CN105118055B - Camera position amendment scaling method and system - Google Patents

Abstract

The invention discloses a kind of camera position amendment scaling method and the system for realizing this method, belong to virtual manufacture technology field.Pass through lens parameters, internal relation between imaging surface and optictracking device, utilize the world coordinates of N number of mark point on background screen, picpointed coordinate and camera lens inner parameter and lens distortion parameter, obtain the translation vector of spin matrix between camera coordinates system and world coordinate system and the video camera centre of perspectivity in world coordinate system, with reference to the current location information that video camera posture external trace device provides under current state, try to achieve video camera amendment demarcation information and the angle of visual field, establish its look-up table with focal distance and with focal length relation, so that work as camera position, lens focus, when focal distance changes, automatic location amendment is carried out to the position of the virtual camera of virtual manufacturing system, so that real scene shooting frame of video picture and virtual two field picture perfect matching caused by computer.

Description

Camera position amendment scaling method and system

Technical field

The present invention relates to a kind of camera position amendment scaling method and the system for realizing this method, belong to virtual system Make technical field.

Background technology

Virtual camera posture and the angle of visual field are two extremely important information needed for computer picture rendering engine. In virtual photography Making programme, for the visual effect obtained, it is desirable to which real scene shooting picture matches with virtual screen.This matching is The shooting effect of real camera can be imitated by referring to the effect of virtual screen, if the focal length of camera lens, focal distance are sent out Raw to change, the angle of visual field of virtual camera is also corresponding to be changed in real time；When video camera seat in the plane changes, computer picture generates Change on position also accordingly occurs for the virtual camera seat in the plane in engine.Newauto (Beijing) Video Technology Co., Ltd. carries Go out the acquisition methods and device (application number 200810223256.3) of a kind of calibrating parameters, this method passes through known enough ginsengs The space coordinates of examination point calculates inner parameter and the outside of video camera using double flat areal coordinate scaling method or Linear Camaera Calibrating Method Parameter, the inner parameter of video camera include the optics and geometrical property, focal length of video camera, scale factor and lens distortion etc., The external parameter of video camera includes position and direction of the camera coordinates relative to world coordinate system, then using ant group algorithm pair Parameter optimizes, and generates evaluation function.But this document does not provide specific embodiment and technical scheme, and also not Which kind of illustrate specifically to be calculated using parameter.A kind of method for calibrating camera parameters that Material Evidence Identification Center, Ministry of Public Security proposes And device (application number 201010144764.X) is although be a kind of method of calibrating camera but it will be solved the problems, such as and this Invention is different, this application according in demarcation target image near principal point orthoscopic zone pixel point coordinates structure virtual grid so as to Distortion of camera coefficient is calculated, completes camera intrinsic parameter demarcation, and it is unrelated with video camera external parameter.Japanese Toyota is automatic A kind of video image positional relationship correction apparatus and set with the video image positional relationship amendment that loom Co., Ltd. proposes Standby steering assistance device and video image positional relationship modification method (application number 200480041109.4), this application are based on logical The video image reference point and virtual target point crossed video camera actual acquisition and the shown drift gage between coordinate on a monitor Coordinate conversion parameter is calculated, so as to the monitor coordinate for deriving virtual target.Beijing Jingwei Hirain Technologies Co., Ltd. proposes One kind emulation stand camera marking method and real-time machine (application number 201510134249.6), pass through the virtual video camera of foundation Collection scaling reference is simultaneously imaged, the relation established between its any point and virtual video camera plane of delineation coordinate, then by true Imaging point of the scaling reference any point in virtual video camera and real camera figure are established in imaging described in real camera acquisition Corresponding relation between image plane coordinate, solve to obtain scaling reference any point and real camera figure using the two relations Corresponding relation between image plane coordinate, so as to eliminate virtual video camera to existing parameter differences between real camera.Should Need first to establish virtual video camera in method, and the present invention directly calculates the angle of visual field being consistent with actual video camera, video camera Attitude information under world coordinate system gives image rendering engine (containing the anglec of rotation and camera position).

