CN102519484B - Multi-disc overall adjustment calibration method of rotary photogrammetry system - Google Patents
Multi-disc overall adjustment calibration method of rotary photogrammetry system Download PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- rotation
- matrix
- coordinate system
- image
- angle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 37
- 239000011159 matrix material Substances 0.000 claims description 165
- 238000012937 correction Methods 0.000 claims description 21
- 238000010276 construction Methods 0.000 claims description 6
- 238000012545 processing Methods 0.000 claims description 2
- 238000006467 substitution reaction Methods 0.000 claims description 2
- HOWHQWFXSLOJEF-MGZLOUMQSA-N systemin Chemical compound NCCCC[C@H](N)C(=O)N[C@@H](CCSC)C(=O)N[C@@H](CCC(N)=O)C(=O)N[C@@H]([C@@H](C)O)C(=O)N[C@@H](CC(O)=O)C(=O)OC(=O)[C@@H]1CCCN1C(=O)[C@H]1N(C(=O)[C@H](CC(O)=O)NC(=O)[C@H](CCCN=C(N)N)NC(=O)[C@H](CCCCN)NC(=O)[C@H](CO)NC(=O)[C@H]2N(CCC2)C(=O)[C@H]2N(CCC2)C(=O)[C@H](CCCCN)NC(=O)[C@H](CO)NC(=O)[C@H](CCC(N)=O)NC(=O)[C@@H](NC(=O)[C@H](C)N)C(C)C)CCC1 HOWHQWFXSLOJEF-MGZLOUMQSA-N 0.000 description 2
- 238000007792 addition Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 108010050014 systemin Proteins 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Images
Landscapes
- Image Processing (AREA)
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
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 horizontallyAnd a vertical rotation axisPoint of intersection ofCentered rectangular spatial coordinate systemIn (1),andare respectively like principal pointsRelative toIs spotted onThe shaft is provided with a plurality of axial holes,shaft andthe offset of the shaft is such that,is the photographic focal length. Wherein the rotary platform of the system is around the horizontal axisAnd a vertical axisWhen rotating, the exterior orientation element of the cameraAnd will vary accordingly. According to the vertical rotation angleAnd horizontal rotation angleThe 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 stationAnd the external orientation angle element when each image is acquiredAnd elements of exterior orientation lineHorizontal angle of rotary platform around vertical rotary shaftAnd the vertical angle of the rotary platform about the horizontal axis of rotationWherein the subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,number of imagesGreater than or equal to 3; angle of exterior orientationAccording toCorner system construction rotation matrixElements of exterior orientation lineConstructing a coordinate matrix of line elements;
Wherein,is an off-machine azimuth element under an object space coordinate systemRotating the matrix under the corner system;is a rotation matrix between an object space coordinate system and a standard photogrammetric coordinate system;a rotation matrix between a standard photographing coordinate system and a rotation coordinate system;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 stationDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner ofAnd taking the obtained resolving result as an initial value of an unknown number, wherein the subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,,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 cornerAnd cornerAccording to the angle of rotationReconstructing 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
WhereinThe 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;a coordinate matrix of the rotation center under an object space coordinate system;
off-center model from camera relative to object coordinate systemAccording 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 systemOutput coordinatesWherein subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,,for the coordinate matrix constructed in step 1,reconstructing the rotation matrix for the step 5;
7, reconstructing the rotation matrix according to the step 5And 6, coordinates of the origin of the image space coordinate system obtained in the step 6 in the rotating coordinate systemThe known external orientation angle element when the first image of the rest stations is acquiredAnd elements of exterior orientation lineHorizontal angle of rotary platform around vertical rotary shaftAnd a vertical angle around the horizontal rotation axisAnd 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(ii) a Wherein the subscriptThe number of the station is shown as,subscript 1 denotes a picture number=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 axisAnd 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 modelAnd elements of exterior orientation lineWherein the subscriptThe number of the station is shown as,subscriptWhich indicates the number of the picture,。
and, according to the rotation model corresponding to the first three images obtained from the 1 st station,Resolving toDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner ofThe concrete implementation mode is as follows,
Wherein,acquired for the 1 st stationA rotation matrix between the standard photographing coordinate system and the rotation coordinate system corresponding to the sheet image,;
