole resolving with the photo centre of sub-camera distance, and precision can be higher.

Concrete each step is as follows:

Preferably, in step S300, described when carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and the elements of exterior orientation initial value of each sub-image is set up model by collinearity equation, with the photo centre of sub-camera distance as given value, be about to described sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation, comprise the steps:

Step S301, the physical arrangement of settling according to camera, cross plane M of photo centre's match of four sub-images, the center of gravity O of four photo centres can be used as the photo centre of virtual image, the camera shooting center is relatively stable, be parallel to S1S3 line direction as Y-axis to cross the O point, set up right-handed coordinate system O-XYZ, O-XYZ is an auxiliary coordinates (referring to Fig. 3) of setting up four sub-camera shooting center line element relations;

Four planimetric coordinatess of sub-camera shooting center in O-XYZ are (Da _i, Db _i, 0), Da wherein _i, Db _iBe given value, establish the rotation angle of sub-image in the virtual image coordinate system and be

Wherein Be given value, then coordinate (the X of photo centre of sub-camera _Sc, Y _Sc, Z _Sc) be:

$\left[\begin{array}{c}{X}_{\mathrm{sc}}\\ Y_{\mathrm{sc}}\\ Z_{\mathrm{sc}}\end{array}\right]=R\left[\begin{array}{c}{\mathrm{Da}}_i\\ {\mathrm{Db}}_i\\ 0\end{array}\right]+\left[\begin{array}{c}{X}_s\\ Y_s\\ Z_s\end{array}\right]$

Wherein:

$R_{\mathrm{\&omega;}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\&omega;}& -\sin \mathrm{\&omega;}\\ 0& \sin \mathrm{\&omega;}& \cos \mathrm{\&omega;}\end{array}\right],$ $R_{\mathrm{\&kappa;}}=\left[\begin{array}{ccc}\cos \mathrm{\&kappa;}& -\sin \mathrm{\&kappa;}& 0\\ \sin \mathrm{\&kappa;}& \cos \mathrm{\&kappa;}& 0\\ 0& 0& 1\end{array}\right]$

Wherein: R is rotation matrix,

Be the angle element of virtual image, (X _S, Y _S, Z _S) be virtual image photo centre line element;

Step S302, set up the mathematical model of collinearity equation; Wherein, the rotation matrix that sub-image is corresponding is R _c=R*R _iAnd

$R_{\mathrm{\&omega;i}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\&omega;}}_i& -\sin {\mathrm{\&omega;}}_i\\ 0& {\sin \mathrm{\&omega;}}_i& {\cos \mathrm{\&omega;}}_i\end{array}\right],$ $R_{\mathrm{\&kappa;i}}=\left[\begin{array}{ccc}{\cos \mathrm{\&kappa;}}_i& {-\sin \mathrm{\&kappa;}}_i& 0\\ {\sin \mathrm{\&kappa;}}_i& {\cos \mathrm{\&kappa;}}_i& 0\\ 0& 0& 1\end{array}\right]$

Value $R_c=\left[\begin{array}{ccc}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right],$ Then collinearity equation is:

$\left\{\begin{array}{c}x=-f\frac{a_1(X-X_{\mathrm{sc}})+b_1(Y-Y_{\mathrm{sc}})+c_1(Z-Z_{\mathrm{sc}})}{a_3(X-X_{\mathrm{sc}})+b_3(Y-Y_{\mathrm{sc}})+c_3(Z-Z_{\mathrm{sc}})}\\ y=-f\frac{a_2(X-X_{\mathrm{sc}})+b_2(Y-Y_{\mathrm{sc}})+c_2(Z-Z_{\mathrm{sc}})}{a_3(X-X_{\mathrm{sc}})+b_3(Y-Y_{\mathrm{sc}})+c_3(Z-Z_{\mathrm{sc}})}\end{array}\right.$

Step S303, with X _Sc, Y _Sc, Z _ScUse X _S, Y _S, Z _SFunction representation, to drawing error equation after the following formula linearization be:

Wherein, each coefficient corresponds to respectively in the following formula:

Step S304, for No. 1 camera

For known, corresponding angle element local derviation item is zero, with the error equation of matrix notation is:

v=At+Bu+Cs-l

Wherein:

$A=\left[\begin{array}{cccccc}{a}_{11}& a_{12}& a_{13}& a_{14}& a_{15}& a_{16}\\ a_{21}& a_{22}& a_{23}& a_{24}& a_{25}& a_{26}\end{array}\right]$

$B=\left[\begin{array}{ccc}-a_{11}& {-a}_{12}& {-a}_{13}\\ {-a}_{21}& -a_{22}& {-a}_{23}\end{array}\right]$

C=0 is the rotation angle initial value of the relative virtual image of 1 work song camera;

$C=\left[\begin{array}{ccccccccc}{a}_{17}& a_{18}& a_{19}& 0& 0& 0& 0& 0& 0\\ a_{27}& a_{28}& a_{29}& 0& 0& 0& 0& 0& 0\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 2 work song cameras;

$C=\left[\begin{array}{ccccccccc}0& 0& 0& a_{110}& a_{111}& a_{112}& 0& 0& 0\\ 0& 0& 0& a_{210}& a_{211}& a_{212}& 0& 0& 0\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 3 work song cameras;

$C=\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& a_{113}& a_{114}& a_{115}\\ 0& 0& 0& 0& 0& 0& a_{213}& a_{214}& a_{215}\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 4 work song cameras;

$u={\left[\begin{array}{ccc}\mathrm{\&Delta;X}& \mathrm{\&Delta;Y}& \mathrm{\&Delta;Z}\end{array}\right]}^T$

$l={\left[\begin{array}{cc}{l}_x& l_y\end{array}\right]}^T$

$v={\left[\begin{array}{cc}{v}_x& v_y\end{array}\right]}^T$

Step S305, for the reference mark, corresponding Δ X Δ Y/delta Z item is zero; The corresponding one group of coefficient matrices A of every group of four sub-image and unknown number t, each object space is put corresponding one group of u, corresponding one group of every sub-camera

With the initial value of the rotation angle C parameter of virtual image elements of exterior orientation A, object space point coordinate B, the relative virtual image of sub-camera and the picpointed coordinate (x of each observation station _i, y _i) the described error equation iterative computation of substitution, until numerical convergence is to threshold value;

After resolving, adjust extremely virtual rotation angle of 1 work song camera according to the modified value of 2,3, the 4 work song camera anglecs of rotation, so that the anglec of rotation of virtual image and 4 sub-images is symmetrical;

Wherein: 9 unknown numbers are arranged among the matrix s; In matrix s Δ ω ₂Δ κ ₂It is the modified value of the relative virtual camera of 2 work song cameras angle element; Δ ω ₃Δ κ ₃It is the modified value of the relative virtual camera of 3 work song cameras angle element;

Δ ω ₄Δ κ ₄It is the modified value of the relative virtual camera of 4 work song cameras angle element.

Need to prove: if be provided with m group virtual image, n observation station, p object space point, q reference mark, then can list 2n equation according to observed reading, 6m+3 (p-q)+9 unknown number is wherein arranged, 9 platform calibration unknown parameters numbers have been increased with respect to traditional bundle adjustment, and in collinearity equation, introduced the line element constant of sub-camera and No. 1 camera to the angle element constant of virtual image as constraint condition, the platform calibration parameter that solves so more meets the actual conditions that sub-camera is installed;

Can find out that from above analysis the constraint condition does not here directly translate into the increase equation of condition, but show as the substitution of known quantity, and the variation of local derviation coefficient in the collinearity equation linearization.

Need to prove: collinearity equation (being that object point, picture point and photo centre are positioned on the straight line) is the key of whole modeling;

Further, after step S300 (be described find the solution in the sub-image elements of exterior orientation after the element of angle), also comprise the steps:

Step S400, selection 47mm are as the focal length of virtual image;

Step S500, will be parallel to M and the coordinate system set up by virtual image photo centre as the image space auxiliary coordinates of virtual image;

Step S600, when calculating the angle element of four sub-cameras, selects a sub-camera as the principal phase machine, select other sub-camera conduct from camera, calculate respectively the anglec of rotation from camera to described principal phase machine;

Step S700, to select the principal phase machine be that benchmark is determined virtual rotation angle, and determine and adjust sub-image to virtual rotation relationship.

