CN102519484B - Multi-disc overall adjustment calibration method of rotary photogrammetry system - Google Patents

Multi-disc overall adjustment calibration method of rotary photogrammetry system Download PDF

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CN102519484B
CN102519484B CN 201110385815 CN201110385815A CN102519484B CN 102519484 B CN102519484 B CN 102519484B CN 201110385815 CN201110385815 CN 201110385815 CN 201110385815 A CN201110385815 A CN 201110385815A CN 102519484 B CN102519484 B CN 102519484B
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rotation
matrix
coordinate system
image
angle
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CN102519484A (en
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张永军
胡堃
柯涛
黄山
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Wuhan University WHU
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Abstract

The invention discloses a multi-disc overall adjustment calibration method of a rotary photogrammetry system. In the method, a single observation station obtains the external orientation elements of multiple images and the horizontal and vertical angles of a rotation platform so as to perform calibration of the rotary photogrammetry system; and then on the premise that other observation stations get the external orientation element of the first image, the external orientation elements of other images can be reversely deduced at high precision according to the calibration result and the horizontal and vertical rotation angles of the rotation platform. The method disclosed by the invention has the advantages that: a single observation station obtains the external orientation elements of themultiple images and the horizontal and vertical rotation angles of the rotation platform; through multi-disc overall adjustment solution, the calibration method can realize high-precision calibrationof the rotary photogrammetry system; and on the premise that other observation stations get the external orientation element of the first image, the external orientation elements of the images can beautomatically solved at high precision by simply providing the horizontal and vertical rotation angles of the rotation platform when other images are imaged.

Description

Multi-sheet integral adjustment calibration method for rotary photogrammetric system
Technical Field
The invention relates to the technical field of photogrammetry, in particular to a multi-sheet integral adjustment calibration method for a rotary photogrammetry system.
Background
The rotary photogrammetry system is a system for carrying out rotary photogrammetry by arranging a camera on a platform capable of rotating vertically and horizontally, and is widely applied to near-field photogrammetryThe acquisition of three-dimensional information in the field of scene photogrammetry and computer vision. As shown in fig. 1, in a state of rotating horizontally
Figure 624487DEST_PATH_IMAGE001
And a vertical rotation axisPoint of intersection of
Figure 928430DEST_PATH_IMAGE003
Centered rectangular spatial coordinate system
Figure 2011103858152100002DEST_PATH_IMAGE004
In (1),
Figure 531449DEST_PATH_IMAGE005
and
Figure 2011103858152100002DEST_PATH_IMAGE006
are respectively like principal points
Figure 968728DEST_PATH_IMAGE007
Relative toIs spotted on
Figure 2011103858152100002DEST_PATH_IMAGE008
The shaft is provided with a plurality of axial holes,
Figure 95133DEST_PATH_IMAGE009
shaft and
Figure 2011103858152100002DEST_PATH_IMAGE010
the offset of the shaft is such that,
Figure 564161DEST_PATH_IMAGE011
is the photographic focal length. Wherein the rotary platform of the system is around the horizontal axis
Figure 62138DEST_PATH_IMAGE001
And a vertical axis
Figure 568206DEST_PATH_IMAGE002
When rotating, the exterior orientation element of the camera
Figure 2011103858152100002DEST_PATH_IMAGE012
And will vary accordingly. According to the vertical rotation angleAnd horizontal rotation angle
Figure 2011103858152100002DEST_PATH_IMAGE014
The method comprises the steps of automatically acquiring external orientation elements of a camera, needing high-precision system calibration, and determining a rotation matrix and an eccentric coordinate of the camera in the system relative to a rotating platform. Calibration of a multi-rotation photogrammetry system is a key step in the process of obtaining three-dimensional information from a two-dimensional plane image, and is an important research subject.
The existing camera calibration methods can be roughly divided into three categories: a conventional calibration method, a self-calibration method and a calibration method based on active vision. In the traditional calibration method, an object with a known shape and size is used as a calibration object, and a camera is used for shooting a plurality of images to solve the corresponding relation between an image space and an object space; the self-calibration method does not need a calibration object, but calibrates through the relation of matching points in a calibration picture shot by a moving camera; the calibration method based on active vision needs to predict detailed motion information of the camera, so expensive equipment is needed to record the motion trail of the camera, and the test cost is high.
Disclosure of Invention
The invention mainly solves the problems in the prior art and provides a method for calibrating a rotary photogrammetric system by acquiring external orientation elements of a plurality of images and horizontal and vertical rotation angles of a rotary platform by using a single observation station.
The technical scheme of the invention is a method for calibrating a multi-sheet integral adjustment of a rotary photogrammetric system, which comprises the following steps:
step 1, importing the number of images acquired by a first station
Figure 791563DEST_PATH_IMAGE015
And the external orientation angle element when each image is acquired
Figure 2011103858152100002DEST_PATH_IMAGE016
And elements of exterior orientation lineHorizontal angle of rotary platform around vertical rotary shaft
Figure DEST_PATH_IMAGE018
And the vertical angle of the rotary platform about the horizontal axis of rotation
Figure 945649DEST_PATH_IMAGE019
Wherein the subscript 1 identifies the station number=1, subscript
Figure 448830DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure DEST_PATH_IMAGE022
number of images
Figure 197344DEST_PATH_IMAGE015
Greater than or equal to 3; angle of exterior orientation
Figure 404334DEST_PATH_IMAGE016
According to
Figure 580100DEST_PATH_IMAGE023
Corner system construction rotation matrix
Figure DEST_PATH_IMAGE024
Elements of exterior orientation line
Figure 567648DEST_PATH_IMAGE017
Constructing a coordinate matrix of line elements
Figure 791956DEST_PATH_IMAGE025
；
Step 2, constructing a rotation model of the camera relative to an object space coordinate system, wherein the rotation model formula is as follows
Wherein,
Figure 181349DEST_PATH_IMAGE027
is an off-machine azimuth element under an object space coordinate system
Figure 465700DEST_PATH_IMAGE023
Rotating the matrix under the corner system;
Figure DEST_PATH_IMAGE028
is a rotation matrix between an object space coordinate system and a standard photogrammetric coordinate system;
Figure 674964DEST_PATH_IMAGE029
a rotation matrix between a standard photographing coordinate system and a rotation coordinate system;
Figure DEST_PATH_IMAGE030
is a rotation matrix between a rotation coordinate system and an image space coordinate system;
respectively corresponding rotary models according to the first three images acquired by the first station
Figure 765280DEST_PATH_IMAGE031
Resolving the correspondence of the first station
Figure 9180DEST_PATH_IMAGE023
Downward rotation torque array of corner systemCorner of
Figure 523819DEST_PATH_IMAGE033
And a rotation matrix
Figure 485959DEST_PATH_IMAGE030
Corner ofAnd taking the obtained resolving result as an initial value of an unknown number, wherein the subscript 1 identifies the station number=1, subscript
Figure 150475DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 776629DEST_PATH_IMAGE035
，
Figure 960485DEST_PATH_IMAGE024
constructing a rotation matrix for the step 1;
