CN102519484A - 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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CN102519484A
CN102519484A CN2011103858152A CN201110385815A CN102519484A CN 102519484 A CN102519484 A CN 102519484A CN 2011103858152 A CN2011103858152 A CN 2011103858152A CN 201110385815 A CN201110385815 A CN 201110385815A CN 102519484 A CN102519484 A CN 102519484A
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matrix
rotation
rotation matrix
image
corner
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CN102519484B (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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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 the multiple 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 calibration of 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 be automatically solved at high precision by simply providing the horizontal and vertical rotation angles of the rotation platform when other images are imaged.

Description

A kind of rotation Digital Photogrammetric System multi-disc overall adjustment scaling method
Technical field
The present invention relates to the photogrammetric technology field, especially relate to a kind of rotation Digital Photogrammetric System multi-disc overall adjustment scaling method.
Background technology
The rotation Digital Photogrammetric System is that camera is placed on the platform of can be vertically and horizontally rotating, and is rotated photogrammetric system, is widely used in obtaining of three-dimensional information in close-range photogrammetry and the computer vision field.As shown in Figure 1; At the intersection point
Figure 928430DEST_PATH_IMAGE003
with feathering axis
Figure 624487DEST_PATH_IMAGE001
and vertical rotating shaft
Figure 2011103858152100002DEST_PATH_IMAGE002
is in the rectangular coordinate system in space
Figure 2011103858152100002DEST_PATH_IMAGE004
at center;
Figure 531449DEST_PATH_IMAGE005
and
Figure 2011103858152100002DEST_PATH_IMAGE006
is respectively principal point
Figure 968728DEST_PATH_IMAGE007
and puts at
Figure 2011103858152100002DEST_PATH_IMAGE008
axle with respect to
Figure 631791DEST_PATH_IMAGE003
; The side-play amount of
Figure 95133DEST_PATH_IMAGE009
axle axle with
Figure 2011103858152100002DEST_PATH_IMAGE010
,
Figure 564161DEST_PATH_IMAGE011
is the photography focal length.Wherein when the rotation platform of system during around transverse axis
Figure 62138DEST_PATH_IMAGE001
and Z-axis
Figure 568206DEST_PATH_IMAGE002
rotation, the elements of exterior orientation of camera
Figure 2011103858152100002DEST_PATH_IMAGE012
also can change thereupon.For obtain the elements of exterior orientation of camera automatically according to vertical rotation angle
Figure 846740DEST_PATH_IMAGE013
and feathering angle ; Need high-precision system calibrating, confirm rotation matrix and the eccentric coordinate of internal system camera with respect to rotation platform.The demarcation of many rotation Digital Photogrammetric System is the committed steps that from two-dimensional image, obtain this process of three-dimensional information, is an important research project.
Existing camera calibration method is broadly divided into three types: traditional scaling method, mark standardization method and based on the scaling method of active vision certainly.The tradition scaling method utilizes the known object of geomery as demarcating thing, takes the corresponding relation that some width of cloth images resolve picture side and object space with video camera; Self-calibrating method need not demarcated thing, but needs to demarcate through the relation of match point in the captured demarcation picture of motion cameras; And need foresee the detailed movement information of video camera based on the scaling method of active vision, and this needs expensive equipment that the movement locus of video camera is carried out record, and experimentation cost is higher.
Summary of the invention
The present invention solves existing in prior technology the problems referred to above, and a kind of level of utilizing single survey station to obtain the elements of exterior orientation of many images and rotation platform, vertical swing angle are provided, and is rotated Digital Photogrammetric System and demarcates the method for handling.
Technical scheme of the present invention is a kind of rotation Digital Photogrammetric System multi-disc overall adjustment scaling method, may further comprise the steps:
Step 1; Import image number
Figure 791563DEST_PATH_IMAGE015
, the foreign side's parallactic angle element when each image obtains
Figure 2011103858152100002DEST_PATH_IMAGE016
and outer orientation line element
Figure 206363DEST_PATH_IMAGE017
that first survey station obtains, rotation platform around the horizontal angle
Figure 2011103858152100002DEST_PATH_IMAGE018
of vertical rotating shaft and rotation platform vertical angle
Figure 945649DEST_PATH_IMAGE019
around feathering axis; Wherein subscript 1 sign is surveyed station number
Figure 2011103858152100002DEST_PATH_IMAGE020
=1; Subscript
Figure 448830DEST_PATH_IMAGE021
expression image number;
Figure 2011103858152100002DEST_PATH_IMAGE022
, image number
Figure 197344DEST_PATH_IMAGE015
is more than or equal to 3; According to
Figure 580100DEST_PATH_IMAGE023
corner system constructing rotation matrix
Figure 2011103858152100002DEST_PATH_IMAGE024
, make up the coordinates matrix of line element by foreign side's parallactic angle element
Figure 404334DEST_PATH_IMAGE016
by outer orientation line element
Figure 567648DEST_PATH_IMAGE017
;
Step 2 makes up the rotating model of camera with respect to object coordinates system, and the rotating model formula is following
Figure 2011103858152100002DEST_PATH_IMAGE026
Wherein,
Figure 181349DEST_PATH_IMAGE027
is camera foreign side parallactic angle element rotation matrix under
Figure 465700DEST_PATH_IMAGE023
corner system under the object coordinates system;
Figure 2011103858152100002DEST_PATH_IMAGE028
is the rotation matrix between object coordinates system and standard photogrammetric coordinate system;
Figure 674964DEST_PATH_IMAGE029
is the rotation matrix between standard photographic coordinate system and rotating coordinate system;
Figure 2011103858152100002DEST_PATH_IMAGE030
is the rotation matrix between rotating coordinate system and image space coordinate system;
First three image according to first survey station obtains is distinguished corresponding rotating model ; Resolve the corner
Figure 523819DEST_PATH_IMAGE033
of rotation matrix under corresponding
Figure 9180DEST_PATH_IMAGE023
the corner system of first survey station and the corner
Figure 2011103858152100002DEST_PATH_IMAGE034
of rotation matrix
Figure 485959DEST_PATH_IMAGE030
; And resolve the initial value of result as unknown number with gained; Wherein, Subscript 1 sign is surveyed station number
Figure 114386DEST_PATH_IMAGE020
=1; Subscript
Figure 150475DEST_PATH_IMAGE021
expression image number;
Figure 776629DEST_PATH_IMAGE035
,
Figure 960485DEST_PATH_IMAGE024
are the rotation matrix that step 1 makes up;
Step 3; Rotating model is converted into error equation; With corner
Figure 330287DEST_PATH_IMAGE033
and corner is unknown number; All images that first survey station is obtained carry out linearization process one by one; Initial value according to unknown number makes up normal equation according to the principle of least square; Overall adjustment solving method equation obtains the unknown number correction;
Step 4, if unknown number correction maximal value surpasses preset iterations threshold value less than preset unknown number correction threshold value or iterations, then execution in step 5; Otherwise the initial value so that current unknown number correction is a unknown number returns iteration execution in step 3;