eliminating one group of unknowns to obtain
Wherein,
order rotation matrixThe element in the middle-right lower corner is 1,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 principleSum constant termResolving the rotation matrixThe formula of the first eight element values, the normal equation is as follows
Obtaining a rotation matrix according to the calculation resultResolving a rotation matrixThen according toRelationship solution for corner systemDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner of。
Furthermore, the specific operation method of step 3 is as follows,
The rotation model is converted into the form of an error equation as follows,
wherein,representing the residual of the error equation, unknowns beingDownward rotation torque array of corner systemThree corners ofAnd a rotation matrixThree corners of, ,,,,Andrespectively solving partial derivatives of the error matrix equation according to the six unknowns in sequence;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=1, subscriptWhich indicates the number of the picture,;
constructing a coefficient array of a normal equation according to the least square principle according to the initial value of the unknown numberSum constant termThe formula of the normal equation is as follows,
。
matrix of unknownsAnd 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
WhereinIs a matrix of the units,for the 1 st stationThe coordinate of the external azimuth line element under the object coordinate system corresponding to each image,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, subscriptWhich indicates the number of the picture,(ii) a The above equation is set forth for all images acquired at station 1
Method equation coefficient array constructed according to least square principleSum constant termThe formula of the normal equation is
Matrix of unknownsAnd integrally solving the coordinates of the origin of the image space coordinate system in the rotating coordinate system according to a normal equationAnd coordinates of the center of rotation in an object coordinate system。
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 acquiredAnd elements of exterior orientation lineHorizontal angle of rotary platform around vertical rotary shaftAnd a vertical angle around the horizontal rotation axis,
Angle of exterior orientationAccording toCorner system construction rotation matrixElements of exterior orientation lineConstructing a coordinate matrix of line elementsFrom a horizontal anglePerpendicular angleConstructing a rotation matrix;
Then reconstructing the rotation matrix from step 5Solving rotation matrix by substituting rotation model,
Will rotate the matrixRotation matrixAnd the coordinates obtained in step 6Substituting the calculation result into the eccentric model to calculate the coordinate matrix
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 axisBuilding a rotation matrixAnd rotating the rotation matrix obtained in the step 7And step 5 reconstructed rotation matrixSubstituting into the rotation model to calculate the external orientation angle element when the image is acquiredDownward rotation torque array of corner systemAnd according toThe corner system further decomposes the external azimuth angle elementThe formula of solution is as follows
Will rotate the matrixRotation matrixThe coordinates obtained in step 6Solution result and coordinate matrix ofSubstituting the eccentric model into a coordinate matrix for solving the elements of the external orientation line during image acquisitionAnd further decomposing the elements of the exterior orientation lineThe formula of solution is as follows
Wherein the subscriptThe number of the station is shown as,subscriptWhich indicates the number of the picture,。
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, whereinIs the intersection point in FIG. 1In the object space coordinate systemCoordinates of the lower part;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;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;andare the same as in FIG. 1, and are the principal pointsRelative toIs spotted onThe shaft is provided with a plurality of axial holes,shaft andthe 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:
whereinIs an off-machine azimuth element under an object space coordinate systemThe expansion form of the rotation matrix under the corner system is as follows:
Is a rotation matrix between the object coordinate system and the standard photogrammetry coordinate system, which is expanded as above:
wherein,is composed ofLower rotation of corner systemMatrix arrayThe corner of (c). For multiple images acquired by a fixed station, the rotation matrixThe value of (a) is not changed.
Is a rotation matrix between a standard photographic coordinate system and a rotation coordinate system, and the expansion form is as follows:
the matrix being formed by the horizontal angle of the rotating platform about the vertical axis of rotationAnd the vertical angle of the rotary platform about the horizontal axis of rotationAnd (5) constructing. For each image, the matrix changes as the rotational pose changes.