step 3, converting the rotation model into an error equation by using a rotation angleAnd cornerFor unknown number, all images obtained by the first survey station are linearized one by one, a normal equation is constructed according to the initial value of the unknown number and the least square principle, and the integral adjustment is solvedSolving an equation to obtain an unknown number correction number;
step 4, if the maximum value of the correction number of the unknown number is smaller than a preset threshold value of the correction number of the unknown number or the iteration number exceeds a preset threshold value of the iteration number, executing step 5; otherwise, taking the current unknown number correction number as the initial value of the unknown number, and returning to the iteration execution step 3;
step 5, outputting the unknown number correction number obtained in the last iteration as a corner
Figure 345833DEST_PATH_IMAGE033
And corner
Figure 16986DEST_PATH_IMAGE034
According to the angle of rotation
Figure 924899DEST_PATH_IMAGE033
Reconstructing the rotation matrix from the calibration results
Figure 997897DEST_PATH_IMAGE032
According to the angle of rotation
Figure 965853DEST_PATH_IMAGE034
Reconstructing the rotation matrix from the calibration results
Figure 61985DEST_PATH_IMAGE030
；
Step 6, constructing an eccentric model of the camera relative to an object space coordinate system, wherein the formula of the eccentric model is as follows
Figure DEST_PATH_IMAGE036
Wherein
Figure 835906DEST_PATH_IMAGE037
The coordinate matrix is a coordinate matrix of the external azimuth line elements under the object space coordinate system;
Figure DEST_PATH_IMAGE038
the coordinates of the origin of the image space coordinate system under the rotating coordinate system;a coordinate matrix of the rotation center under an object space coordinate system;
off-center model from camera relative to object coordinate system
Figure DEST_PATH_IMAGE040
According to the image obtained by the first measuring station, an error equation and a normal equation are constructed one by one, and according to the least square principle, the coordinate of the origin of the image space coordinate system under the rotating coordinate system is solved by the integral adjustment
Figure 233094DEST_PATH_IMAGE038
And coordinates of the center of rotation in an object coordinate systemOutput coordinates
Figure 128555DEST_PATH_IMAGE038
Wherein subscript 1 identifies the station number
Figure 176145DEST_PATH_IMAGE020
=1, subscriptWhich indicates the number of the picture,
Figure 353366DEST_PATH_IMAGE022
，
Figure DEST_PATH_IMAGE042
for the coordinate matrix constructed in step 1,
Figure 406772DEST_PATH_IMAGE032
reconstructing the rotation matrix for the step 5;
7, reconstructing the rotation matrix according to the step 5
Figure 308869DEST_PATH_IMAGE030
And 6, coordinates of the origin of the image space coordinate system obtained in the step 6 in the rotating coordinate system
Figure 789529DEST_PATH_IMAGE038
The known external orientation angle element when the first image of the rest stations is acquiredAnd elements of exterior orientation line
Figure DEST_PATH_IMAGE044
Horizontal angle of rotary platform around vertical rotary shaft
Figure 63702DEST_PATH_IMAGE045
And a vertical angle around the horizontal rotation axis
Figure DEST_PATH_IMAGE046
And resolving the rotation matrix between the object coordinate system and the standard photogrammetric coordinate system under the condition of other stations through the rotation model and the eccentric model
Figure 106392DEST_PATH_IMAGE047
And coordinates of the center of rotation in an object coordinate system
Figure DEST_PATH_IMAGE048
(ii) a Wherein the subscriptThe number of the station is shown as,
Figure 662324DEST_PATH_IMAGE049
subscript 1 denotes a picture number
Figure 57534DEST_PATH_IMAGE021
=1；
Step 8, according to the known horizontal angle of the rotating platform around the vertical rotating shaft when other images except the first image of the other measuring stations are obtainedAnd a vertical angle around the horizontal rotation axis
Figure 934223DEST_PATH_IMAGE051
And resolving external orientation angle elements when other images except the first image of the rest stations are acquired through the rotation model and the eccentric model
Figure DEST_PATH_IMAGE052
And elements of exterior orientation line
Figure 819002DEST_PATH_IMAGE053
Wherein the subscript
Figure 148352DEST_PATH_IMAGE020
The number of the station is shown as,subscript
Figure 517596DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure DEST_PATH_IMAGE054
。
and, according to the rotation model corresponding to the first three images obtained from the 1 st station
Figure 573277DEST_PATH_IMAGE024
，
Figure 327606DEST_PATH_IMAGE035
Resolving to
Figure 392514DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 915899DEST_PATH_IMAGE032
Corner of
Figure 139552DEST_PATH_IMAGE033
And a rotation matrix
Figure 381177DEST_PATH_IMAGE030
Corner of
Figure 984197DEST_PATH_IMAGE034
The concrete implementation mode is as follows,
the rotation model corresponding to the 1 st image is
Figure 362088DEST_PATH_IMAGE055
，
The 2 nd image corresponds to a rotation model of
Figure DEST_PATH_IMAGE056
，
The 3 rd image corresponds to a rotation model of
Figure 25151DEST_PATH_IMAGE057
，
Wherein,
Figure DEST_PATH_IMAGE058
acquired for the 1 st station
Figure 550810DEST_PATH_IMAGE021
A rotation matrix between the standard photographing coordinate system and the rotation coordinate system corresponding to the sheet image,
Figure 895204DEST_PATH_IMAGE035
；
eliminating one group of unknowns to obtain
Figure DEST_PATH_IMAGE060
Wherein,
Figure 23883DEST_PATH_IMAGE061
Figure DEST_PATH_IMAGE062
Figure 36838DEST_PATH_IMAGE063
order rotation matrixThe element in the middle-right lower corner is 1,
Figure 981660DEST_PATH_IMAGE064
the other eight elements in the matrix are used as unknowns
Figure 334144DEST_PATH_IMAGE008
Expanding two formulas obtained by eliminating one group of unknowns into nine equations about the eight unknowns respectively; coefficient array for constructing normal equation according to least square principle
Figure 341939DEST_PATH_IMAGE065
Sum constant termResolving the rotation matrix
Figure 842191DEST_PATH_IMAGE064
The formula of the first eight element values, the normal equation is as follows
Figure 528387DEST_PATH_IMAGE067
Obtaining a rotation matrix according to the calculation resultResolving a rotation matrixThen according to
Figure 898691DEST_PATH_IMAGE023
Relationship solution for corner system
Figure 122999DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 512392DEST_PATH_IMAGE032
Corner of
Figure 531164DEST_PATH_IMAGE033
And a rotation matrixCorner of
Figure 34006DEST_PATH_IMAGE034
。
Furthermore, the specific operation method of step 3 is as follows,
order to
Figure DEST_PATH_IMAGE068
The rotation model is converted into the form of an error equation as follows,
Figure 277906DEST_PATH_IMAGE069
wherein,
Figure DEST_PATH_IMAGE070
representing the residual of the error equation, unknowns being
Figure 795475DEST_PATH_IMAGE023
Downward rotation torque array of corner systemThree corners of
Figure 55216DEST_PATH_IMAGE033
And a rotation matrixThree corners of，
Figure 166895DEST_PATH_IMAGE071
,
Figure DEST_PATH_IMAGE072
,
Figure 599013DEST_PATH_IMAGE073
,
Figure DEST_PATH_IMAGE074
,And
Figure DEST_PATH_IMAGE076
respectively solving partial derivatives of the error matrix equation according to the six unknowns in sequence;
Figure 676876DEST_PATH_IMAGE077
is a constant term of the error equation;
the error equations sequentially calculate the partial derivatives according to the six unknowns and sequentially list the partial derivatives to obtain nine basic forms of the error equations, and the error equations are listed for all the images acquired by the 1 st observation station; subscript 1 identifies the station number
Figure 285712DEST_PATH_IMAGE020
=1, subscript
Figure 255942DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 266624DEST_PATH_IMAGE022
；
constructing a coefficient array of a normal equation according to the least square principle according to the initial value of the unknown number
Figure DEST_PATH_IMAGE078
Sum constant term
Figure 296897DEST_PATH_IMAGE079
The formula of the normal equation is as follows,
。
matrix of unknowns
Figure 455345DEST_PATH_IMAGE081
And solving the correction numbers of the six unknowns according to a normal equation.