Step 5; Export the unknown number correction that obtains in the last iteration; Calibration result as corner and corner
Figure 16986DEST_PATH_IMAGE034
; Again set up rotation matrix
Figure 997897DEST_PATH_IMAGE032
according to the calibration result of corner , follow according to the calibration result of corner
Figure 965853DEST_PATH_IMAGE034
and set up rotation matrix
Figure 61985DEST_PATH_IMAGE030
again;
Step 6 makes up the eccentric model of camera with respect to object coordinates system, and eccentric model formation is following
Figure 2011103858152100002DEST_PATH_IMAGE036
Wherein
Figure 835906DEST_PATH_IMAGE037
is the coordinates matrix of camera outer orientation line element under the object coordinates system;
Figure 2011103858152100002DEST_PATH_IMAGE038
is the coordinate of image space coordinate system initial point under rotating coordinate system; is the coordinates matrix of rotation center under object coordinates system;
According to the eccentric model
Figure 2011103858152100002DEST_PATH_IMAGE040
of camera with respect to object coordinates system; The image that obtains according to first survey station makes up error equation and normal equation one by one; According to the principle of least square; Overall adjustment is resolved coordinate
Figure 233094DEST_PATH_IMAGE038
and rotation center the coordinate under object coordinates system of image space coordinate system initial point under rotating coordinate system; Output coordinate
Figure 128555DEST_PATH_IMAGE038
resolve the result; Wherein, Subscript 1 sign is surveyed station number =1; Subscript
Figure 485904DEST_PATH_IMAGE021
expression image number;
Figure 353366DEST_PATH_IMAGE022
;
Figure 2011103858152100002DEST_PATH_IMAGE042
is the coordinates matrix that step 1 makes up, and
Figure 406772DEST_PATH_IMAGE032
is the rotation matrix that step 5 is set up again;
Step 7; Again rotation matrix of setting up according to step 5
Figure 308869DEST_PATH_IMAGE030
and the coordinate of step 6 gained image space coordinate system initial point under rotating coordinate system resolve result, the foreign side's parallactic angle element
Figure 409866DEST_PATH_IMAGE043
when known first image of all the other survey stations obtains and outer orientation line element
Figure 2011103858152100002DEST_PATH_IMAGE044
, rotation platform around the horizontal angle
Figure 63702DEST_PATH_IMAGE045
of vertical rotating shaft with around the vertical angle
Figure 2011103858152100002DEST_PATH_IMAGE046
of feathering axis; Again resolve under all the other survey station conditions rotation matrix
Figure 106392DEST_PATH_IMAGE047
between object coordinates system and standard photogrammetric coordinate system and the rotation center coordinate
Figure 2011103858152100002DEST_PATH_IMAGE048
under object coordinates system through rotating model and eccentric model; Wherein station number is surveyed in subscript expression; , subscript 1 expression image number
Figure 57534DEST_PATH_IMAGE021
=1;
Step 8; Rotation platform is around the horizontal angle
Figure 2011103858152100002DEST_PATH_IMAGE050
of vertical rotating shaft with around the vertical angle
Figure 934223DEST_PATH_IMAGE051
of feathering axis when obtaining according to other images beyond first of all the other known survey station; Foreign side's parallactic angle element
Figure 2011103858152100002DEST_PATH_IMAGE052
and outer orientation line element
Figure 819002DEST_PATH_IMAGE053
when resolving through rotating model and eccentric model that other images obtain beyond first of all the other survey station; Wherein station number is surveyed in subscript expression; ; Subscript
Figure 517596DEST_PATH_IMAGE021
expression image number,
Figure 2011103858152100002DEST_PATH_IMAGE054
.
Moreover, according to the first station to obtain an image corresponding to the first three rotation model ,
Figure 327606DEST_PATH_IMAGE035
, solver corner system rotation matrix
Figure 915899DEST_PATH_IMAGE032
corner
Figure 139552DEST_PATH_IMAGE033
and the rotation matrix
Figure 381177DEST_PATH_IMAGE030
corner
Figure 984197DEST_PATH_IMAGE034
,? specific implementation in the following manner,
The 1st the corresponding rotating model of image is
Figure 362088DEST_PATH_IMAGE055
The 2nd the corresponding rotating model of image is
Figure 2011103858152100002DEST_PATH_IMAGE056
The 3rd the corresponding rotating model of image is
Figure 25151DEST_PATH_IMAGE057
Wherein,
Figure 2011103858152100002DEST_PATH_IMAGE058
is that the 1st
Figure 550810DEST_PATH_IMAGE021
that survey station obtains opens corresponding standard photographic coordinate system of image and the rotation matrix between rotating coordinate system,
Figure 895204DEST_PATH_IMAGE035
;
Eliminate wherein one group of unknown number, obtain
Figure 189919DEST_PATH_IMAGE059
Wherein,
Figure 2011103858152100002DEST_PATH_IMAGE062
Figure 36838DEST_PATH_IMAGE063
Making the element in the lower right corner in the rotation matrix
Figure 2011103858152100002DEST_PATH_IMAGE064
is 1; All the other eight elements are as unknown number
Figure 334144DEST_PATH_IMAGE008
in
Figure 981660DEST_PATH_IMAGE064
matrix, and one group of unknown number gained two formula expands into nine equations about these eight unknown numbers respectively with eliminating wherein; Make up the factor arrays
Figure 341939DEST_PATH_IMAGE065
and the constant term
Figure 2011103858152100002DEST_PATH_IMAGE066
of normal equation according to the principle of least square; Resolve the value of the first eight element in the rotation matrix
Figure 842191DEST_PATH_IMAGE064
, the formula of normal equation is following
Figure 528387DEST_PATH_IMAGE067
Gained rotation matrix
Figure 797694DEST_PATH_IMAGE064
resolves rotation matrix
Figure 911144DEST_PATH_IMAGE030
according to resolving as a result, resolves the corner of rotation matrix under corner system and the corner
Figure 34006DEST_PATH_IMAGE034
of rotation matrix
Figure 6007DEST_PATH_IMAGE030
according to the relation of corner system then.
And step 3 concrete operation method is following,
Make
Figure 2011103858152100002DEST_PATH_IMAGE068
It is following that rotating model is converted into the error equation form,
Figure 277906DEST_PATH_IMAGE069
Wherein, The residual error of
Figure 2011103858152100002DEST_PATH_IMAGE070
expression error equation; Unknown number is three corners of rotation matrix
Figure 429719DEST_PATH_IMAGE032
under
Figure 795475DEST_PATH_IMAGE023
corner system; And three corners
Figure 45355DEST_PATH_IMAGE034
of rotation matrix
Figure 356885DEST_PATH_IMAGE030
;
Figure 166895DEST_PATH_IMAGE071
;
Figure 2011103858152100002DEST_PATH_IMAGE072
;
Figure 599013DEST_PATH_IMAGE073
;
Figure 2011103858152100002DEST_PATH_IMAGE074
, and
Figure 2011103858152100002DEST_PATH_IMAGE076
is respectively the error matrix equation according to above-mentioned six partial derivatives that unknown number is found the solution successively;
Figure 676876DEST_PATH_IMAGE077
is the constant term of error equation;
Error equation is asked local derviation successively according to these six unknown numbers and is listed successively, obtains the citation form of nine error equations, lists error equation for all images that the 1st survey station obtains by this; Subscript 1 sign is surveyed station number
Figure 285712DEST_PATH_IMAGE020
=1; Subscript
Figure 255942DEST_PATH_IMAGE021
expression image number,
Figure 266624DEST_PATH_IMAGE022
;
Initial value according to unknown number; Make up the factor arrays and the constant term
Figure 296897DEST_PATH_IMAGE079
of normal equation according to the principle of least square; The formula of normal equation is following
Figure 2011103858152100002DEST_PATH_IMAGE080
。
Unknown number matrix is according to the correction of six unknown numbers of solution of normal equation.