Preferably, in step S600, during the angle element of four sub-cameras of described calculating, select a sub-camera as the principal phase machine, select other sub-camera as from camera, calculate respectively the anglec of rotation from camera to described principal phase machine, comprise the steps:

Step S601, selection 1 work song camera are as the principal phase machine, select the conduct of 2,3,4 work song cameras from camera, 1 work song camera is made as an initial fixed value to virtual rotation angle, transitive relation according to the angle element, can be converted to from the rotation angle of camera with respect to virtual from the rotation angle of camera with respect to the principal phase machine, platform calibration parameter to be asked like this is actual be 3 from 9 angle elements of camera.

Preferably, in step S700, described selection principal phase machine is that benchmark is determined virtual rotation angle, and determines and adjust sub-image to virtual rotation relationship, comprises the steps:

Step S701, selection 1 work song camera are as the principal phase machine;

Step S702, get four axial geometric mean directions of sub-camera key light as the primary optical axis direction of virtual camera, adjust the principal phase machine to virtual rotation angle fixed value according to 3 angle element corrections from camera, so that 4 sub-images are symmetrical to the anglec of rotation of virtual image.

Angle for fear of the sub-camera of difference and M plane differs greatly, cause and project to uneven (Fig. 5 of pixel sampling ratio behind the virtual image, dotted line is symmetrical sub-image drop shadow spread, solid line is asymmetrically distributed sub-image drop shadow spread), get four axial geometric means of sub-camera key light as the primary optical axis direction of virtual camera, can adjust the principal phase machine to virtual rotation angle fixed value according to 3 angle element corrections from camera during calculating, so that 4 sub-images are symmetrical as far as possible to the anglec of rotation of virtual image.

In the prior art, because the image ground coverage is large, the ground calibration field can't satisfy the requirement of the method, and the mode platform calibration of cross overlay region can only be undertaken by the data that airflight is obtained, and the cost of calibration experiment is higher.But the calibration method that the embodiment of the invention provides is less to the calibration field area requirement, can carry out at the ground calibration field, has reduced the required cost of flight calibration.

Those skilled in the art are to be understood that, the embodiment of the invention provides the calibration method, ultimate principle is the bundle block adjustment aerotriangulation, the method with Ray Of Light that every photo was formed as the compensating computation elementary cell, with the basic equation of collinearity equation as adjustment, by rotation and the translation of each light beam in the space, make the light of common point between the model realize best intersection, and whole zone is brought in the known reference mark coordinate system go.So set up region-wide unified error equation, solution is tried to achieve the elements of exterior orientation of each photo and the ground coordinate of pass point.Obviously after having retrained sub-camera line element, the elements of exterior orientation of each photo of finding the solution and the ground coordinate of pass point are more accurate, have prior meaning for the accuracy Design of calibration parameter.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. the multiaspect battle array aerial surveying camera platform calibration method of a Problem with Some Constrained Conditions is characterized in that, comprises the steps:

Adopt that cross flying is a plurality of to be taken the photograph the station exposure and obtain adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carry out the tie point coupling of many sub-images;

Utilize the reference mark of ground calibration field, calculate photo centre's distance and the sub-camera line element of sub-camera;

When carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and the elements of exterior orientation initial value of each sub-image is set up model by collinearity equation, with the photo centre of sub-camera distance as given value, be about to sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation;

Wherein, each is taken the photograph and is provided with four cameras on the station, and each takes the photograph four sub-images of station synchronization exposure.

2. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 1 is characterized in that,

Described employing cross flying is a plurality of to be taken the photograph the station exposure and obtains adjacent virtual image overlap degree greater than many groups sub-image of 80%, and carries out also comprising the steps: before the tie point coupling of many sub-images

Each is taken the photograph station sub-cameras of upper four of arranging adopt high strength supports to be fastened on the platform, the distance between four sub-cameras is fixed, and does four sub-cameras as a whole.

3. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 2 is characterized in that,

Photo centre distance and the sub-camera line element of sub-camera are calculated in the described reference mark that utilizes the ground calibration field, comprise the steps:

Utilize the reference mark of ground calibration field, calculate photo centre's distance of sub-camera and the line element mean value between sub-camera by space resection's method;

With the line element mean value between the sub-camera that calculates as sub-camera line element.

4. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 3 is characterized in that,

Described when carrying out aerotriangulation, carry out bundle block adjustment, according to the tie point between the sub-image after reference mark coordinate, the coupling, and the elements of exterior orientation initial value of each sub-image is set up model by collinearity equation, the photo centre of sub-camera distance as given value, is about to sub-camera line element constant as constraint condition, platform calibration parameter is done as a whole resolving, find the solution angle element in the sub-image elements of exterior orientation, comprise the steps:

Physical arrangement according to the camera arrangement, cross plane M of photo centre's match of four sub-images, the center of gravity O of four photo centres can be used as the photo centre of virtual image, set up rectangular coordinate system in space O-XYZ, described rectangular coordinate system in space O-XYZ is an auxiliary coordinates setting up four sub-camera shooting center line element relations;

Four planimetric coordinatess of sub-camera shooting center in O-XYZ are (Da _i, Db _i, 0), Da wherein _i, Db _iBe given value, establish the rotation angle of sub-image in the virtual image coordinate system and be

, wherein

Be given value, then coordinate (the X of photo centre of sub-camera _Sc, Y _Sc, Z _Sc) be:

$\left[\begin{array}{c}{X}_{\mathrm{sc}}\\ Y_{\mathrm{sc}}\\ Z_{\mathrm{sc}}\end{array}\right]=R\left[\begin{array}{c}{\mathrm{Da}}_i\\ {\mathrm{Db}}_i\\ 0\end{array}\right]+\left[\begin{array}{c}{X}_s\\ Y_s\\ Z_s\end{array}\right]$

Wherein:

$R_{\mathrm{\&omega;}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\&omega;}& -\sin \mathrm{\&omega;}\\ 0& \sin \mathrm{\&omega;}& \cos \mathrm{\&omega;}\end{array}\right],$ $R_{\mathrm{\&kappa;}}=\left[\begin{array}{ccc}\cos \mathrm{\&kappa;}& -\sin \mathrm{\&kappa;}& 0\\ \sin \mathrm{\&kappa;}& \cos \mathrm{\&kappa;}& 0\\ 0& 0& 1\end{array}\right]$

Wherein: R is rotation matrix,

Be the angle element of virtual image, (X _S, Y _S, Z _S) be virtual image photo centre line element;

Set up the mathematical model of collinearity equation; Wherein, the rotation matrix that sub-image is corresponding is R _c=R*R _iAnd

$R_{\mathrm{\&omega;i}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\&omega;}}_i& -\sin {\mathrm{\&omega;}}_i\\ 0& {\sin \mathrm{\&omega;}}_i& {\cos \mathrm{\&omega;}}_i\end{array}\right],$ $R_{\mathrm{\&kappa;i}}=\left[\begin{array}{ccc}{\cos \mathrm{\&kappa;}}_i& {-\sin \mathrm{\&kappa;}}_i& 0\\ {\sin \mathrm{\&kappa;}}_i& {\cos \mathrm{\&kappa;}}_i& 0\\ 0& 0& 1\end{array}\right]$

Value $R_c=\left[\begin{array}{ccc}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right],$ Then collinearity equation is:

$\left\{\begin{array}{c}x=-f\frac{a_1(X-X_{\mathrm{sc}})+b_1(Y-Y_{\mathrm{sc}})+c_1(Z-Z_{\mathrm{sc}})}{a_3(X-X_{\mathrm{sc}})+b_3(Y-Y_{\mathrm{sc}})+c_3(Z-Z_{\mathrm{sc}})}\\ y=-f\frac{a_2(X-X_{\mathrm{sc}})+b_2(Y-Y_{\mathrm{sc}})+c_2(Z-Z_{\mathrm{sc}})}{a_3(X-X_{\mathrm{sc}})+b_3(Y-Y_{\mathrm{sc}})+c_3(Z-Z_{\mathrm{sc}})}\end{array}\right.$

With X _Sc, Y _Sc, Z _ScUse X _S, Y _S, Z _SFunction representation, to drawing error equation after the following formula linearization be:

Wherein, each coefficient corresponds to respectively in the following formula:

For No. 1 camera

For known, corresponding angle element local derviation item is zero, with the error equation of matrix notation is:

v=At+Bu+Cs-l

Wherein:

$A=\left[\begin{array}{cccccc}{a}_{11}& a_{12}& a_{13}& a_{14}& a_{15}& a_{16}\\ a_{21}& a_{22}& a_{23}& a_{24}& a_{25}& a_{26}\end{array}\right]$

$B=\left[\begin{array}{ccc}-a_{11}& {-a}_{12}& {-a}_{13}\\ {-a}_{21}& -a_{22}& {-a}_{23}\end{array}\right]$