Furthermore, the specific operation method of step 6 for constructing error equations and normal equations one by one based on the images acquired at the first station is as follows,
the eccentric model is converted into the equation form
Wherein
Figure 232196DEST_PATH_IMAGE083
Is a matrix of the units,
Figure 97384DEST_PATH_IMAGE042
for the 1 st station
Figure 298558DEST_PATH_IMAGE021
The coordinate of the external azimuth line element under the object coordinate system corresponding to each image,
Figure 881986DEST_PATH_IMAGE041
for the coordinates of the rotation center corresponding to the 1 st station in the object space coordinate system, the subscript 1 indicates the station number=1, subscript
Figure 241609DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 551368DEST_PATH_IMAGE022
(ii) a The above equation is set forth for all images acquired at station 1
Method equation coefficient array constructed according to least square principle
Figure DEST_PATH_IMAGE084
Sum constant term
Figure 684409DEST_PATH_IMAGE085
The formula of the normal equation is
Figure DEST_PATH_IMAGE086
Matrix of unknowns
Figure 800133DEST_PATH_IMAGE087
And integrally solving the coordinates of the origin of the image space coordinate system in the rotating coordinate system according to a normal equation
Figure 702229DEST_PATH_IMAGE038
And coordinates of the center of rotation in an object coordinate system
Figure 182889DEST_PATH_IMAGE041
。
Furthermore, the specific operation method of step 7 is as follows,
according to the known external orientation angle element when the first image of the rest stations is acquired
Figure 803227DEST_PATH_IMAGE043
And elements of exterior orientation line
Figure 394745DEST_PATH_IMAGE044
Horizontal angle of rotary platform around vertical rotary shaft
Figure 148419DEST_PATH_IMAGE045
And a vertical angle around the horizontal rotation axis
Figure 65559DEST_PATH_IMAGE046
，
Angle of exterior orientation
Figure 845296DEST_PATH_IMAGE043
According toCorner system construction rotation matrix
Figure DEST_PATH_IMAGE088
Elements of exterior orientation line
Figure 179511DEST_PATH_IMAGE044
Constructing a coordinate matrix of line elements
Figure 64291DEST_PATH_IMAGE089
From a horizontal angle
Figure 393641DEST_PATH_IMAGE045
Perpendicular angle
Figure 592541DEST_PATH_IMAGE046
Constructing a rotation matrix；
Then reconstructing the rotation matrix from step 5
Figure 323737DEST_PATH_IMAGE030
Solving rotation matrix by substituting rotation model，
Figure 196064DEST_PATH_IMAGE091
Will rotate the matrix
Figure 933076DEST_PATH_IMAGE090
Rotation matrix
Figure 521707DEST_PATH_IMAGE047
And the coordinates obtained in step 6
Figure 951552DEST_PATH_IMAGE038
Substituting the calculation result into the eccentric model to calculate the coordinate matrix
Figure 255494DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE092
Wherein the subscript
Figure 592935DEST_PATH_IMAGE020
The number of the station is shown as,subscript 1 denotes a picture number
Figure 633889DEST_PATH_IMAGE021
=1。
Furthermore, the specific operation method of step 8 is as follows,
according to the horizontal angle of the rotary platform around the vertical rotary shaft when other images except the first image of other stations are obtainedAnd a vertical angle around the horizontal rotation axis
Figure 503942DEST_PATH_IMAGE051
Building a rotation matrix
Figure 1919DEST_PATH_IMAGE093
And rotating the rotation matrix obtained in the step 7
Figure 835883DEST_PATH_IMAGE047
And step 5 reconstructed rotation matrix
Figure 786521DEST_PATH_IMAGE030
Substituting into the rotation model to calculate the external orientation angle element when the image is acquired
Figure 731344DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure DEST_PATH_IMAGE094
And according to
Figure 146145DEST_PATH_IMAGE023
The corner system further decomposes the external azimuth angle element
Figure 88693DEST_PATH_IMAGE052
The formula of solution is as follows
Will rotate the matrixRotation matrix
Figure 564956DEST_PATH_IMAGE093
The coordinates obtained in step 6
Figure 678405DEST_PATH_IMAGE038
Solution result and coordinate matrix of
Figure 665953DEST_PATH_IMAGE048
Substituting the eccentric model into a coordinate matrix for solving the elements of the external orientation line during image acquisition
Figure DEST_PATH_IMAGE096
And further decomposing the elements of the exterior orientation lineThe formula of solution is as follows
Figure 14075DEST_PATH_IMAGE097
Wherein the subscript
Figure 360742DEST_PATH_IMAGE020
The number of the station is shown as,
Figure 773269DEST_PATH_IMAGE049
subscript
Figure 863585DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 45167DEST_PATH_IMAGE054
。
according to the method, a single measuring station is used for obtaining external orientation elements of a plurality of images and horizontal and vertical rotation angles of a rotating platform, and through calculation of a plurality of integral adjustment differences, the calibration method can realize high-precision automatic positioning and orientation of a rotary photogrammetric system; on the premise that other stations know the external orientation element of the first image, the external orientation element of the image can be automatically reversely deduced with high precision only by providing horizontal and vertical rotation angles of the rotating platform during imaging of other images.
Drawings
FIG. 1 is a block diagram of a rotational scanning camera system;
FIG. 2 is a schematic view of the geometric relationship between coordinate systems according to the present invention;
FIG. 3 is a flow chart of calibrating a rotation and eccentricity matrix according to an embodiment of the present invention;
FIG. 4 is a flow chart of resolving an exterior orientation element according to the calibration result according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following by combining the drawings and the embodiment.