And it is following that the image that step 6 is obtained according to first survey station makes up the concrete operation method of error equation and normal equation one by one,
It is following that eccentric model is converted into equation form
Figure 2011103858152100002DEST_PATH_IMAGE082
Wherein
Figure 232196DEST_PATH_IMAGE083
is unit matrix;
Figure 97384DEST_PATH_IMAGE042
is the corresponding object coordinates system of the individual image of the 1st survey station
Figure 298558DEST_PATH_IMAGE021
coordinate of camera outer orientation line element down;
Figure 881986DEST_PATH_IMAGE041
is the coordinate of the corresponding rotation center of the 1st survey station under object coordinates system; Station number
Figure 521915DEST_PATH_IMAGE020
=1 is surveyed in subscript 1 expression; Subscript
Figure 241609DEST_PATH_IMAGE021
expression image number,
Figure 551368DEST_PATH_IMAGE022
; All images for the 1st survey station obtains are all listed above-mentioned equation
Make up normal equation factor arrays
Figure 2011103858152100002DEST_PATH_IMAGE084
and constant term
Figure 684409DEST_PATH_IMAGE085
according to the principle of least square, the formula of normal equation does
Figure DEST_PATH_IMAGE086
Unknown number matrix
Figure 800133DEST_PATH_IMAGE087
is calculated the image space coordinate system initial point at coordinate under the rotating coordinate system and the coordinate
Figure 182889DEST_PATH_IMAGE041
of rotation center under object coordinates system according to the normal equation global solution.
And step 7 concrete operation method is following,
According to the known remaining stations when the first image for the outer azimuth elements and the outer bearing line elements
Figure 394745DEST_PATH_IMAGE044
, rotating platform around the vertical axis of rotation of the horizontal angle
Figure 148419DEST_PATH_IMAGE045
, and the vertical axis of rotation around the horizontal angle
Figure 65559DEST_PATH_IMAGE046
,
By foreign side's parallactic angle element
Figure 845296DEST_PATH_IMAGE043
basis
Figure 365139DEST_PATH_IMAGE023
corner system constructing rotation matrix
Figure DEST_PATH_IMAGE088
; By the coordinates matrix
Figure 64291DEST_PATH_IMAGE089
of outer orientation line element
Figure 179511DEST_PATH_IMAGE044
structure line element, make up rotation matrix
Figure DEST_PATH_IMAGE090
by horizontal angle
Figure 393641DEST_PATH_IMAGE045
, vertical angle
Figure 592541DEST_PATH_IMAGE046
;
Resolve spin matrix
Figure 379418DEST_PATH_IMAGE047
in the spin matrix that step 5 is set up again the substitution rotating model then
Figure 196064DEST_PATH_IMAGE091
The rotation matrix
Figure 933076DEST_PATH_IMAGE090
, the rotation matrix
Figure 521707DEST_PATH_IMAGE047
, and proceeds to Step 6 coordinate
Figure 951552DEST_PATH_IMAGE038
solvers result into eccentric model solver coordinate matrix
Figure 255494DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE092
Wherein station number is surveyed in subscript
Figure 592935DEST_PATH_IMAGE020
expression;
Figure 236406DEST_PATH_IMAGE049
, subscript 1 expression image number
Figure 633889DEST_PATH_IMAGE021
=1.
And step 8 concrete operation method is following,
Rotation platform is around the horizontal angle
Figure 362810DEST_PATH_IMAGE050
of vertical rotating shaft with around the vertical angle
Figure 503942DEST_PATH_IMAGE051
of feathering axis when obtaining according to other images beyond first of all the other survey station; Make up rotation matrix ; And the foreign side's parallactic angle element rotation matrix
Figure DEST_PATH_IMAGE094
under
Figure 731344DEST_PATH_IMAGE023
corner system when resolving image in rotation matrix
Figure 786521DEST_PATH_IMAGE030
the substitution rotating model that step 7 gained rotation matrix
Figure 835883DEST_PATH_IMAGE047
and step 5 are set up again and obtaining; And further decompositing foreign side's parallactic angle element
Figure 88693DEST_PATH_IMAGE052
according to
Figure 146145DEST_PATH_IMAGE023
corner system, solution formula is following
The coordinates matrix
Figure DEST_PATH_IMAGE096
of the outer orientation line element when resolving of rotation matrix
Figure 30069DEST_PATH_IMAGE047
, rotation matrix
Figure 564956DEST_PATH_IMAGE093
, step 6 gained coordinate
Figure 678405DEST_PATH_IMAGE038
resolved image in result and the eccentric model of coordinates matrix substitution and obtained; And further decompositing outer orientation line element
Figure 952578DEST_PATH_IMAGE053
, solution formula is following
Wherein station number is surveyed in subscript
Figure 360742DEST_PATH_IMAGE020
expression; ; Subscript
Figure 863585DEST_PATH_IMAGE021
expression image number,
Figure 45167DEST_PATH_IMAGE054
.
The present invention utilizes single survey station to obtain the level of the elements of exterior orientation of many images and rotation platform, vertical swing angle, resolves through the multi-disc overall adjustment, and this scaling method can realize rotating the high-precision automatic positioning and directing of Digital Photogrammetric System; Under the prerequisite of known first the image elements of exterior orientation of other survey stations, the level of rotation platform, vertical swing angle in the time of only other video imagings need being provided just can the high-precision anti-elements of exterior orientation that pushes away this image automatically.
Description of drawings
Fig. 1 is the structural drawing of rotation sweep camera chain;
Fig. 2 is the geometric relationship synoptic diagram that the present invention relates between coordinate system;
Fig. 3 demarcates the process flow diagram of rotation and eccentric matrix for the embodiment of the invention;
Fig. 4 resolves the process flow diagram of elements of exterior orientation according to calibration result for the embodiment of the invention.
Embodiment
Specify technical scheme of the present invention below in conjunction with accompanying drawing and embodiment.
Referring to Fig. 2, wherein is the coordinate of intersection point among Fig. 1
Figure 297157DEST_PATH_IMAGE003
under object coordinates system ;
Figure DEST_PATH_IMAGE100
is system at the standard photographic coordinate system of camera standard under the object position; Wherein X is a course-and-bearing; Y is a zenith direction, and Z is a depth direction;
Figure 890654DEST_PATH_IMAGE101
is the rotating coordinate system of system behind horizontal rotational shaft V angle and Z-axis rotation H angle; Same meaning among
Figure 254639DEST_PATH_IMAGE005
and
Figure 615214DEST_PATH_IMAGE006
and Fig. 1; Be respectively principal point
Figure 64649DEST_PATH_IMAGE007
and put at
Figure 387363DEST_PATH_IMAGE008
axle with respect to
Figure 434451DEST_PATH_IMAGE003
, the side-play amount of
Figure 184418DEST_PATH_IMAGE009
axle axle with
Figure 855571DEST_PATH_IMAGE010
.
The embodiment of the invention is set up following two models:
Camera with respect to the rotating model of object coordinates system based on following formula:
Figure 29063DEST_PATH_IMAGE026
Wherein is camera foreign side parallactic angle element rotation matrix under
Figure 70017DEST_PATH_IMAGE023
corner system under the object coordinates system, and its expansion form is:
Figure 228466DEST_PATH_IMAGE062
Wherein,
Figure DEST_PATH_IMAGE102
is foreign side's parallactic angle element.
Figure 61774DEST_PATH_IMAGE028
is the rotation matrix between object coordinates system and standard photogrammetric coordinate system, and its expansion is the same:
Figure 926962DEST_PATH_IMAGE103
Wherein,
Figure DEST_PATH_IMAGE104
is the corner of rotation matrix
Figure 773881DEST_PATH_IMAGE028
under
Figure 128137DEST_PATH_IMAGE023
corner system.For many images that a certain fixedly survey station obtains, the value of this rotation matrix
Figure 23597DEST_PATH_IMAGE028
is constant.