In order to reach such purpose, we allow for obtaining in real time under given coordinate system the position of video camera, Posture and visual field angle information.Usual way be on video camera install video camera posture external trace device such as optics with Track equipment, by the skew of the sensing station and optictracking device of photogrammetric camera, estimate that the position of video camera, posture are believed Breath.Existing real-time imaging virtually previews the video camera tracking of system, mainly measures in a manual manner, then according to green curtain Mark point or other characteristic points, are manually adjusted, and also do not account for the factor such as focal distance and the angle of visual field in addition, thus are led Cause less efficient and precision relatively low, cause the virtual scene that the video image from video camera and computer generate to misplace Phenomenon, virtual scene is caused to give people a kind of false sensation, the Overlay of virtual scene and real scene is undesirable.

The content of the invention

In order to reach the purpose of virtual background and real scene shooting image perfect matching, the position of video camera should be with computer picture wash with watercolours The position for contaminating the virtual camera that engine receives is identical.Aperture is obeyed in the imaging of the virtual camera of computer picture rendering engine Image-forming principle, so matching real camera position is then the intersection point of the centre of perspectivity, i.e. entrance pupil and optical axis of video camera. So it is video camera posture external trace device (such as optictracking device) and photography to finally obtain video camera amendment demarcation information The alternate position spike information of the machine centre of perspectivity.Based on above-mentioned principle, present invention offer is a kind of to be modified demarcation to camera position Method and system, by the internal relation between lens parameters, imaging surface and optictracking device, to the void of virtual manufacturing system Intend video camera position carry out automatic location amendment, and calculate be consistent with actual video camera the angle of visual field, camera position, Video camera posture gives image rendering engine, so that when camera position, lens focus, focal distance change, from It is dynamic to obtain video camera demarcation corrected parameter in real time, and the virtual of computer picture rendering engine is obtained according to demarcation corrected parameter Camera coordinates and posture so that real scene shooting frame of video picture and virtual two field picture perfect matching caused by computer.

In order to solve the above-mentioned technical problem, the invention provides a kind of method that demarcation is modified to camera position, Comprise the following steps：

S1. N number of mark point A on background screen is obtained₁..., A_NCoordinate under world coordinate system：A₁(x₁, y₁, z₁) ..., A_N(x_N, y_N, z_N), wherein coordinate of i-th of mark point under world coordinate system is A_i(x_i, y_i, z_i), i=1~N；Institute State N number of mark point and comprise at least 3 not collinear mark points；The mark point coordinates is the home position of mark point and described Mark point is respectively positioned in the picture of video camera collection；

S2. the focal distance sampled point FD of numerical value from small to large is determined₁, FD₂..., FD_j..., FD_J；Wherein j=1~J, FD₁And FD_JIt is the minimum focal distance of camera lens and maximum focal distance respectively；

If camera lens is zoom lens, also need to determine the focal length sampled point FL of numerical value from small to large₁, FL₂..., FL_k..., FL_K；Wherein k=1~K, FL₁And FL_KIt is the minimum focus and maximum focal length of camera lens respectively；

If S3. camera lens is tight shot, each focal distance sampled point FD is obtained_jIn corresponding camera lens Portion's parameter and lens distortion parameter；

If camera lens is zoom lens, each focal distance sampled point FD is obtained_jWith each focal length sampled point FL_kIt is right The camera lens inner parameter and lens distortion parameter answered；

The camera lens inner parameter and lens distortion parameter are obtained by camera lens calibration process；

If S4. camera lens is tight shot, when focal distance takes j-th of focal distance sampled point FD_jWhen, adjustment is taken the photograph Put the mark point blur-free imaging enabled on background screen in shadow seat in the plane；

If camera lens is zoom lens, when focal distance takes j-th of focal distance sampled point FD_jAnd focal length is in kth Individual sampled point FL_kDuring place, adjustment camera position enables the mark point blur-free imaging on background screen；

S5. the current location information that video camera posture external trace device provides under current state is obtained, including to make generation Boundary's coordinate system after translation successively respectively around its X-axis, Y-axis and Z axis rotation after with video camera posture external trace device from The rotation Eulerian angles that the coordinate system of definition overlaps, and position of the video camera posture external trace device under world coordinate system are sat Mark；