See fig. 2, wherein
Figure DEST_PATH_IMAGE098
Is the intersection point in FIG. 1
Figure 297157DEST_PATH_IMAGE003
In the object space coordinate system
Figure 259297DEST_PATH_IMAGE099
Coordinates of the lower part;
Figure DEST_PATH_IMAGE100
a standard photographing coordinate system of the system at a position where the camera standard is opposite to a target object is adopted, wherein X is a course direction, Y is a zenith direction, and Z is a depth direction;
Figure 890654DEST_PATH_IMAGE101
a rotating coordinate system is formed after the system rotates around a horizontal axis by an angle V and rotates around a vertical axis by an angle H;
Figure 254639DEST_PATH_IMAGE005
andare the same as in FIG. 1, and are the principal points
Figure 64649DEST_PATH_IMAGE007
Relative to
Figure 434451DEST_PATH_IMAGE003
Is spotted on
Figure 387363DEST_PATH_IMAGE008
The shaft is provided with a plurality of axial holes,
Figure 184418DEST_PATH_IMAGE009
shaft and
Figure 855571DEST_PATH_IMAGE010
the offset of the shaft.
The embodiment of the invention establishes the following two models:
1. the rotation model of the camera with respect to the object coordinate system is based on the following formula:
Figure 29063DEST_PATH_IMAGE026
wherein
Figure 102061DEST_PATH_IMAGE027
Is an off-machine azimuth element under an object space coordinate system
Figure 70017DEST_PATH_IMAGE023
The expansion form of the rotation matrix under the corner system is as follows:
Figure 228466DEST_PATH_IMAGE062
wherein,
Figure DEST_PATH_IMAGE102
is an exterior orientation angle element.
Figure 61774DEST_PATH_IMAGE028
Is a rotation matrix between the object coordinate system and the standard photogrammetry coordinate system, which is expanded as above:
Figure 926962DEST_PATH_IMAGE103
wherein,
Figure DEST_PATH_IMAGE104
is composed of
Figure 128137DEST_PATH_IMAGE023
Lower rotation of corner systemMatrix array
Figure 773881DEST_PATH_IMAGE028
The corner of (c). For multiple images acquired by a fixed station, the rotation matrixThe value of (a) is not changed.
Figure 71188DEST_PATH_IMAGE029
Is a rotation matrix between a standard photographic coordinate system and a rotation coordinate system, and the expansion form is as follows:
Figure 380946DEST_PATH_IMAGE063
Figure 513987DEST_PATH_IMAGE029
the matrix being formed by the horizontal angle of the rotating platform about the vertical axis of rotation
Figure 567394DEST_PATH_IMAGE014
And the vertical angle of the rotary platform about the horizontal axis of rotation
Figure 469491DEST_PATH_IMAGE013
And (5) constructing. For each image, the matrix changes as the rotational pose changes.
Figure 950151DEST_PATH_IMAGE030
Is a rotation matrix between a rotation coordinate system and an image space coordinate system, the matrix still following
Figure 304909DEST_PATH_IMAGE023
And constructing a corner system. The matrix is the internal parameters of the system to be calibrated and is obtained for all the stationsThe matrix remains unchanged for all images taken.
Figure 162006DEST_PATH_IMAGE105
Figure 918610DEST_PATH_IMAGE034
Is composed of
Figure 570171DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 680734DEST_PATH_IMAGE030
The corner of (c).
2. The decentration model of the camera with respect to the object coordinate system is based on the following formula:
Figure 75943DEST_PATH_IMAGE036
wherein
Figure 687053DEST_PATH_IMAGE037
Is an external azimuth line element under the object space coordinate system
Figure DEST_PATH_IMAGE106
The coordinate matrix of (2).
Figure 775095DEST_PATH_IMAGE038
The coordinates of the origin of the image space coordinate system in the rotating coordinate system are determined by the distances between the photographing centers of the cameras and the horizontal and vertical rotating shafts under the standard positive position of the rotating matrix, wherein the coordinates
Figure 104445DEST_PATH_IMAGE038
Value on the X axis
Figure 365662DEST_PATH_IMAGE107
Coordinates of the same
Figure 768962DEST_PATH_IMAGE038
Value on the Y axis
Figure DEST_PATH_IMAGE108
Coordinates of the same
Figure 152538DEST_PATH_IMAGE038
Value in Z axis
Figure 969185DEST_PATH_IMAGE109
The matrix remains unchanged for all images acquired at all stations for the system internal parameters that need to be calibrated.Is a center of rotation
Figure 291899DEST_PATH_IMAGE098
And in the coordinate matrix of the object space coordinate system, the value of the rotation matrix is unchanged for a plurality of images acquired by a certain fixed measuring station.
The invention can adopt computer software technology to realize automatic execution flow. The multi-slice overall adjustment calibration process of the rotational photogrammetry system of the embodiment of the invention is described below, and based on the rotational model and the eccentric model of the camera relative to the object coordinate system, each step is described as follows. Reference may be made to fig. 3 and 4, wherein fig. 3 provides a flow of calibrating the rotation and eccentricity matrices, steps 1-6; fig. 4 provides a flow for solving the external orientation element based on the calibration results, i.e. steps 7, 8.
Step 1, importing the number of images acquired by a first station
Figure 721743DEST_PATH_IMAGE015
(at least three) and elements of external orientation (including elements of external orientation angle) at the time of acquiring each imageAnd elements of exterior orientation line) Horizontal angle of rotary platform around vertical rotary shaft
Figure 3667DEST_PATH_IMAGE018
And the vertical angle of the rotary platform about the horizontal axis of rotation
Figure 401150DEST_PATH_IMAGE019
Wherein the subscript 1 identifies the station number
Figure 130072DEST_PATH_IMAGE020
=1, subscript
Figure 271203DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 831498DEST_PATH_IMAGE022
(ii) a Angle of exterior orientationAccording to
Figure 616100DEST_PATH_IMAGE023
Corner system construction rotation matrix
Figure 498605DEST_PATH_IMAGE024
Elements of exterior orientation line
Figure 851089DEST_PATH_IMAGE017
Constructing a coordinate matrix of line elements
Figure 855954DEST_PATH_IMAGE025
。
Step 2, constructing a rotation model of the camera relative to an object space coordinate system, wherein the rotation model formula is as follows
Figure 293889DEST_PATH_IMAGE026
Wherein,is an off-machine azimuth element under an object space coordinate system
Figure 249392DEST_PATH_IMAGE023
Rotating the matrix under the corner system;
Figure 162509DEST_PATH_IMAGE028
is a rotation matrix between an object space coordinate system and a standard photogrammetric coordinate system;
Figure 87740DEST_PATH_IMAGE029
the horizontal angle is the rotation matrix between the standard photographic coordinate system and the rotation coordinate system according to step 1
Figure 312048DEST_PATH_IMAGE018
And vertical angle
Figure 701441DEST_PATH_IMAGE019
Constructing;is a rotation matrix between a rotation coordinate system and an image space coordinate system;
respectively corresponding rotary models according to the first three images acquired by the first stationResolving the correspondence of the first station
Figure 223055DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 404638DEST_PATH_IMAGE032
Corner ofAnd a rotation matrix
Figure 822030DEST_PATH_IMAGE030
Corner of
Figure 388140DEST_PATH_IMAGE034
And taking the obtained resolving result as an initial value of an unknown number, wherein the subscript 1 identifies the station number=1, subscript
Figure 112700DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 562136DEST_PATH_IMAGE035
，
Figure 666358DEST_PATH_IMAGE024
the rotation matrix constructed for step 1.