Figure 71188DEST_PATH_IMAGE029
is the rotation matrix between standard photographic coordinate system and rotating coordinate system, and its expansion form is:
matrix by the rotation around the vertical axis of rotation of the platform horizontal
Figure 567394DEST_PATH_IMAGE014
and rotate around a horizontal axis of rotation of the platform vertical angle
Figure 469491DEST_PATH_IMAGE013
build.For every image, this matrix changes with the variation of rotation attitude.
Figure 950151DEST_PATH_IMAGE030
is the rotation matrix between rotating coordinate system and image space coordinate system, and this matrix is still according to
Figure 304909DEST_PATH_IMAGE023
corner system constructing.The internal system parameter of this matrix for needing to demarcate, for all images that all survey stations obtain, this matrix all remains unchanged.
Figure 162006DEST_PATH_IMAGE105
Figure 918610DEST_PATH_IMAGE034
is Corner system rotation matrix
Figure 680734DEST_PATH_IMAGE030
the corner.
Camera with respect to the eccentric model of object coordinates system based on following formula:
Wherein
Figure 687053DEST_PATH_IMAGE037
is the coordinates matrix of camera outer orientation line element
Figure DEST_PATH_IMAGE106
under the object coordinates system.
Figure 775095DEST_PATH_IMAGE038
is the coordinate of image space coordinate system initial point under rotating coordinate system; This coordinate by rotation matrix in standard under the position; The photo centre of camera is apart from the distance decision of level and vertical rotating shaft; Wherein coordinate
Figure 104445DEST_PATH_IMAGE038
is the internal system parameter that need demarcation at value
Figure DEST_PATH_IMAGE108
, the coordinate of Y axle in the value
Figure 969185DEST_PATH_IMAGE109
of Z axle at value
Figure 365662DEST_PATH_IMAGE107
, the coordinate of X axle; For all images that all survey stations obtain, this matrix all remains unchanged.
Figure 706197DEST_PATH_IMAGE039
; Be the coordinates matrix of rotation center
Figure 291899DEST_PATH_IMAGE098
under object coordinates system; For many images that a certain fixedly survey station obtains, the value of this rotation matrix is constant.
Can adopt computer software technology to realize automatically performing flow process during practical implementation of the present invention.Introduce the rotation Digital Photogrammetric System multi-disc overall adjustment of the embodiment of the invention below and demarcate flow process, based on rotating model and the eccentric model of camera with respect to object coordinates system, each step explanation as follows.Can be referring to Fig. 3 and Fig. 4, wherein Fig. 3 provides the flow process of demarcating rotation and eccentric matrix, i.e. step 1～6; Fig. 4 provides the flow process of resolving elements of exterior orientation according to calibration result, i.e. step 7,8.
Step 1; Import image number
Figure 721743DEST_PATH_IMAGE015
(at least three), the elements of exterior orientation when each image obtains (comprising foreign side's parallactic angle element
Figure 757176DEST_PATH_IMAGE016
and outer orientation line element
Figure 360196DEST_PATH_IMAGE017
) that first survey station obtains, rotation platform around the horizontal angle
Figure 3667DEST_PATH_IMAGE018
of vertical rotating shaft and rotation platform vertical angle
Figure 401150DEST_PATH_IMAGE019
around feathering axis; Wherein subscript 1 sign is surveyed station number
Figure 130072DEST_PATH_IMAGE020
=1; Subscript
Figure 271203DEST_PATH_IMAGE021
expression image number,
Figure 831498DEST_PATH_IMAGE022
; According to corner system constructing rotation matrix
Figure 498605DEST_PATH_IMAGE024
, make up the coordinates matrix of line element by foreign side's parallactic angle element
Figure 337565DEST_PATH_IMAGE016
by outer orientation line element
Figure 851089DEST_PATH_IMAGE017
.
Step 2 makes up the rotating model of camera with respect to object coordinates system, and the rotating model formula is following
Figure 293889DEST_PATH_IMAGE026
Wherein,
Figure 776823DEST_PATH_IMAGE027
is camera foreign side parallactic angle element rotation matrix under
Figure 249392DEST_PATH_IMAGE023
corner system under the object coordinates system;
Figure 162509DEST_PATH_IMAGE028
is the rotation matrix between object coordinates system and standard photogrammetric coordinate system;
Figure 87740DEST_PATH_IMAGE029
is the rotation matrix between standard photographic coordinate system and rotating coordinate system, makes up according to said horizontal angle of step 1
Figure 312048DEST_PATH_IMAGE018
and vertical angle
Figure 701441DEST_PATH_IMAGE019
;
Figure 985792DEST_PATH_IMAGE030
is the rotation matrix between rotating coordinate system and image space coordinate system;
First three image according to first survey station obtains is distinguished corresponding rotating model
Figure 460635DEST_PATH_IMAGE031
; Resolve the corner of rotation matrix
Figure 404638DEST_PATH_IMAGE032
under corresponding
Figure 223055DEST_PATH_IMAGE023
the corner system of first survey station and the corner
Figure 388140DEST_PATH_IMAGE034
of rotation matrix
Figure 822030DEST_PATH_IMAGE030
; And resolve the initial value of result as unknown number with gained; Wherein, Subscript 1 sign is surveyed station number
Figure 486546DEST_PATH_IMAGE020
=1; Subscript
Figure 112700DEST_PATH_IMAGE021
expression image number;
Figure 562136DEST_PATH_IMAGE035
,
Figure 666358DEST_PATH_IMAGE024
are the rotation matrix that step 1 makes up.
Embodiment According to the first an measured stations Gets of the former three image respectively correspond to by the Rotary model
Figure 884849DEST_PATH_IMAGE024
,
Figure 681904DEST_PATH_IMAGE035
, Xie count
Figure 290740DEST_PATH_IMAGE023
corner System under the rotation matrix
Figure 526549DEST_PATH_IMAGE032
's corner
Figure 537231DEST_PATH_IMAGE033
and the rotation matrix
Figure 564574DEST_PATH_IMAGE030
's corner
Figure 660706DEST_PATH_IMAGE034
,? concrete realization the following manner,
The 1st the corresponding rotating model of image is
The 2nd the corresponding rotating model of image is
Figure 299815DEST_PATH_IMAGE056
The 3rd the corresponding rotating model of image is
Figure 438672DEST_PATH_IMAGE057
Wherein, is that the 1st
Figure 334133DEST_PATH_IMAGE021
that survey station obtains opens corresponding standard photographic coordinate system of image and the rotation matrix between rotating coordinate system;
Figure 381723DEST_PATH_IMAGE035
, the rotation platform that imports according to step 1 gets final product around vertical angle
Figure 762206DEST_PATH_IMAGE019
structure of feathering axis around the horizontal angle
Figure 691482DEST_PATH_IMAGE018
and the rotation platform of vertical rotating shaft;
Eliminate wherein one group of unknown number; Like rotation matrix
Figure 877929DEST_PATH_IMAGE030
, arrangement can get:
Figure 717709DEST_PATH_IMAGE059
Wherein,
Figure 553127DEST_PATH_IMAGE103
Figure 410225DEST_PATH_IMAGE062
Figure 166828DEST_PATH_IMAGE063
The result of calculation of
Figure DEST_PATH_IMAGE110
is one 3 * 3 matrix, totally 9 elements.Making the element in the lower right corner in the rotation matrix
Figure 880706DEST_PATH_IMAGE064
is 1; All the other eight elements are as unknown number
Figure 386479DEST_PATH_IMAGE008
in matrix, and one group of unknown number gained two formula expands into nine equations about these eight unknown numbers respectively with eliminating wherein; Make up the factor arrays
Figure 935272DEST_PATH_IMAGE065
and the constant term
Figure 85630DEST_PATH_IMAGE066
of normal equation according to the principle of least square; Resolve the value of the first eight element in the rotation matrix , the formula of normal equation is following:
Figure 285985DEST_PATH_IMAGE067
Gained rotation matrix
Figure 17180DEST_PATH_IMAGE064
resolves rotation matrix
Figure 276123DEST_PATH_IMAGE030
according to resolving as a result; Concrete mode is: rearrange
Figure 827190DEST_PATH_IMAGE064
matrix; Calculate the value of its determinant, and with the cubic root of elements all in the matrix divided by determinant.Can be normalized to the form of rotation matrix.After obtaining
Figure 829781DEST_PATH_IMAGE064
matrix; In the rotating model
Figure 353167DEST_PATH_IMAGE055
that can first image of its substitution is corresponding, resolve the value of
Figure 579749DEST_PATH_IMAGE030
matrix.