S6. sat using the picture point of the world coordinates of the S1 N number of mark points obtained, mark point under video camera imaging coordinate system The camera lens inner parameter and lens distortion parameter that mark and S3 are obtained, are obtained between camera coordinates system and world coordinate system Spin matrix and the video camera centre of perspectivity in the translation vector of world coordinate system, i.e. appearance of the video camera under world coordinate system State information；

S7. the current location information that video camera posture external trace device provides under the current state obtained using S5, and Attitude information of the video camera tried to achieve in S6 under world coordinate system, try to achieve video camera amendment demarcation information and the angle of visual field；

S8. if camera lens is tight shot：Focal distance is adjusted, to each focal distance sampled point FD_jPerform step Rapid S4~S7, until traveling through all focal distance sampled points, obtain the amendment demarcation letter corresponding to each focal distance sampled point Breath and the angle of visual field, establish the look-up table LUT1 of focal distance-amendment demarcation information-angle of visual field；

If camera lens is zoom lens：Focal distance and focal length are adjusted, to each focal distance sampled point FD_jWith it is every Individual focal length sampled point FL_kStep S4~S7 is performed, until traveling through all focal distance sampled points and focal length sampled point, is obtained each Amendment demarcation information and the angle of visual field corresponding to focal distance sampled point and focal length sampled point, establish focal distance-focal length-amendment Demarcate the look-up table LUT2 of information-angle of visual field；

S9. if camera lens is tight shot：Then according to the look-up table LUT1, obtained by focal distance corresponding Amendment demarcation information and the angle of visual field.

If camera lens is zoom lens：Then according to the look-up table LUT2, phase is obtained by focal distance and focal length The amendment demarcation information and the angle of visual field answered.

Further, camera position amendment scaling method proposed by the invention also includes following preferable technical side Case：

First, preferably, in step S3,

(1) when camera lens is tight shot：

For j-th of focal distance sampled point FD_j, corresponding camera lens inner parameter is：f_xj, f_yj, c_xj, c_yj, its In：

f_xj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith photography The ratio between horizontal width dx of each unit of machine imager, i.e.,

f_yj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith photography The ratio between vertical height dy of each unit of machine imager, i.e.,

c_xj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, with the level at imaging surface center partially The pixel count of shifting；

c_yj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, it is vertical with imaging surface center partially The pixel count of shifting；

For j-th of focal distance sampled point FD_j, corresponding camera lens distortions parameter is：k_1j, k_2j, k_3j, p_1jWith p_2j, wherein k_1j, k_2j, k_3jIt is FD for focal distance_jWhen radial distortion parameter, wherein k_3jFor selected parameter, when camera lens is flake K is used during camera lens_1j, k_2j, k_3jThese three radial distortion parameters, when camera lens is non-fish eye lens, k_3j=0, i.e. other camera lenses Use k_1j, k_2jThis two radial distortion parameter；p_1j, p_2jIt is FD for focal distance_jWhen tangential distortion parameter；

Also, obtain each focal distance FD_jUnder internal reference matrix M_jFor：

(2) when camera lens is zoom lens：

For j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding camera lens inside is joined Number is：f_xjk, f_yjk, c_xjk, c_yjk, wherein：

f_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the emergent pupil of camera lens and camera lens optical axis intersection point to imaging surface away from From f_jkThe ratio between with the horizontal width dx of each unit of imager, i.e.,

f_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the emergent pupil of camera lens and camera lens optical axis intersection point to imaging surface away from From f_jkThe ratio between with the vertical height dy of each unit of imager, i.e.,

c_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface, the water with imaging surface center The pixel count of flat skew；

c_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface, with hanging down for imaging surface center The pixel count directly offset；