Is a rotation matrix between a rotation coordinate system and an image space coordinate system, the matrix still followingAnd 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.
2. The decentration model of the camera with respect to the object coordinate system is based on the following formula:
whereinIs an external azimuth line element under the object space coordinate systemThe coordinate matrix of (2).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 coordinatesValue on the X axisCoordinates of the sameValue on the Y axisCoordinates of the sameValue in Z axisThe matrix remains unchanged for all images acquired at all stations for the system internal parameters that need to be calibrated.Is a center of rotationAnd 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(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 shaftAnd the vertical angle of the rotary platform about the horizontal axis of rotationWherein the subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,(ii) a Angle of exterior orientationAccording toCorner system construction rotation matrixElements of exterior orientation lineConstructing a coordinate matrix of line elements。
Wherein,is an off-machine azimuth element under an object space coordinate systemRotating the matrix under the corner system;is a rotation matrix between an object space coordinate system and a standard photogrammetric coordinate system;the horizontal angle is the rotation matrix between the standard photographic coordinate system and the rotation coordinate system according to step 1And vertical angleConstructing;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 stationDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner ofAnd taking the obtained resolving result as an initial value of an unknown number, wherein the subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,,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,Resolving toDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner ofThe concrete implementation mode is as follows,
Wherein,acquired for the 1 st stationA rotation matrix between the standard photographing coordinate system and the rotation coordinate system corresponding to the sheet image,horizontal angle of the rotary platform about vertical axis of rotation introduced according to step 1And the vertical angle of the rotary platform about the horizontal axis of rotationConstructing;
wherein,
the result of the calculation of (a) is a 3 × 3 matrix of 9 elements in total. Order rotation matrixThe element in the middle-right lower corner is 1,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 principleSum constant termResolving the rotation matrixThe formula of the first eight element values, the normal equation, is as follows:
obtaining a rotation matrix according to the calculation resultResolving a rotation matrixThe concrete mode is as follows: rearrangementThe 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 byAfter the matrix is obtained, the matrix can be substituted into the rotation model corresponding to the first imageIn (1) resolvingThe values of the matrix.
Then followRelationship solution for corner systemDownward rotation torque array of corner systemCorner ofAnd a rotation matrixCorner of。
Step 3, converting the rotation model into an error equation by using a rotation angleAnd cornerAnd (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.
Example a rotation model is converted into the form of an error equation as follows,
wherein,representing the residual of the error equation, unknowns beingDownward rotation torque array of corner systemThree corners ofAnd a rotation matrixThree corners of;
,,,,Andpartial derivatives respectively solved for the error matrix equation according to the six unknowns in turn;Is a constant term of the error equation.
The matrices in the error equation are all 3And 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=1, subscriptWhich indicates the number of the picture,. In step 2Andthe 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 principleSum constant term。
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 cornerAnd cornerAccording to the angle of rotationReconstructing 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
WhereinThe 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;a coordinate matrix of the rotation center under an object space coordinate system;
off-center model from camera relative to object coordinate systemAccording 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 systemOutput coordinatesWherein subscript 1 identifies the station number=1, subscriptWhich indicates the number of the picture,,for the coordinate matrix constructed in step 1,the rotation matrix reconstructed for step 5.