Then follow
Figure 821374DEST_PATH_IMAGE023
corner relations system solver corner system rotation matrix
Figure 802285DEST_PATH_IMAGE032
corner
Figure 403031DEST_PATH_IMAGE033
and the rotation matrix
Figure 928690DEST_PATH_IMAGE030
corner
Figure 273084DEST_PATH_IMAGE034
.
Step 3; Rotating model is converted into error equation; With corner
Figure 833378DEST_PATH_IMAGE033
and corner
Figure 339446DEST_PATH_IMAGE034
is unknown number; All images that first survey station is obtained carry out linearization process one by one; Initial value according to unknown number makes up normal equation according to the principle of least square; Overall adjustment solving method equation obtains the unknown number correction.
Make
Figure 450988DEST_PATH_IMAGE068
It is following that embodiment is converted into the error equation form with rotating model,
Figure 333494DEST_PATH_IMAGE069
Wherein, The residual error of
Figure 685978DEST_PATH_IMAGE070
expression error equation; Unknown number is three corners
Figure 611711DEST_PATH_IMAGE033
of rotation matrix
Figure 863198DEST_PATH_IMAGE032
under
Figure 425264DEST_PATH_IMAGE023
corner system, and three corners
Figure 932151DEST_PATH_IMAGE034
of rotation matrix
Figure 818702DEST_PATH_IMAGE030
;
Figure 919699DEST_PATH_IMAGE071
;
Figure 144007DEST_PATH_IMAGE072
;
Figure 533400DEST_PATH_IMAGE073
;
Figure 817751DEST_PATH_IMAGE074
,
Figure 964698DEST_PATH_IMAGE075
and
Figure 55014DEST_PATH_IMAGE076
is respectively the error matrix equation according to above-mentioned six partial derivatives that unknown number is found the solution successively;
Figure 236597DEST_PATH_IMAGE077
is the constant term of error equation.
Matrix in the above-mentioned error equation be 3
Figure 754166DEST_PATH_IMAGE111
3 matrixes; Can extract the item of all matrix correspondence positions thus; Obtain the citation form of nine error equations, find the solution convenient like this.During practical implementation,, get the item of all the 1st positions of matrix the 1st row, obtain the citation form of an error equation according to error equation ... The rest may be inferred.All images for the 1st survey station obtains are listed error equation by this; Subscript 1 sign is surveyed station number
Figure DEST_PATH_IMAGE112
=1; Subscript
Figure 653988DEST_PATH_IMAGE021
expression image number,
Figure 282416DEST_PATH_IMAGE022
.The rotation angle of
Figure 318505DEST_PATH_IMAGE032
in the step 2 and
Figure 9905DEST_PATH_IMAGE030
is resolved the initial value of result as unknown number in the iteration adjustment, make up the factor arrays
Figure 131445DEST_PATH_IMAGE078
and the constant term
Figure 563563DEST_PATH_IMAGE079
of normal equation according to the principle of least square.
The formula of normal equation is following,
Figure 719738DEST_PATH_IMAGE080
Correction according to six unknown numbers of solution of normal equation.
Step 4, if unknown number correction maximal value surpasses preset iterations threshold value less than preset unknown number correction threshold value or iterations, then execution in step 5; Otherwise the initial value so that current unknown number correction is a unknown number returns iteration execution in step 3.
During practical implementation, unknown number correction threshold value and iterations threshold value can be set up by those skilled in the art as the case may be voluntarily.If unknown number correction maximal value surpasses any decision condition of iterations threshold value less than unknown number correction threshold value or iterations, then execution in step 5; Otherwise, return execution in step 3.
Step 5; Export the unknown number correction that obtains in the last iteration; Calibration result as corner
Figure 579110DEST_PATH_IMAGE033
and corner ; Again set up rotation matrix
Figure 168857DEST_PATH_IMAGE032
according to the calibration result of corner
Figure 95859DEST_PATH_IMAGE033
, follow according to the calibration result of corner
Figure 199130DEST_PATH_IMAGE034
and set up rotation matrix
Figure 357579DEST_PATH_IMAGE030
again.
Step 6 makes up the eccentric model of camera with respect to object coordinates system, and eccentric model formation is following
Wherein
Figure 262267DEST_PATH_IMAGE037
is the coordinates matrix of camera outer orientation line element under the object coordinates system;
Figure 401124DEST_PATH_IMAGE038
is the coordinate of image space coordinate system initial point under rotating coordinate system;
Figure 781290DEST_PATH_IMAGE039
is the coordinates matrix of rotation center under object coordinates system;
According to the eccentric model
Figure 296585DEST_PATH_IMAGE040
of camera with respect to object coordinates system; The image that obtains according to first survey station makes up error equation and normal equation one by one; According to the principle of least square; Overall adjustment is resolved coordinate and rotation center the coordinate
Figure 651004DEST_PATH_IMAGE041
under object coordinates system of image space coordinate system initial point under rotating coordinate system; Output coordinate resolve the result; Wherein, Subscript 1 sign is surveyed station number
Figure 571872DEST_PATH_IMAGE020
=1; Subscript
Figure 473969DEST_PATH_IMAGE021
expression image number;
Figure 954629DEST_PATH_IMAGE022
; is the coordinates matrix that step 1 makes up, and
Figure 166485DEST_PATH_IMAGE032
is the rotation matrix that step 5 is set up again.
It is following that embodiment is converted into equation form with eccentric model
Figure 188667DEST_PATH_IMAGE082
Wherein
Figure 840229DEST_PATH_IMAGE083
is unit matrix;
Figure 619966DEST_PATH_IMAGE042
is the corresponding object coordinates system of the individual image of the 1st survey station
Figure 77492DEST_PATH_IMAGE021
coordinate of camera outer orientation line element down;
Figure 891864DEST_PATH_IMAGE041
is the coordinate of the corresponding rotation center of the 1st survey station under object coordinates system; Station number
Figure 776644DEST_PATH_IMAGE020
=1 is surveyed in subscript 1 expression; Subscript expression image number,
Figure 242577DEST_PATH_IMAGE022
; All images for the 1st survey station obtains are all listed above-mentioned equation.
Make up normal equation factor arrays
Figure 973773DEST_PATH_IMAGE084
and constant term
Figure 967137DEST_PATH_IMAGE085
according to the principle of least square, the formula of normal equation does
Figure 786712DEST_PATH_IMAGE086
Unknown number matrix
Figure 789304DEST_PATH_IMAGE087
is calculated the image space coordinate system initial point at coordinate under the rotating coordinate system
Figure 312689DEST_PATH_IMAGE038
and the coordinate
Figure 539271DEST_PATH_IMAGE041
of rotation center under object coordinates system according to the normal equation global solution.