The embodiment is based on the rotation model corresponding to the first three images obtained by the 1 st station
Figure 884849DEST_PATH_IMAGE024
，
Figure 681904DEST_PATH_IMAGE035
Resolving toDownward rotation torque array of corner system
Figure 526549DEST_PATH_IMAGE032
Corner of
Figure 537231DEST_PATH_IMAGE033
And a rotation matrix
Figure 564574DEST_PATH_IMAGE030
Corner of
Figure 660706DEST_PATH_IMAGE034
The concrete implementation mode is as follows,
the rotation model corresponding to the 1 st image is
Figure 106731DEST_PATH_IMAGE055
，
The 2 nd image corresponds to a rotation model of
Figure 299815DEST_PATH_IMAGE056
，
The 3 rd image corresponds to a rotation model of
Figure 438672DEST_PATH_IMAGE057
，
Wherein,
Figure 84417DEST_PATH_IMAGE058
acquired for the 1 st station
Figure 334133DEST_PATH_IMAGE021
A rotation matrix between the standard photographing coordinate system and the rotation coordinate system corresponding to the sheet image,
Figure 381723DEST_PATH_IMAGE035
horizontal angle of the rotary platform about vertical axis of rotation introduced according to step 1
Figure 691482DEST_PATH_IMAGE018
And the vertical angle of the rotary platform about the horizontal axis of rotation
Figure 762206DEST_PATH_IMAGE019
Constructing;
removing one set of unknowns, e.g. rotation matrix
Figure 877929DEST_PATH_IMAGE030
And finishing to obtain:
Figure 717709DEST_PATH_IMAGE059
Figure 260686DEST_PATH_IMAGE060
wherein,
Figure 553127DEST_PATH_IMAGE103
Figure 410225DEST_PATH_IMAGE062
Figure 166828DEST_PATH_IMAGE063
the result of the calculation of (a) is a 3 × 3 matrix of 9 elements in total. Order rotation matrix
Figure 880706DEST_PATH_IMAGE064
The element in the middle-right lower corner is 1,
Figure 926023DEST_PATH_IMAGE064
the other eight elements in the matrix are used as unknownsExpanding two formulas obtained by eliminating one group of unknowns into nine equations about the eight unknowns respectively; coefficient array for constructing normal equation according to least square principle
Figure 935272DEST_PATH_IMAGE065
Sum constant term
Figure 85630DEST_PATH_IMAGE066
Resolving the rotation matrix
Figure 352664DEST_PATH_IMAGE064
The formula of the first eight element values, the normal equation, is as follows:
Figure 285985DEST_PATH_IMAGE067
obtaining a rotation matrix according to the calculation result
Figure 17180DEST_PATH_IMAGE064
Resolving a rotation matrix
Figure 276123DEST_PATH_IMAGE030
The concrete mode is as follows: rearrangement
Figure 827190DEST_PATH_IMAGE064
The matrix, whose determinant values are calculated, divides all elements in the matrix by the cube root of the determinant value. Can be normalized to the form of a rotation matrix. Is obtained by
Figure 829781DEST_PATH_IMAGE064
After the matrix is obtained, the matrix can be substituted into the rotation model corresponding to the first image
Figure 353167DEST_PATH_IMAGE055
In (1) resolving
Figure 579749DEST_PATH_IMAGE030
The values of the matrix.
Then follow
Figure 821374DEST_PATH_IMAGE023
Relationship solution for corner system
Figure 424394DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 802285DEST_PATH_IMAGE032
Corner of
Figure 403031DEST_PATH_IMAGE033
And a rotation matrix
Figure 928690DEST_PATH_IMAGE030
Corner of
Figure 273084DEST_PATH_IMAGE034
。
Step 3, converting the rotation model into an error equation by using a rotation angle
Figure 833378DEST_PATH_IMAGE033
And corner
Figure 339446DEST_PATH_IMAGE034
And (3) carrying out linearization processing on all images acquired by the first observation station one by one for the unknown number, constructing a normal equation according to the initial value of the unknown number and the least square principle, solving the normal equation by integral adjustment to obtain the correction number of the unknown number.
Order to
Figure 450988DEST_PATH_IMAGE068
Example a rotation model is converted into the form of an error equation as follows,
Figure 333494DEST_PATH_IMAGE069
wherein,
Figure 685978DEST_PATH_IMAGE070
representing the residual of the error equation, unknowns being
Figure 425264DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 863198DEST_PATH_IMAGE032
Three corners of
Figure 611711DEST_PATH_IMAGE033
And a rotation matrixThree corners of；
Figure 919699DEST_PATH_IMAGE071
,
Figure 144007DEST_PATH_IMAGE072
,,,
Figure 964698DEST_PATH_IMAGE075
Andpartial derivatives respectively solved for the error matrix equation according to the six unknowns in turn；
Figure 236597DEST_PATH_IMAGE077
Is a constant term of the error equation.
The matrices in the error equation are all 3
Figure 754166DEST_PATH_IMAGE111
And 3, the matrix can extract the items of the corresponding positions of all the matrixes to obtain nine basic forms of error equations, so that the solution is more convenient. In specific implementation, the term of the 1 st position in the 1 st row of all the matrices is taken according to the error equation to obtain a basic form … of the error equation, and so on. Error equations are listed according to the error equations of all the images acquired by the 1 st measuring station; subscript 1 identifies the station number
Figure DEST_PATH_IMAGE112
=1, subscriptWhich indicates the number of the picture,
Figure 282416DEST_PATH_IMAGE022
. In step 2
Figure 318505DEST_PATH_IMAGE032
And
Figure 9905DEST_PATH_IMAGE030
the rotation angle calculation result is used as an initial value of an unknown number in the iterative adjustment, and a coefficient array of a normal equation is constructed according to the least square principle
Figure 131445DEST_PATH_IMAGE078
Sum constant term
Figure 563563DEST_PATH_IMAGE079
。
The formula of the normal equation is as follows,
and solving the correction numbers of the six unknowns according to a law equation.
Step 4, if the maximum value of the correction number of the unknown number is smaller than a preset threshold value of the correction number of the unknown number or the iteration number exceeds a preset threshold value of the iteration number, executing step 5; otherwise, taking the current unknown number correction number as the initial value of the unknown number, and returning to the iteration and executing the step 3.
In specific implementation, the unknown number correction threshold and the iteration number threshold can be set by a person skilled in the art according to specific situations. If the maximum value of the correction number of the unknown number is smaller than the threshold value of the correction number of the unknown number or the iteration number exceeds any judgment condition of the threshold value of the iteration number, executing the step 5; otherwise, returning to execute the step 3.