Example conversion of the eccentric model into equation form
WhereinIs a matrix of the units,for the 1 st stationThe coordinate of the external azimuth line element under the object coordinate system corresponding to each image,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, 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 principleSum constant termThe formula of the normal equation is
Matrix of unknownsAnd integrally solving the coordinates of the origin of the image space coordinate system in the rotating coordinate system according to a normal equationAnd coordinates of the center of rotation in an object coordinate system。
7, reconstructing the rotation matrix according to the step 5And 6, coordinates of the origin of the image space coordinate system obtained in the step 6 in the rotating coordinate systemThe calculation result of (a), the known external orientation element (external orientation angle element) of the first image of the rest stations during the acquisitionAnd elements of exterior orientation line) Horizontal angle of rotary platform around vertical rotary shaftAnd a vertical angle around the horizontal rotation axisAnd 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(ii) a Wherein the subscriptThe number of the station is shown as,subscript 1 denotes a picture number=1。
The embodiment introduces the known elements of the external orientation angle at the first image acquisition of the remaining stationsAnd elements of exterior orientation lineThe rotary platform being about a vertical axis of rotationHorizontal angleAnd a vertical angle around the horizontal rotation axis,
Angle of exterior orientationAccording toCorner system construction rotation matrixElements of exterior orientation lineConstructing a coordinate matrix of line elementsFrom a horizontal anglePerpendicular angleConstructing a rotation matrix;
Then reconstructing the rotation matrix from step 5Solving rotation matrix by substituting rotation model,
Will rotate the matrixRotation matrixAnd the coordinates obtained in step 6Substituting the calculation result into the eccentric model to calculate the coordinate matrix
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 axisAnd 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 modelAnd elements of exterior orientation lineWherein the subscriptThe number of the station is shown as,subscriptWhich indicates the number of the picture,。
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 axisBuilding a rotation matrixAnd rotating the rotation matrix obtained in the step 7And step 5 reconstructed rotation matrixSolving images in substitution rotation modelThe external orientation angle element at the time of acquisition isDownward rotation torque array of corner systemAnd according toThe corner system further decomposes the external azimuth angle elementThe formula of solution is as follows
Will rotate the matrixRotation matrixThe coordinates obtained in step 6Solution result and coordinate matrix ofSubstituting the eccentric model into a coordinate matrix for solving the elements of the external orientation line during image acquisitionAnd further decomposing the elements of the exterior orientation lineThe formula of solution is as follows
Wherein the subscriptThe number of the station is shown as,,is the actual total number of camera stations, subscriptWhich indicates the number of the picture,,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 orientationω1j,κ1jAccording toRotation 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 systemRotating 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 stationRotation matrix R under corner systemSC1Corner ofωSC1,κSC1And a rotation matrix RICorner ofωI,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 cornerωI,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 cornerωSC1,κSC1And cornerωI,κIAccording to the angle of rotationωSC1,κSC1Reconstructing the rotation matrix R from the calibration resultsSC1According to the angle of rotationωI,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 acquiredωi1,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 modelωij,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 resolvingRotation matrix R under corner systemSC1Corner ofωSC1,κSC1And a rotation matrix RICorner ofωI,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
Wherein,
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
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,
where V represents the residual of the error equation and the unknowns areRotation matrix R under corner systemSC1Three corners ofωSC1,κSC1And a rotation matrix RIThree corners ofωI,κI,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'
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
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 acquiredωi1,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 orientationωi1,κi1According toRotation 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,
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 acquiredRotation matrix R under corner systemijAnd according toThe corner system further decomposes the external azimuth angle elementωij,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.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN 201110385815 CN102519484B (en) | 2011-11-29 | 2011-11-29 | Multi-disc overall adjustment calibration method of rotary photogrammetry system |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN 201110385815 CN102519484B (en) | 2011-11-29 | 2011-11-29 | Multi-disc overall adjustment calibration method of rotary photogrammetry system |