Step 7; Again rotation matrix of setting up according to step 5
Figure 780896DEST_PATH_IMAGE030
and the coordinate
Figure 383916DEST_PATH_IMAGE038
of step 6 gained image space coordinate system initial point under rotating coordinate system resolve result, the elements of exterior orientation (foreign side's parallactic angle element
Figure 761808DEST_PATH_IMAGE043
and outer orientation line element
Figure 362553DEST_PATH_IMAGE044
) when known first image of all the other survey stations obtains, rotation platform around the horizontal angle
Figure 888213DEST_PATH_IMAGE045
of vertical rotating shaft with around the vertical angle
Figure 232606DEST_PATH_IMAGE046
of feathering axis; Again resolve under all the other survey station conditions rotation matrix
Figure 527321DEST_PATH_IMAGE047
between object coordinates system and standard photogrammetric coordinate system and the rotation center coordinate
Figure 298968DEST_PATH_IMAGE048
under object coordinates system through rotating model and eccentric model; Wherein station number is surveyed in subscript
Figure 311924DEST_PATH_IMAGE020
expression;
Figure 194429DEST_PATH_IMAGE049
, subscript 1 expression image number
Figure 546913DEST_PATH_IMAGE021
=1.
Example import the rest of the known stations when the first image for the outer azimuth elements
Figure 551778DEST_PATH_IMAGE043
and the outer bearing line elements
Figure 989713DEST_PATH_IMAGE044
, rotating platform around the vertical axis of rotation of the horizontal angle , and the vertical axis of rotation around the horizontal angle
Figure 945216DEST_PATH_IMAGE046
,
By foreign side's parallactic angle element basis
Figure 43284DEST_PATH_IMAGE023
corner system constructing rotation matrix
Figure 267591DEST_PATH_IMAGE088
; By the coordinates matrix of outer orientation line element
Figure 594668DEST_PATH_IMAGE044
structure line element, make up rotation matrix
Figure 360181DEST_PATH_IMAGE090
by horizontal angle
Figure 88283DEST_PATH_IMAGE045
, vertical angle
Figure 178599DEST_PATH_IMAGE046
;
Resolve spin matrix
Figure 511994DEST_PATH_IMAGE047
in the spin matrix that step 5 is set up again
Figure 815433DEST_PATH_IMAGE030
the substitution rotating model then
Figure 78104DEST_PATH_IMAGE091
Will rotation matrix
Figure 442090DEST_PATH_IMAGE090
, rotation matrix
Figure 68243DEST_PATH_IMAGE047
as well as to Step 6 the proceeds coordinates of
Figure 189783DEST_PATH_IMAGE038
's solver results of substituted into the eccentric the model solver coordinates of matrix
Figure 621901DEST_PATH_IMAGE048
Wherein station number is surveyed in subscript expression; , subscript 1 expression image number =1.
Step 8; Rotation platform is around the horizontal angle
Figure 227195DEST_PATH_IMAGE050
of vertical rotating shaft with around the vertical angle
Figure 195151DEST_PATH_IMAGE051
of feathering axis when obtaining according to other images beyond first of all the other known survey station; Foreign side's parallactic angle element
Figure 356530DEST_PATH_IMAGE052
and outer orientation line element
Figure 68134DEST_PATH_IMAGE053
when resolving through rotating model and eccentric model that other images obtain beyond first of all the other survey station; Wherein station number is surveyed in subscript expression;
Figure 134496DEST_PATH_IMAGE049
; Subscript
Figure 717924DEST_PATH_IMAGE021
expression image number,
Figure 233219DEST_PATH_IMAGE054
.
Rotation platform was around the horizontal angle
Figure 15230DEST_PATH_IMAGE050
of vertical rotating shaft with around the vertical angle
Figure 324988DEST_PATH_IMAGE051
of feathering axis when embodiment obtained according to other images beyond first of all the other survey station; Make up rotation matrix
Figure 458030DEST_PATH_IMAGE093
; And the foreign side's parallactic angle element rotation matrix
Figure 452213DEST_PATH_IMAGE094
under
Figure 894193DEST_PATH_IMAGE023
corner system when resolving image in rotation matrix
Figure 351216DEST_PATH_IMAGE030
the substitution rotating model that step 7 gained rotation matrix
Figure 511436DEST_PATH_IMAGE047
and step 5 are set up again and obtaining; And further decompositing foreign side's parallactic angle element
Figure 800335DEST_PATH_IMAGE052
according to
Figure 106049DEST_PATH_IMAGE023
corner system, solution formula is following
Figure 779792DEST_PATH_IMAGE095
The coordinates matrix
Figure 980311DEST_PATH_IMAGE096
of the outer orientation line element when resolving of rotation matrix
Figure 559530DEST_PATH_IMAGE047
, rotation matrix
Figure 954739DEST_PATH_IMAGE093
, step 6 gained coordinate
Figure 831428DEST_PATH_IMAGE038
resolved image in result and the eccentric model of coordinates matrix
Figure 653890DEST_PATH_IMAGE048
substitution and obtained; And further decompositing outer orientation line element
Figure 179211DEST_PATH_IMAGE053
, solution formula is following
Wherein station number is surveyed in subscript
Figure 903771DEST_PATH_IMAGE020
expression;
Figure 658100DEST_PATH_IMAGE049
; The maximum occurrences of
Figure 457429DEST_PATH_IMAGE020
is the actual station total number of taking the photograph; Subscript
Figure 980814DEST_PATH_IMAGE021
expression image number;
Figure 410658DEST_PATH_IMAGE054
, the maximum occurrences of
Figure 714601DEST_PATH_IMAGE021
is the actual corresponding station image total number of taking the photograph.