Step 5, outputting the unknown number correction number obtained in the last iteration as a corner
Figure 579110DEST_PATH_IMAGE033
And corner
Figure 187945DEST_PATH_IMAGE034
According to the angle of rotation
Figure 95859DEST_PATH_IMAGE033
Reconstructing the rotation matrix from the calibration resultsAccording to the angle of rotationReconstructing the rotation matrix from the calibration results。
Step 6, constructing an eccentric model of the camera relative to an object space coordinate system, wherein the formula of the eccentric model is as follows
Figure 69183DEST_PATH_IMAGE036
Wherein
Figure 262267DEST_PATH_IMAGE037
The coordinate matrix is a coordinate matrix of the external azimuth line elements under the object space coordinate system;the coordinates of the origin of the image space coordinate system under the rotating coordinate system;
Figure 781290DEST_PATH_IMAGE039
a coordinate matrix of the rotation center under an object space coordinate system;
off-center model from camera relative to object coordinate system
Figure 296585DEST_PATH_IMAGE040
According to the image obtained by the first measuring station, an error equation and a normal equation are constructed one by one, and according to the least square principle, the coordinate of the origin of the image space coordinate system under the rotating coordinate system is solved by the integral adjustmentAnd coordinates of the center of rotation in an object coordinate system
Figure 651004DEST_PATH_IMAGE041
Output coordinates
Figure 518466DEST_PATH_IMAGE038
Wherein subscript 1 identifies the station number
Figure 571872DEST_PATH_IMAGE020
=1, subscript
Figure 473969DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 954629DEST_PATH_IMAGE022
，
Figure 574966DEST_PATH_IMAGE042
for the coordinate matrix constructed in step 1,the rotation matrix reconstructed for step 5.
Example conversion of the eccentric model into equation form
Figure 188667DEST_PATH_IMAGE082
WhereinIs a matrix of the units,
Figure 619966DEST_PATH_IMAGE042
for the 1 st station
Figure 77492DEST_PATH_IMAGE021
The coordinate of the external azimuth line element under the object coordinate system corresponding to each image,
Figure 891864DEST_PATH_IMAGE041
for the coordinates of the rotation center corresponding to the 1 st station in the object space coordinate system, the subscript 1 indicates the station number
Figure 776644DEST_PATH_IMAGE020
=1, subscriptWhich indicates the number of the picture,(ii) a The above equation is listed for all images acquired at station 1.
Method equation coefficient array constructed according to least square principle
Figure 973773DEST_PATH_IMAGE084
Sum constant term
Figure 967137DEST_PATH_IMAGE085
The formula of the normal equation is
Matrix of unknowns
Figure 789304DEST_PATH_IMAGE087
And integrally solving the coordinates of the origin of the image space coordinate system in the rotating coordinate system according to a normal equation
Figure 312689DEST_PATH_IMAGE038
And coordinates of the center of rotation in an object coordinate system
Figure 539271DEST_PATH_IMAGE041
。
7, reconstructing the rotation matrix according to the step 5
Figure 780896DEST_PATH_IMAGE030
And 6, coordinates of the origin of the image space coordinate system obtained in the step 6 in the rotating coordinate system
Figure 383916DEST_PATH_IMAGE038
The calculation result of (a), the known external orientation element (external orientation angle element) of the first image of the rest stations during the acquisition
Figure 761808DEST_PATH_IMAGE043
And elements of exterior orientation line) Horizontal angle of rotary platform around vertical rotary shaft
Figure 888213DEST_PATH_IMAGE045
And a vertical angle around the horizontal rotation axis
Figure 232606DEST_PATH_IMAGE046
And resolving the rotation matrix between the object coordinate system and the standard photogrammetric coordinate system under the condition of other stations through the rotation model and the eccentric modelAnd coordinates of the center of rotation in an object coordinate system
Figure 298968DEST_PATH_IMAGE048
(ii) a Wherein the subscript
Figure 311924DEST_PATH_IMAGE020
The number of the station is shown as,
Figure 194429DEST_PATH_IMAGE049
subscript 1 denotes a picture number
Figure 546913DEST_PATH_IMAGE021
=1。
The embodiment introduces the known elements of the external orientation angle at the first image acquisition of the remaining stations
Figure 551778DEST_PATH_IMAGE043
And elements of exterior orientation line
Figure 989713DEST_PATH_IMAGE044
The rotary platform being about a vertical axis of rotationHorizontal angle
Figure 738226DEST_PATH_IMAGE045
And a vertical angle around the horizontal rotation axis
Figure 945216DEST_PATH_IMAGE046
，
Angle of exterior orientation
Figure 58666DEST_PATH_IMAGE043
According toCorner system construction rotation matrix
Figure 267591DEST_PATH_IMAGE088
Elements of exterior orientation line
Figure 594668DEST_PATH_IMAGE044
Constructing a coordinate matrix of line elementsFrom a horizontal angle
Figure 88283DEST_PATH_IMAGE045
Perpendicular angle
Figure 178599DEST_PATH_IMAGE046
Constructing a rotation matrix
Figure 360181DEST_PATH_IMAGE090
；
Then reconstructing the rotation matrix from step 5
Figure 815433DEST_PATH_IMAGE030
Solving rotation matrix by substituting rotation model
Figure 511994DEST_PATH_IMAGE047
，
Figure 78104DEST_PATH_IMAGE091
Will rotate the matrix
Figure 442090DEST_PATH_IMAGE090
Rotation matrix
Figure 68243DEST_PATH_IMAGE047
And the coordinates obtained in step 6Substituting the calculation result into the eccentric model to calculate the coordinate matrix
Figure 621901DEST_PATH_IMAGE048
Figure 778076DEST_PATH_IMAGE092
Wherein the subscript
Figure 637448DEST_PATH_IMAGE020
The number of the station is shown as,
Figure 246284DEST_PATH_IMAGE049
subscript 1 denotes a picture number
Figure 154197DEST_PATH_IMAGE021
=1。
Step 8, according to the known horizontal angle of the rotating platform around the vertical rotating shaft when other images except the first image of the other measuring stations are obtained
Figure 227195DEST_PATH_IMAGE050
And a vertical angle around the horizontal rotation axis
Figure 195151DEST_PATH_IMAGE051
And resolving external orientation angle elements when other images except the first image of the rest stations are acquired through the rotation model and the eccentric model
Figure 356530DEST_PATH_IMAGE052
And elements of exterior orientation line
Figure 68134DEST_PATH_IMAGE053
Wherein the subscript
Figure 933321DEST_PATH_IMAGE020
The number of the station is shown as,
Figure 134496DEST_PATH_IMAGE049
subscript
Figure 717924DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 233219DEST_PATH_IMAGE054
。
embodiments rely on the horizontal angle of the rotating platform about the vertical axis of rotation for the acquisition of images from other stations than the firstAnd a vertical angle around the horizontal rotation axis
Figure 324988DEST_PATH_IMAGE051
Building a rotation matrix
Figure 458030DEST_PATH_IMAGE093
And rotating the rotation matrix obtained in the step 7
Figure 511436DEST_PATH_IMAGE047
And step 5 reconstructed rotation matrix
Figure 351216DEST_PATH_IMAGE030
Solving images in substitution rotation modelThe external orientation angle element at the time of acquisition is
Figure 894193DEST_PATH_IMAGE023
Downward rotation torque array of corner system
Figure 452213DEST_PATH_IMAGE094