For j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding camera lens distortions ginseng Number is：k_1jk, k_2jk, k_3jk, p_1jkAnd p_2jk, wherein k_1jk, k_2jkAnd k_3jkIt is FD for focal distance_jAnd focal length is FL_kWhen radial direction it is abnormal Variable element, wherein k_3jkFor selected parameter, k is used when camera lens is fish eye lens_1jk, k_2jkAnd k_3jkThese three radial distortions are joined Number；When camera lens is non-fish eye lens, k_3jk=0, i.e. other camera lenses only use k_1jk, k_2jkThe two radial distortion parameters；p_1jk, p_2jkIt is FD for focal distance_jAnd focal length is FL_kWhen tangential distortion parameter；

And obtain each focal distance FD_jWith focal length FL_kUnder internal reference matrix be M_jk：

2nd, preferably, in step S5,

(1) when camera lens is tight shot：

The current location information that the video camera posture external trace device provides is [θ_xj, θ_yj, θ_zj, T_xj, T_yj, T_zj]； Wherein [θ_xj, θ_yj, θ_zj] for make world coordinate system after translation successively respectively around X-axis, Y-axis and Z axis rotation after with video camera The rotation Eulerian angles that the customized coordinate system of posture external trace device overlaps, [T_xj, T_yj, T_zj] for outside video camera posture with Position coordinates of the track equipment under world coordinate system, the current location information that video camera posture external trace device is provided represent For following matrix form：

Here

T_Ij=[T_xj T_yj T_zj]^T

0=[0,0,0]；

(2) when camera lens is zoom lens：

The current location information that the video camera posture external trace device provides is [θ_xjk, θ_yjk, θ_zjk, T_xjk, T_yjk, T_zjk]；Wherein [θ_xjk, θ_yjk, θ_zjk] it is after world coordinate system is surrounded X-axis, Y-axis and Z axis rotation respectively successively after translation The rotation Eulerian angles overlapped with the customized coordinate system of video camera posture external trace device, [T_xjk, T_yjk, T_zjk] it is video camera Position coordinates of the posture external trace device under world coordinate system；The present bit that video camera posture external trace device is provided Confidence breath is expressed as matrix form：

Here

T_Ijk=[T_xjk T_yjk T_zjk]^T

0=[0,0,0]

3rd, preferably, in step S6：

(1) when camera lens is tight shot：

Current focal distance is FD_jWhen, obtain the spin matrix R between camera coordinates system and world coordinate system_pj, photography Translation vector T of the machine centre of perspectivity in world coordinate system_pj, attitude matrix H of the video camera under world coordinate system_pjMethod be：

According to the picpointed coordinate of i-th of mark pointAnd current focal distance FD_jUnder lens distortion ginseng Number, obtain the picpointed coordinate (x ' of i-th of mark point after correction_ij, y '_ij)：

Wherein if camera lens is non-fish eye lens, k_3j=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ij, y '_ij) it Between relation be expressed as：

Wherein λ_jReferred to as scale factor,

Spin matrix R wherein between camera coordinates system and world coordinate system_pjFor orthogonal matrix, T_pjIt is saturating for video camera Depending on center world coordinate system translation vector：

Pass through the world coordinates (x of formula (1) (2) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x '_ij, y′_ij), obtain matrix O_j=λ_j[R_pj, T_pj] and attitude information of the video camera under world coordinate system WhereinFor make world coordinate system after translation successively respectively around X-axis, Y-axis and Z axis rotation after with photography The rotation Eulerian angles that machine coordinate system overlaps,For translation of the video camera centre of perspectivity under world coordinate system Vector；

Again because matrix R_pjIt is unit orthogonal matrix, has：

λ_j=1/ | | O_j(：, 1) | |；

Wherein O_j(：, 1) and it is matrix O_jThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjAnd the video camera centre of perspectivity In the translation vector T of world coordinate system_pj, attitude information of the video camera under world coordinate system is expressed as matrix H_pj：

(2) when camera lens is zoom lens：

Current focal distance is FD_jAnd current focus is FL_kWhen, obtain between camera coordinates system and world coordinate system Spin matrix R_pjk, the video camera centre of perspectivity world coordinate system translation vector T_pjk, appearance of the video camera under world coordinate system State matrix H_pjkMethod be：