Specific embodiment described herein only is that the present invention's spirit is illustrated.Person of ordinary skill in the field of the present invention can make various modifications or replenishes or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (6)

1. a rotation Digital Photogrammetric System multi-disc overall adjustment scaling method is characterized in that, may further comprise the steps:
Step 1; Import image number
Figure 171246DEST_PATH_IMAGE001
, the foreign side's parallactic angle element when each image obtains and outer orientation line element
Figure 150703DEST_PATH_IMAGE003
that first survey station obtains, rotation platform around the horizontal angle of vertical rotating shaft and rotation platform vertical angle around feathering axis; Wherein subscript 1 sign is surveyed station number
Figure 2011103858152100001DEST_PATH_IMAGE006
=1; Subscript
Figure 385037DEST_PATH_IMAGE007
expression image number;
Figure 2011103858152100001DEST_PATH_IMAGE008
, image number
Figure 261726DEST_PATH_IMAGE001
is more than or equal to 3; According to
Figure 351222DEST_PATH_IMAGE009
corner system constructing rotation matrix
Figure 2011103858152100001DEST_PATH_IMAGE010
, make up the coordinates matrix
Figure 281317DEST_PATH_IMAGE011
of line element by foreign side's parallactic angle element
Figure 84188DEST_PATH_IMAGE002
by outer orientation line element
Figure 612439DEST_PATH_IMAGE003
;
Step 2 makes up the rotating model of camera with respect to object coordinates system, and the rotating model formula is following
Figure 2011103858152100001DEST_PATH_IMAGE012
Wherein,
Figure 336998DEST_PATH_IMAGE013
is camera foreign side parallactic angle element rotation matrix under
Figure 91327DEST_PATH_IMAGE009
corner system under the object coordinates system;
Figure 2011103858152100001DEST_PATH_IMAGE014
is the rotation matrix between object coordinates system and standard photogrammetric coordinate system;
Figure 890656DEST_PATH_IMAGE015
is the rotation matrix between standard photographic coordinate system and rotating coordinate system;
Figure 2011103858152100001DEST_PATH_IMAGE016
is the rotation matrix between rotating coordinate system and image space coordinate system;
First three image according to first survey station obtains is distinguished corresponding rotating model
Figure 414041DEST_PATH_IMAGE017
; Resolve the corner
Figure 147828DEST_PATH_IMAGE019
of rotation matrix
Figure 2011103858152100001DEST_PATH_IMAGE018
under corresponding the corner system of first survey station and the corner
Figure DEST_PATH_IMAGE020
of rotation matrix
Figure 485269DEST_PATH_IMAGE016
; And resolve the initial value of result as unknown number with gained; Wherein, Subscript 1 sign is surveyed station number
Figure 128740DEST_PATH_IMAGE006
=1; Subscript expression image number;
Figure 255144DEST_PATH_IMAGE021
,
Figure 333959DEST_PATH_IMAGE010
are the rotation matrix that step 1 makes up;
Step 3; Rotating model is converted into error equation; With corner
Figure 897183DEST_PATH_IMAGE019
and corner
Figure 668830DEST_PATH_IMAGE020
is unknown number; All images that first survey station is obtained carry out linearization process one by one; Initial value according to unknown number makes up normal equation according to the principle of least square; Overall adjustment solving method equation obtains the unknown number correction;
Step 4, if unknown number correction maximal value surpasses preset iterations threshold value less than preset unknown number correction threshold value or iterations, then execution in step 5; Otherwise the initial value so that current unknown number correction is a unknown number returns iteration execution in step 3;
Step 5; Export the unknown number correction that obtains in the last iteration; Calibration result as corner
Figure 619468DEST_PATH_IMAGE019
and corner
Figure 564291DEST_PATH_IMAGE020
; Again set up rotation matrix according to the calibration result of corner
Figure 916774DEST_PATH_IMAGE019
, follow according to the calibration result of corner
Figure 359574DEST_PATH_IMAGE020
and set up rotation matrix
Figure 780191DEST_PATH_IMAGE016
again;
Step 6 makes up the eccentric model of camera with respect to object coordinates system, and eccentric model formation is following
Figure DEST_PATH_IMAGE022
Wherein
Figure 315078DEST_PATH_IMAGE023
is the coordinates matrix of camera outer orientation line element under the object coordinates system;
Figure DEST_PATH_IMAGE024
is the coordinate of image space coordinate system initial point under rotating coordinate system;
Figure 428527DEST_PATH_IMAGE025
is the coordinates matrix of rotation center under object coordinates system;
According to the eccentric model
Figure DEST_PATH_IMAGE026
of camera with respect to object coordinates system; The image that obtains according to first survey station makes up error equation and normal equation one by one; According to the principle of least square; Overall adjustment is resolved coordinate
Figure 416075DEST_PATH_IMAGE024
and rotation center the coordinate
Figure 640383DEST_PATH_IMAGE027
under object coordinates system of image space coordinate system initial point under rotating coordinate system; Output coordinate
Figure 764197DEST_PATH_IMAGE024
resolve the result; Wherein, Subscript 1 sign is surveyed station number
Figure 48547DEST_PATH_IMAGE006
=1; Subscript
Figure 461074DEST_PATH_IMAGE007
expression image number;
Figure 551390DEST_PATH_IMAGE008
; is the coordinates matrix that step 1 makes up, and
Figure 732973DEST_PATH_IMAGE018
is the rotation matrix that step 5 is set up again;
Step 7; Again rotation matrix of setting up according to step 5
Figure 984962DEST_PATH_IMAGE016
and the coordinate
Figure 884785DEST_PATH_IMAGE024
of step 6 gained image space coordinate system initial point under rotating coordinate system resolve result, the foreign side's parallactic angle element
Figure 450896DEST_PATH_IMAGE029
when known first image of all the other survey stations obtains and outer orientation line element
Figure DEST_PATH_IMAGE030
, rotation platform around the horizontal angle
Figure 835389DEST_PATH_IMAGE031
of vertical rotating shaft with around the vertical angle
Figure DEST_PATH_IMAGE032
of feathering axis; Again resolve under all the other survey station conditions rotation matrix
Figure 258280DEST_PATH_IMAGE033
between object coordinates system and standard photogrammetric coordinate system and the rotation center coordinate
Figure DEST_PATH_IMAGE034
under object coordinates system through rotating model and eccentric model; Wherein station number is surveyed in subscript expression;
Figure 77517DEST_PATH_IMAGE035
, subscript 1 expression image number
Figure 968113DEST_PATH_IMAGE007
=1;
Step 8; Rotation platform is around the horizontal angle of vertical rotating shaft with around the vertical angle
Figure 827484DEST_PATH_IMAGE037
of feathering axis when obtaining according to other images beyond first of all the other known survey station; Foreign side's parallactic angle element and outer orientation line element
Figure 498637DEST_PATH_IMAGE039
when resolving through rotating model and eccentric model that other images obtain beyond first of all the other survey station; Wherein station number is surveyed in subscript
Figure 672130DEST_PATH_IMAGE006
expression;
Figure 745128DEST_PATH_IMAGE035
; Subscript
Figure 713084DEST_PATH_IMAGE007
expression image number, .
(2) as claimed in claim 1, wherein said rotating multi-chip integrated photogrammetric adjustment system calibration method characterized in that: according to the first stations in the acquired image corresponding to each of the first three rotating the model
Figure 809216DEST_PATH_IMAGE010
,
Figure 583137DEST_PATH_IMAGE021
solver corner system rotation matrix
Figure 587182DEST_PATH_IMAGE018
corner
Figure 232927DEST_PATH_IMAGE019
and the rotation matrix
Figure 482643DEST_PATH_IMAGE016
corner
Figure 533163DEST_PATH_IMAGE020
,? specific implementation in the following manner,
The 1st the corresponding rotating model of image is
The 2nd the corresponding rotating model of image is
Figure DEST_PATH_IMAGE042
The 3rd the corresponding rotating model of image is
Figure 975962DEST_PATH_IMAGE043
Wherein,
Figure DEST_PATH_IMAGE044
is that the 1st
Figure 91686DEST_PATH_IMAGE007
that survey station obtains opens corresponding standard photographic coordinate system of image and the rotation matrix between rotating coordinate system,
Figure 931466DEST_PATH_IMAGE021
;
Eliminate wherein one group of unknown number, obtain
Figure 412126DEST_PATH_IMAGE045
Figure DEST_PATH_IMAGE046
Wherein,
Figure 829201DEST_PATH_IMAGE047
Figure DEST_PATH_IMAGE048
Figure 686298DEST_PATH_IMAGE049
Making the element in the lower right corner in the rotation matrix
Figure DEST_PATH_IMAGE050
is 1; All the other eight elements are as unknown number
Figure 94463DEST_PATH_IMAGE051
in
Figure 442902DEST_PATH_IMAGE050
matrix, and one group of unknown number gained two formula expands into nine equations about these eight unknown numbers respectively with eliminating wherein; Make up the factor arrays
Figure DEST_PATH_IMAGE052
and the constant term
Figure 202096DEST_PATH_IMAGE053
of normal equation according to the principle of least square; Resolve the value of the first eight element in the rotation matrix , the formula of normal equation is following
Figure DEST_PATH_IMAGE054
Gained rotation matrix
Figure 208415DEST_PATH_IMAGE050
resolves rotation matrix
Figure 296457DEST_PATH_IMAGE016
according to resolving as a result, resolves the corner
Figure 546337DEST_PATH_IMAGE019
of rotation matrix
Figure 225077DEST_PATH_IMAGE018
under
Figure 821778DEST_PATH_IMAGE009
corner system with the corner
Figure 37678DEST_PATH_IMAGE020
of rotation matrix
Figure 300667DEST_PATH_IMAGE016
according to the relation of
Figure 622878DEST_PATH_IMAGE009
corner system then.