And according toThe corner system further decomposes the external azimuth angle element
Figure 800335DEST_PATH_IMAGE052
The formula of solution is as follows
Will rotate the matrix
Figure 559530DEST_PATH_IMAGE047
Rotation matrixThe coordinates obtained in step 6
Figure 831428DEST_PATH_IMAGE038
Solution result and coordinate matrix of
Figure 653890DEST_PATH_IMAGE048
Substituting the eccentric model into a coordinate matrix for solving the elements of the external orientation line during image acquisition
Figure 980311DEST_PATH_IMAGE096
And further decomposing the elements of the exterior orientation line
Figure 179211DEST_PATH_IMAGE053
The formula of solution is as follows
Figure 848090DEST_PATH_IMAGE097
Wherein the subscript
Figure 903771DEST_PATH_IMAGE020
The number of the station is shown as,，
Figure 457429DEST_PATH_IMAGE020
is the actual total number of camera stations, subscript
Figure 980814DEST_PATH_IMAGE021
Which indicates the number of the picture,
Figure 410658DEST_PATH_IMAGE054
，the maximum value of (a) is the actual total number of corresponding camera images.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (6)

1. A multi-sheet integral adjustment calibration method for a rotary photogrammetric system is characterized by comprising the following steps:
step 1, importing the number N of images acquired by a first survey station and external orientation angle elements when each image is acquiredω1j,κ1jAnd the exterior orientation line element Xs1j,Ys1j,Zs1jHorizontal angle H of rotary platform around vertical rotary shaft1jAnd rotatingVertical angle V of rotary platform around horizontal rotary shaft1jWherein subscript 1 identifies station number i =1, subscript j denotes image number, j is 1, 2.. N, and the number of images N is greater than or equal to 3; angle of exterior orientation
Figure FDA00003386308900012
ω1j,κ1jAccording to
Figure FDA00003386308900013
Rotation angle system construction rotation matrix R1jFrom the exterior orientation line element Xs1j,Ys1j,Zs1jConstructing a coordinate matrix P of line elements1j＝(Xs1j,Ys1j,Zs1j)T；
Step 2, constructing a rotation model of the camera relative to an object space coordinate system, wherein the rotation model formula is as follows
R＝RSCRHVRI
Wherein R is an external azimuth element of the phase under the object space coordinate system
Figure FDA00003386308900014
Rotating the matrix under the corner system; rSCIs a rotation matrix between an object space coordinate system and a standard photogrammetric coordinate system; rHVA rotation matrix between a standard photographing coordinate system and a rotation coordinate system; rIIs a rotation matrix between a rotation coordinate system and an image space coordinate system;
respectively corresponding to the first three images obtained by the first measuring station1j＝RSC1RHV1jRIResolving the correspondence of the first station
Figure FDA00003386308900015
Rotation matrix R under corner systemSC1Corner of
Figure FDA00003386308900016
ωSC1,κSC1And a rotation matrix RICorner of
Figure FDA00003386308900017
ωI,κIAnd taking the obtained resolving result as an initial value of the unknown number, wherein a subscript 1 identifies a station number i =1, a subscript j represents an image number, j is 1,2,3, and R1jConstructing a rotation matrix for the step 1;
step 3, converting the rotation model into an error equation by using a rotation angleωSC1,κSC1And corner
Figure FDA00003386308900019
ωI,κIPerforming linearization processing on all images acquired by a first survey station one by one for an unknown number, constructing a normal equation according to an initial value of the unknown number and a least square principle, and solving the normal equation by integral adjustment to obtain an unknown number correction number;
step 4, if the maximum value of the correction number of the unknown number is smaller than a preset threshold value of the correction number of the unknown number or the iteration number exceeds a preset threshold value of the iteration number, executing step 5; otherwise, taking the current unknown number correction number as the initial value of the unknown number, and returning to the iteration execution step 3;
step 5, outputting the unknown number correction number obtained in the last iteration as a corner
Figure FDA000033863089000110
ωSC1,κSC1And corner
Figure FDA00003386308900021
ωI,κIAccording to the angle of rotation
Figure FDA00003386308900022
ωSC1,κSC1Reconstructing the rotation matrix R from the calibration resultsSC1According to the angle of rotation
Figure FDA00003386308900023
ωI,κIReconstructing the rotation matrix R from the calibration resultsI；
Step 6, constructing an eccentric model of the camera relative to an object space coordinate system, wherein the formula of the eccentric model is as follows
P＝RSCRHVTI+PC
Wherein P ═ Xs,Ys,Zs)TThe coordinate matrix is a coordinate matrix of the external azimuth line elements under the object space coordinate system; t isIThe coordinates of the origin of the image space coordinate system under the rotating coordinate system; pC＝(XC,YC,ZC)TA coordinate matrix of the rotation center under an object space coordinate system;
according to the eccentric model P of the camera relative to the object coordinate system1j＝RSC1RHV1jTI+PC1According to the image obtained by the first measuring station, an error equation and a normal equation are constructed one by one, and according to the least square principle, the coordinate T of the origin of the image space coordinate system under the rotating coordinate system is solved by the integral adjustmentIAnd the coordinate P of the rotation center in the object space coordinate systemC1Output the coordinate TIWherein, subscript 1 identifies station number i =1, subscript j denotes image number, j is 1,21jCoordinate matrix, R, constructed for step 1SC1Reconstructing the rotation matrix for the step 5;
7, reconstructing the rotation matrix R according to the step 5IAnd 6, obtaining the coordinate T of the origin of the image space coordinate system under the rotating coordinate systemIThe known external orientation angle element when the first image of the rest stations is acquired
Figure FDA00003386308900024
ωi1,κi1And the exterior orientation line element Xsi1,Ysi1,Zsi1Horizontal angle H of rotary platform around vertical rotary shafti1And a vertical angle V around the horizontal axis of rotationi1Re-solving in the rest by the rotation model and the eccentric modelRotation matrix R between object coordinate system and standard photogrammetric coordinate system under station-finding conditionSCiAnd the coordinate P of the rotation center in the object space coordinate systemCi(ii) a Wherein subscript i denotes a station number, i ═ 2, 3., and subscript 1 denotes an image number j = 1;
step 8, according to the horizontal angle H of the rotating platform around the vertical rotating shaft when other images except the first image of the other measuring stations are obtainedijAnd a vertical angle V around the horizontal axis of rotationijAnd resolving external orientation angle elements when other images except the first image of the rest stations are acquired through the rotation model and the eccentric model
Figure FDA00003386308900025
ωij,κijAnd the exterior orientation line element Xsij,Ysij,ZsijWherein the index i denotes the station number, i 2, 3.