According to current focal distance FD_jWith current focus FL_kThe picpointed coordinate of lower i-th of mark point And Lens distortion parameter obtains the picpointed coordinate (x ' after its correction_ijk, y '_ijk)：

Wherein if camera lens is non-fish eye lens, k_3jk=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ijk, y '_ijk) it Between relation be expressed as：

Wherein λ_jkReferred to as scale factor,

Spin matrix R wherein between camera coordinates system and world coordinate system_pjkFor orthogonal matrix, T_pjkIt is saturating for video camera Depending on center world coordinate system translation vector：

Pass through the world coordinates (x of formula (3) (4) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x′_ijk, y '_ijk), obtain matrix O_jk=λ_jk[R_pjk, T_pjk] and attitude information of the video camera under world coordinate systemWhereinFor make world coordinate system after translation successively The rotation Eulerian angles overlapped respectively after X-axis, Y-axis and Z axis rotation with camera coordinates system, For translation vector of the video camera centre of perspectivity under world coordinate system；

Because matrix R_pjkIt is unit orthogonal matrix, has：

λ_jk=1/ | | O_jk(：, 1) | |；

Wherein O_jk(：, 1) and it is matrix O_jkThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjkAnd the video camera centre of perspectivity In the translation vector T of world coordinate system_pjk, attitude information of the video camera under world coordinate system is expressed as matrix H_pjk：

4th, preferably, step S7 comprises the following steps：

(1) when camera lens is tight shot：

S7.1 calculates video camera attitude rectification matrix H_j：

S7.2 is by video camera attitude rectification matrix H_jIt is transformed to correct quaternary number (θ_j, n_xj, n_yj, n_zj) and translation vector T_j：

The video camera attitude rectification matrix H_jIt is 4 × 4 matrix, its live part is H_j(1：3,1：4), i.e. H_jBefore Three rows, by H_j(1：3,1：4) it is expressed as form：

H_j(1：3,1：4)=[R_j, T_j]；

Wherein spin matrix R_jFor 3 × 3 real number matrix, translation vector T_j=[t_xj, t_yj, t_zj]^TFor 3-dimensional column vector；

By spin matrix R_jAmendment quaternary number (θ is converted to according to following formula_j, n_xj, n_yj, n_zj)：

HereFor 3-dimensional row vector；

Thus storage R_jAmendment quaternary number (θ need to only be stored_j, n_xj, n_yj, n_zj), therefore video camera attitude rectification matrix H_jBe converted to video camera amendment demarcation information (θ_j, n_xj, n_yj, n_zj, t_xj, t_yj, t_zj)；

S7.3 calculates camera coverage angle：When focal distance is FD_jWhen, camera coverage angle α is calculated according to following formula_j：

Wherein W, H are respectively the width of video camera, high-resolution.

(2) when camera lens is zoom lens：

S7.1 calculates video camera attitude rectification matrix H_jk：

S7.2 is by video camera attitude rectification matrix H_jkIt is transformed to correct quaternary number (θ_jk, n_xjk, n_yjk, n_zjk) and translation vector T_jk：

The video camera attitude rectification matrix H_jkIt is 4 × 4 matrix, its live part is H_jk(1：3,1：4), i.e. H_jk's First three rows, by H_jk(1：3,1：4) it is expressed as form：

H_jk(1：3,1：4)=[R_jk, T_jk]；

Wherein spin matrix R_jkFor 3 × 3 real number matrix, translation vector T_jk=[t_xjk, t_yjk, t_zjk]^TFor 3-dimensional column vector；

By spin matrix R_jkAmendment quaternary number (θ is converted to according to following formula_jk, n_xjk, n_yjk, n_zjk)：

HereFor 3-dimensional row vector；

Thus storage R_jkAmendment quaternary number (θ need to only be stored_jk, n_xjk, n_yjk, n_zjk), therefore video camera attitude rectification Matrix H_jkBe converted to video camera amendment demarcation information (θ_jk, n_xjk, n_yjk, n_zjk, t_xjk, t_yjk, t_zjk)；

S7.3 calculates camera coverage angle：When focal distance is FD_jAnd focal length is FL_kWhen, video camera is calculated according to following formula and regarded Rink corner α_jk：

Wherein W, H are respectively the width of video camera, high-resolution.