3. according to the said rotation Digital Photogrammetric System of claim 1 multi-disc overall adjustment scaling method, it is characterized in that: step 3 concrete operation method is following,
Make
Figure 623381DEST_PATH_IMAGE055
It is following that rotating model is converted into the error equation form,
Figure DEST_PATH_IMAGE056
Wherein, The residual error of
Figure 53225DEST_PATH_IMAGE057
expression error equation; Unknown number is three corners
Figure 275762DEST_PATH_IMAGE019
of rotation matrix
Figure 632291DEST_PATH_IMAGE018
under
Figure 91588DEST_PATH_IMAGE009
corner system; And three corners
Figure 402167DEST_PATH_IMAGE020
of rotation matrix
Figure 673245DEST_PATH_IMAGE016
; ;
Figure 543298DEST_PATH_IMAGE059
;
Figure DEST_PATH_IMAGE060
;
Figure 41275DEST_PATH_IMAGE061
,
Figure DEST_PATH_IMAGE062
and
Figure 609660DEST_PATH_IMAGE063
is respectively the error matrix equation according to above-mentioned six partial derivatives that unknown number is found the solution successively; is the constant term of error equation;
Error equation is asked local derviation successively according to these six unknown numbers and is listed successively, obtains the citation form of nine error equations, lists error equation for all images that the 1st survey station obtains by this; Subscript 1 sign is surveyed station number =1; Subscript
Figure 770700DEST_PATH_IMAGE007
expression image number, ;
Initial value according to unknown number; Make up the factor arrays
Figure 130979DEST_PATH_IMAGE065
and the constant term
Figure DEST_PATH_IMAGE066
of normal equation according to the principle of least square; The formula of normal equation is following
Unknown number matrix
Figure DEST_PATH_IMAGE068
is according to the correction of six unknown numbers of solution of normal equation.
4. according to claim 1 or 2 or 3 said rotation Digital Photogrammetric System multi-disc overall adjustment scaling methods, it is characterized in that: it is following that the image that step 6 is obtained according to first survey station makes up the concrete operation method of error equation and normal equation one by one,
It is following that eccentric model is converted into the error equation form
Figure 114164DEST_PATH_IMAGE069
Wherein
Figure DEST_PATH_IMAGE070
is unit matrix;
Figure 586734DEST_PATH_IMAGE028
is the corresponding object coordinates system of the individual image of the 1st survey station
Figure 496921DEST_PATH_IMAGE007
coordinate of camera outer orientation line element down;
Figure 422152DEST_PATH_IMAGE027
is the coordinate of the corresponding rotation center of the 1st survey station under object coordinates system; Station number
Figure 708776DEST_PATH_IMAGE006
=1 is surveyed in subscript 1 expression; Subscript expression image number,
Figure 382520DEST_PATH_IMAGE008
; All images for the 1st survey station obtains are all listed above-mentioned equation,
Make up normal equation factor arrays and constant term
Figure DEST_PATH_IMAGE072
according to the principle of least square, the formula of normal equation does
Figure 619784DEST_PATH_IMAGE073
Unknown number matrix
Figure DEST_PATH_IMAGE074
is calculated the image space coordinate system initial point at coordinate under the rotating coordinate system
Figure 863683DEST_PATH_IMAGE024
and the coordinate
Figure 378322DEST_PATH_IMAGE027
of rotation center under object coordinates system according to the normal equation global solution.
5. according to the said rotation Digital Photogrammetric System of claim 4 multi-disc overall adjustment scaling method, it is characterized in that: step 7 concrete operation method is following,
According to the known remaining stations when the first image for the outer azimuth elements
Figure 278145DEST_PATH_IMAGE029
and the outer bearing line elements
Figure 906573DEST_PATH_IMAGE030
, rotating platform around the vertical axis of rotation of the horizontal angle
Figure 942662DEST_PATH_IMAGE031
and around horizontal rotation axis vertical angle
Figure 568815DEST_PATH_IMAGE032
,
By foreign side's parallactic angle element
Figure 18251DEST_PATH_IMAGE029
basis
Figure 122473DEST_PATH_IMAGE009
corner system constructing rotation matrix ; By the coordinates matrix
Figure DEST_PATH_IMAGE076
of outer orientation line element
Figure 138020DEST_PATH_IMAGE030
structure line element, make up rotation matrix by horizontal angle
Figure 809173DEST_PATH_IMAGE031
, vertical angle
Figure 44982DEST_PATH_IMAGE032
;
Resolve spin matrix
Figure 182068DEST_PATH_IMAGE033
in the spin matrix that step 5 is set up again
Figure 85936DEST_PATH_IMAGE016
the substitution rotating model then
Figure DEST_PATH_IMAGE078
The rotation matrix
Figure 690410DEST_PATH_IMAGE077
, the rotation matrix
Figure 886424DEST_PATH_IMAGE033
, and proceeds to Step 6 coordinate solvers result into eccentric model solver coordinate matrix
Figure 671026DEST_PATH_IMAGE034
Figure 920742DEST_PATH_IMAGE079
Wherein station number is surveyed in subscript
Figure 906015DEST_PATH_IMAGE006
expression;
Figure 278091DEST_PATH_IMAGE035
, subscript 1 expression image number
Figure 348815DEST_PATH_IMAGE007
=1.
6. according to the said rotation Digital Photogrammetric System of claim 5 multi-disc overall adjustment scaling method, it is characterized in that: step 8 concrete operation method is following,
Rotation platform is around the horizontal angle
Figure 402221DEST_PATH_IMAGE036
of vertical rotating shaft with around the vertical angle of feathering axis when obtaining according to other images beyond first of all the other survey station; Make up rotation matrix
Figure DEST_PATH_IMAGE080
; And the foreign side's parallactic angle element rotation matrix
Figure 753437DEST_PATH_IMAGE081
under
Figure 996834DEST_PATH_IMAGE009
corner system when resolving image in rotation matrix
Figure 139736DEST_PATH_IMAGE016
the substitution rotating model that step 7 gained rotation matrix
Figure 847295DEST_PATH_IMAGE033
and step 5 are set up again and obtaining; And further decompositing foreign side's parallactic angle element
Figure 512632DEST_PATH_IMAGE038
according to
Figure 404998DEST_PATH_IMAGE009
corner system, solution formula is following
Figure DEST_PATH_IMAGE082
The coordinates matrix
Figure 866734DEST_PATH_IMAGE083
of the outer orientation line element when resolving of rotation matrix
Figure 907841DEST_PATH_IMAGE033
, rotation matrix
Figure 518951DEST_PATH_IMAGE080
, step 6 gained coordinate
Figure 606993DEST_PATH_IMAGE024
resolved image in result and the eccentric model of coordinates matrix
Figure 874026DEST_PATH_IMAGE034
substitution and obtained; And further decompositing outer orientation line element
Figure 535613DEST_PATH_IMAGE039
, solution formula is following
Wherein station number is surveyed in subscript
Figure 856873DEST_PATH_IMAGE006
expression;
Figure 345623DEST_PATH_IMAGE035
; Subscript expression image number,
Figure 933916DEST_PATH_IMAGE040
.
CN 201110385815 2011-11-29 2011-11-29 Multi-disc overall adjustment calibration method of rotary photogrammetry system Active CN102519484B (en)

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CN106595602A (en) * 2016-10-31 2017-04-26 武汉市工程科学技术研究院 Relative orientation method based on homonymous line features
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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
CN108447100A (en) * 2018-04-26 2018-08-24 王涛 A kind of eccentric vector sum Collimation axis eccentricity angle scaling method of airborne TLS CCD camera

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