C=0 is the rotation angle initial value of the relative virtual image of 1 work song camera;

$C=\left[\begin{array}{ccccccccc}{a}_{17}& a_{18}& a_{19}& 0& 0& 0& 0& 0& 0\\ a_{27}& a_{28}& a_{29}& 0& 0& 0& 0& 0& 0\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 2 work song cameras;

$C=\left[\begin{array}{ccccccccc}0& 0& 0& a_{110}& a_{111}& a_{112}& 0& 0& 0\\ 0& 0& 0& a_{210}& a_{211}& a_{212}& 0& 0& 0\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 3 work song cameras;

$C=\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& a_{113}& a_{114}& a_{115}\\ 0& 0& 0& 0& 0& 0& a_{213}& a_{214}& a_{215}\end{array}\right],$ It is the rotation angle initial value of the relative virtual image of 4 work song cameras;

$u={\left[\begin{array}{ccc}\mathrm{\&Delta;X}& \mathrm{\&Delta;Y}& \mathrm{\&Delta;Z}\end{array}\right]}^T$

$l={\left[\begin{array}{cc}{l}_x& l_y\end{array}\right]}^T$

$v={\left[\begin{array}{cc}{v}_x& v_y\end{array}\right]}^T$

For the reference mark, corresponding Δ X Δ Y/delta Z item is zero; The corresponding one group of coefficient matrices A of every group of four sub-image and unknown number t, each object space is put corresponding one group of u, corresponding one group of every sub-camera

Δ ω _iΔ κ _i

With the initial value of the rotation angle C parameter of virtual image elements of exterior orientation A, object space point coordinate B, the relative virtual image of sub-camera and the picpointed coordinate (x of each observation station _i, y _i) the described error equation iterative computation of substitution, until numerical convergence is to threshold value;

After resolving, adjust extremely virtual rotation angle of 1 work song camera according to the modified value of 2,3, the 4 work song camera anglecs of rotation, so that the anglec of rotation of virtual image and 4 sub-images is symmetrical;

Wherein: 9 unknown numbers are arranged among the matrix s; In matrix s

Δ ω ₂Δ κ ₂It is the modified value of the relative virtual camera of 2 work song cameras angle element;

Δ ω ₃Δ κ ₃It is the modified value of the relative virtual camera of 3 work song cameras angle element; Δ ω ₄Δ κ ₄It is the modified value of the relative virtual camera of 4 work song cameras angle element.

5. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 4 is characterized in that,

Find the solution in the sub-image elements of exterior orientation after the element of angle described, also comprise the steps:

Select 47mm as the focal length of virtual image;

The coordinate system that will be parallel to M and set up by virtual image photo centre is as the image space auxiliary coordinates of virtual image;

When calculating the angle element of four sub-cameras, selects a sub-camera as the principal phase machine, select other sub-camera conduct from camera, calculate respectively the anglec of rotation from camera to described principal phase machine;

Selecting the principal phase machine is that benchmark is determined virtual rotation angle, and determines and adjust sub-image to virtual rotation relationship.

6. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 5 is characterized in that,

During the angle element of four sub-cameras of described calculating, select a sub-camera as the principal phase machine, select other sub-camera as from camera, calculate respectively the anglec of rotation from camera to described principal phase machine, comprise the steps:

Select 1 work song camera as the principal phase machine, select the conduct of 2,3,4 work song cameras from camera, 1 work song camera is made as an initial fixed value to virtual rotation angle, transitive relation according to the angle element, can be converted to from the rotation angle of camera with respect to virtual from the rotation angle of camera with respect to the principal phase machine, platform calibration parameter to be asked like this is actual be 3 from 9 angle elements of camera.

7. the multiaspect battle array aerial surveying camera platform calibration method of Problem with Some Constrained Conditions as claimed in claim 6 is characterized in that,

Described selection principal phase machine is that benchmark is determined virtual rotation angle, and determines and adjust sub-image to virtual rotation relationship, comprises the steps:

Select 1 work song camera as the principal phase machine;

Get the geometric mean direction of four sub-camera primary optical axis as the primary optical axis direction of virtual camera, adjust the principal phase machine to virtual rotation angle fixed value according to 3 angle element corrections from camera, so that 4 sub-images are symmetrical to the anglec of rotation of virtual image.

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