Publications (2)
Publication Number | Publication Date |
---|---|
CN102519484A CN102519484A (en) | 2012-06-27 |
CN102519484B true CN102519484B (en) | 2013-09-18 |
Family
ID=46290487
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN 201110385815 Active CN102519484B (en) | 2011-11-29 | 2011-11-29 | Multi-disc overall adjustment calibration method of rotary photogrammetry system |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN102519484B (en) |
Families Citing this family (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106595602B (en) * | 2016-10-31 | 2019-06-25 | 武汉市工程科学技术研究院 | Relative orientation method based on homonymous line feature |
CN108303117B (en) * | 2017-01-12 | 2020-06-02 | 中国农业大学 | Method and system for measuring parameters of cloud mirror camera system based on back intersection measurement |
CN107192375B (en) * | 2017-04-28 | 2019-05-24 | 北京航空航天大学 | A kind of unmanned plane multiple image adaptive location bearing calibration based on posture of taking photo by plane |
CN108447100B (en) * | 2018-04-26 | 2020-02-11 | 王涛 | Method for calibrating eccentricity vector and visual axis eccentricity angle of airborne three-linear array CCD camera |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
GB727235A (en) * | ||||
CN101196396A (en) * | 2007-12-12 | 2008-06-11 | 武汉大学 | Linear array push-broom type image optimum scanning line search method based on object space projection geometrical constraint |
CN101464149A (en) * | 2008-12-31 | 2009-06-24 | 武汉大学 | POS auxiliary aviation image matching method |
-
2011
- 2011-11-29 CN CN 201110385815 patent/CN102519484B/en active Active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
GB727235A (en) * | ||||
CN101196396A (en) * | 2007-12-12 | 2008-06-11 | 武汉大学 | Linear array push-broom type image optimum scanning line search method based on object space projection geometrical constraint |
CN101464149A (en) * | 2008-12-31 | 2009-06-24 | 武汉大学 | POS auxiliary aviation image matching method |
Non-Patent Citations (2)
Title |
---|
旋转多基线数字近景摄影测量;柯涛等;《武汉大学学报·信息科学版》;20090131;第34卷(第1期);第44-47,51页 * |
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. |
Also Published As
Publication number | Publication date |
---|---|
CN102519484A (en) | 2012-06-27 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN113532311B (en) | Point cloud splicing method, device, equipment and storage equipment | |
CN109118545B (en) | Three-dimensional imaging system calibration method and system based on rotating shaft and binocular camera | |
CN103759716B (en) | The dynamic target position of mechanically-based arm end monocular vision and attitude measurement method | |
CN107367229B (en) | Free binocular stereo vision rotating shaft parameter calibration method | |
CN106403902A (en) | Satellite-ground cooperative in-orbit real-time geometric positioning method and system for optical satellites | |
CN106643669B (en) | A kind of more camera lens multi-detector aerial camera single centre projection transform methods | |
CN104537707B (en) | Image space type stereoscopic vision moves real-time measurement system online | |
CN110969665B (en) | External parameter calibration method, device, system and robot | |
CN104501779A (en) | High-accuracy target positioning method of unmanned plane on basis of multi-station measurement | |
CN108106637B (en) | Precision calibration method and device for distributed POS (point of sale) | |
CN106885585B (en) | Integrated calibration method of satellite-borne photogrammetry system based on light beam adjustment | |
CN103697864B (en) | A kind of narrow visual field double camera image splicing method based on large virtual camera | |
CN107038753B (en) | Stereoscopic vision three-dimensional reconstruction system and method | |
CN110782498B (en) | Rapid universal calibration method for visual sensing network | |
CN102519484B (en) | Multi-disc overall adjustment calibration method of rotary photogrammetry system | |
CN108663043B (en) | Single-camera-assisted distributed POS main node and sub node relative pose measurement method | |
CN106871900A (en) | Image matching positioning method in ship magnetic field dynamic detection | |
CN110246194A (en) | Method for quickly calibrating rotation relation between camera and inertia measurement unit | |
CN113870366B (en) | Calibration method and calibration system of three-dimensional scanning system based on pose sensor | |
CN105374067A (en) | Three-dimensional reconstruction method based on PAL cameras and reconstruction system thereof | |
CN110793542A (en) | Area array optical remote sensing satellite in-orbit geometric calibration method based on generalized probe element pointing angle | |
CN101545775A (en) | Method for calculating orientation elements of photo and the height of building by utilizing digital map | |
Pi et al. | On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite | |
CN109029379B (en) | High-precision small-base-height-ratio three-dimensional mapping method | |
Wu | Photogrammetry: 3-D from imagery |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
C14 | Grant of patent or utility model | ||
GR01 | Patent grant |