5th, preferably, in step S9,

When actual focal distance FD is not in any one focal distance sampled point FD_jPlace, or real focal length FL be not in office What focal length sampled point FL_kPlace, or when actual focal distance FD is not in any one focal distance sampled point FD_jPlace and Real focal length FL is not also in any one focal length sampled point FL_kDuring place, obtained by the way of following interpolation arithmetic corresponding to it Amendment demarcation information and the angle of visual field：

Row interpolation is entered using SLERP interpolation methods for the amendment quaternary number that amendment is demarcated in information, translation vector uses Linear interpolation；The angle of visual field enters row interpolation using linear interpolation method.

Further,

(1) when camera lens is tight shot：

When actual focal distance FD is not in any one focal distance sampled point FD_jPlace, using SLERP algorithms to amendment four The method that first number enters row interpolation is as follows：

If FD_j＜ FD ＜ FD_j+1, video camera is in focal distance FD_jAnd FD_j+1The video camera attitude rectification matrix at place is respectively H_jWith H_j+1, its spin matrix is respectively R_jAnd R_j+1, spin matrix is expressed as to correct quaternary number WithAmendment quaternary number q when then for currently practical focal distance FD is by following formula Calculate：

HereIt is q_jIt is inverse,

(2) when camera lens is zoom lens：

When actual focal distance FD is not in any one focal distance sampled point FD_jPlace, or real focal length FL be not in office What focal length sampled point FL_kPlace, or when actual focal distance FD is not in any one focal distance sampled point FD_jPlace and Real focal length FL is not also in any one focal length sampled point FL_kDuring place, row interpolation is entered to amendment quaternary number using SLERP algorithms Method is as follows：

If 1. FD_j＜ FD ＜ FD_j+1And FL_k＜ FL ＜ FL_k+1, i.e., when actual focal distance FD is not in any one focusing From sampled point FD_jPlace, and real focal length FL is not also in any one focal length sampled point FL_kPlace, using with its closest to focusing Distance and focal length sampled point combination (FD_j, FL_k), (FD_j, FL_k+1), (FD_j+1, FL_k), (FD_j+1, FL_k+1) corresponding to amendment four First number q_{J, k}, q_{J, k+1}, q_{J+1, k}, q_{J+1, k+1}, enter row interpolation according to the following formula, then for currently practical focal distance FD and actual Jiao Away from for FL when amendment quaternary number q_{L, d}Calculated by following formula：

Wherein：

If 2. FD_j＜ FD ＜ FD_j+1, FL=FL_kWhen, i.e., when actual focal distance FD does not sample in any one focal distance Point FD_jPlace and real focal length FL is focal length sampled point FL_kWhen, using with its closest to focal distance sampled point combine (FD_j, FL_k), (FD_j+1, FL_k) corresponding to amendment quaternary number information q_{J, k}, q_{J+1, k}, enter row interpolation according to the following formula, then for currently practical Focal distance FD and amendment quaternary number q when real focal length is FL_{L, d}Calculated by following formula

Wherein

If 3. FD=FD_j, FL_k＜ FL ＜ FL_k+1When, i.e., when actual focal distance FD is focal distance sampled point FD_jIt is and real Border focal length FL is not in any one focal length sampled point FL_kDuring place, using with its closest to focal length sampled point combine (FD_j, FL_k), (FD_j, FL_k+1) corresponding to amendment quaternary number information q_{J, k}, q_{J, k+1}, enter row interpolation according to the following formula, then for currently practical focusing Distance FD and amendment quaternary number q when real focal length is FL_{L, d}Calculated by following formula：

Wherein

In addition, according to as above method, the present invention also proposes a kind of camera position amendment calibration system, including：Servo horse Up at control system, video camera, video camera posture external trace device, background screen, mark point, space measurement equipment, data Manage equipment, computer picture rendering engine；