2. The multi-slice integral adjustment calibration method for the rotational photogrammetry system of claim 1, characterized in that: respectively corresponding to the first three images obtained by the 1 st measuring station1jJ is 1,2,3, and resolving
Figure FDA00003386308900026
Rotation matrix R under corner systemSC1Corner of
Figure FDA00003386308900027
ωSC1,κSC1And a rotation matrix RICorner of
Figure FDA00003386308900028
ωI,κIThe concrete implementation mode is as follows,
the rotation model corresponding to the 1 st image is R11＝RSC1RHV11RI，
The rotation model corresponding to the 2 nd image is R12＝RSC1RHV12RI，
The rotation model corresponding to the 3 rd image is R13＝RSC1RHV13RI，
Wherein R isHV1jA rotation matrix between a standard shooting coordinate system and a rotation coordinate system corresponding to the j image acquired by the 1 st measuring station, wherein j is 1,2 and 3;
eliminating one group of unknowns to obtain
( R 11 R 12 - 1 ) R SC 1 = R SC 1 ( R HV 11 R HV 12 - 1 )
( R 12 R 13 - 1 ) R SC 1 = R SC 1 ( R HV 12 R HV 13 - 1 )
Wherein,
Figure FDA00003386308900031
Figure FDA00003386308900032
R HV = cos H 0 - sin H 0 1 0 sin H 0 cos H 1 0 0 0 cos V - sin V 0 sin V cos V
let the rotation matrix RSC1The middle lower right corner element is 1, RSC1The other eight elements in the matrix are used as unknown numbers X, and two formulas obtained by eliminating one group of unknown numbers are respectively expanded into nine equations about the eight unknown numbers; constructing a coefficient array A and a constant term L of a normal equation according to the least square principle, and resolving a rotation matrix RSC1The formula of the first eight element values, the normal equation is as follows
X＝(ATA)-1ATL
Obtaining a rotation matrix R according to the calculation resultSC1Solving the rotation matrix RIThen according toRelationship solution for corner systemRotation matrix R under corner systemSC1Corner of
Figure FDA00003386308900035
ωSC1,κSC1And a rotation matrix RICorner of
Figure FDA00003386308900036
ωI,κI。
The multi-slice global adjustment calibration method for the rotational photogrammetry system of claim 1, characterized in that: the specific operation method of the step 3 is as follows,
let F be R1j-RSC1RHV1jRI＝0
The rotation model is converted into the form of an error equation as follows,
Figure FDA00003386308900041
where V represents the residual of the error equation and the unknowns are
Figure FDA00003386308900042
Rotation matrix R under corner systemSC1Three corners of
Figure FDA00003386308900043
ωSC1,κSC1And a rotation matrix RIThree corners of
Figure FDA00003386308900044
ωI,κI，
Figure FDA00003386308900045
Andrespectively solving partial derivatives of the error matrix equation according to the six unknowns in sequence; v0Is a constant term of the error equation;
the error equations sequentially calculate the partial derivatives according to the six unknowns and sequentially list the partial derivatives to obtain nine basic forms of the error equations, and the error equations are listed for all the images acquired by the 1 st observation station; subscript 1 identifies station number i =1, subscript j denotes image number, j ═ 1, 2.. N;
constructing a coefficient array A 'and a constant term L' of a normal equation according to the least square principle according to the initial value of the unknown number, wherein the formula of the normal equation is as follows,
X'＝(A'TA')-1A'TL'
matrix of unknowns
Figure FDA00003386308900047
And solving the correction numbers of the six unknowns according to a law equation.
4. The multi-slice integral adjustment calibration method for the rotational photogrammetry system of claim 1,2 or 3, characterized in that: step 6 the specific operation method of constructing error equations and normal equations one by one from the images acquired at the first station is as follows,
the eccentric model is converted into an error equation form as follows
P 1 j = R SC 1 R HV 1 j E T I P C 1
Wherein E is an identity matrix, P1jIs the coordinate of the external azimuth line element under the object space coordinate system corresponding to the jth image of the 1 st station, PC1The index 1 represents the coordinate of the rotation center corresponding to the 1 st station in the object coordinate system, the index j represents the image number, and j is 1, 2.. N; the above equation is listed for all images acquired at the 1 st station;
constructing a coefficient array A 'and a constant term L' of a normal equation according to the least square principle, wherein the formula of the normal equation is
X"＝(A"TA")-1A"TL"
Unknown matrix X ═ (T)I,PC1)TAnd integrally solving the coordinate T of the origin of the image space coordinate system in the rotating coordinate system according to a normal equationIAnd the coordinate P of the rotation center in the object space coordinate systemC1。
5. The multi-slice integral adjustment calibration method for the rotational photogrammetry system of claim 4, characterized in that: the specific operation method of the step 7 is as follows,
according to the known external orientation angle element when the first image of the rest stations is acquired
Figure FDA00003386308900051
ωi1,κi1And the exterior orientation line element Xsi1,Ysi1,Zsi1Horizontal angle H of rotary platform around vertical rotary shafti1And a vertical angle V around the horizontal axis of rotationi1，
Angle of exterior orientation
Figure FDA00003386308900052
ωi1,κi1According to
Figure FDA00003386308900053
Rotation angle system construction rotation matrix Ri1From the exterior orientation line element Xsi1,Ysi1,Zsi1Building a line elementCoordinate matrix P of elementsi1＝(Xsi1,Ysi1,Zsi1)TFrom horizontal angle Hi1Perpendicular angle Vi1Constructing a rotation matrix RHVi1；
Then reconstructing the rotation matrix R reconstructed in the step 5ISolving a rotation matrix R in a substitution rotation modelSCi，
R SCi = R i 1 R I - 1 R HVi 1 - 1
Will rotate the matrix RHVi1A rotation matrix RSCiAnd the coordinates T obtained in step 6ISubstituting the calculation result into the eccentric model to calculate the coordinate matrix PCi
PCi＝Pi1-RSCiRHVi1TI
Where subscript i denotes the station number, i ═ 2, 3.
6. The multi-slice integral adjustment calibration method for the rotational photogrammetry system of claim 5, characterized in that: the specific operation method of the step 8 is as follows,
according to the horizontal angle H of the rotating platform around the vertical rotating shaft when other images except the first image of other measuring stations are obtainedijAnd a vertical angle V around the horizontal axis of rotationijBuilding a rotation matrix RHVijAnd the rotation matrix R obtained in the step 7 is usedSCiAnd step 5. reconstructed rotation matrix RISubstituting into the rotation model to calculate the external orientation angle element when the image is acquired
Figure FDA00003386308900055
Rotation matrix R under corner systemijAnd according to
Figure FDA00003386308900056
The corner system further decomposes the external azimuth angle element
Figure FDA00003386308900057
ωij,κijThe formula of solution is as follows
Rij＝RSCiRHVijRI
Will rotate the matrix RSCiA rotation matrix RHVijAnd 6, obtaining a coordinate TIThe result of the solution and the coordinate matrix PCiSubstituting the obtained coordinate matrix P of the exterior orientation line elements into the eccentric model to solve the image acquisitionijAnd further decomposing an exterior orientation line element Xsij,Ysij,ZsijThe formula of solution is as follows
Pij＝RSCiRHVijTI+PCi
Where the index i denotes the station number, i 2, 3.
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柯涛等.旋转多基线数字近景摄影测量.《武汉大学学报·信息科学版》.2009,第34卷(第1期),第44-47,51页.

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