Wherein, servo-motor control system is connected with video camera, for adjusting the focal length and focal distance of camera lens；Servo horse Also it is connected up to control system with data processing equipment, the focal length for sending camera lens to data processing equipment is believed with focal distance Breath, so that data processing equipment calculates amendment demarcation information and the angle of visual field and establishes look-up table；

Data processing equipment is also connected with video camera, for reading video stream data in real time；

Video camera posture external trace device is arranged at outside video camera, for the position by photogrammetric camera and photography The skew of machine posture external trace device, estimate position and the attitude information of video camera；Video camera posture external trace device is also It is connected with data processing equipment, for sending measurement data information；

At least three not conllinear mark point is set on background screen, and these mark point radiuses are identical, color and background screen With contrast；

Space measurement equipment and image rendering engine are connected with data processing equipment respectively, and space measurement equipment is used to measure The world coordinates of mark point home position is simultaneously sent to data processing equipment, and image rendering engine is used for according to data processing equipment The look-up table of foundation obtains corresponding amendment demarcation information and the angle of visual field.

Compared with prior art, the beneficial effects of the present invention are not only realize video camera amendment calibration process completely certainly Dynamicization, without manual intervention, and the position of video camera, posture and angle of visual field letter under given coordinate system can be calculated in real time Breath, and engine is generated according to above- mentioned information accurately image by image so that real scene shooting frame of video picture and void caused by computer Intend two field picture perfect matching.

Brief description of the drawings

Fig. 1 is the composition schematic diagram of camera position amendment calibration system proposed by the present invention；Wherein, 1- servo motors control System processed；2- video cameras, 3- camera lens, 4- video camera posture external trace devices；5- background screens；6- mark points；7- Data processing equipment；

Fig. 2 is the method flow diagram proposed by the present invention that demarcation is modified to tight shot camera position；

Fig. 3 is the method flow diagram proposed by the present invention that demarcation is modified to zoom lens camera position.

Embodiment

The present invention is described in detail below in conjunction with drawings and examples, while also describes technical solution of the present invention Technical problem, principle and the beneficial effect of solution.

As shown in figure 1, be the structure chart according to camera position amendment calibration system proposed by the present invention, as illustrated, Camera position amendment calibration system proposed by the present invention includes：Servo-motor control system, video camera, outside video camera posture Tracking equipment, background screen, mark point, space measurement equipment (not shown), data processing equipment, image rendering engine (not shown)；

Wherein, servo-motor control system is connected with video camera, for adjusting the focal length and focal distance of camera lens；Servo horse Also it is connected up to control system with data processing equipment, the focal length for sending camera lens to data processing equipment is believed with focal distance Breath, so that data processing equipment calculates amendment demarcation information and the angle of visual field and establishes look-up table；

Data processing equipment is also connected with video camera, for reading video stream data in real time；

Video camera posture external trace device is arranged at outside video camera, for the position by photogrammetric camera and photography The skew of machine posture external trace device, estimate position and the attitude information of video camera；Video camera posture external trace device is also It is connected with data processing equipment, for sending measurement data information；

At least three not conllinear mark point is set on background screen, and these mark point radiuses are identical, color and background screen With contrast；

Space measurement equipment and image rendering engine are connected with data processing equipment respectively, and space measurement equipment is used to measure The world coordinates of mark point home position is simultaneously sent to data processing equipment, and image rendering engine is used for according to data processing equipment The look-up table of foundation obtains corresponding amendment demarcation information and the angle of visual field.

Preferably, background screen is green curtain or blue curtain.

Preferably, the video camera posture external trace device is optictracking device or mechanical arm.

The workflow of camera position amendment calibration system proposed by the present invention comprises the following steps：

S1. coordinate of N number of mark point under world coordinate system on background screen, A are obtained using space measurement equipment₁(x₁, y₁, z₁) ..., A_N(x_N, y_N, z_N), and the world coordinates of mark point is sent to data processing equipment, N number of mark point is at least Including 3 not collinear mark points；

S2. the focal distance sampled point FD of multiple numerical value from small to large is determined₁, FD₂..., FD_j..., FD_J(j=1~J), FD₁And FD_JIt is the minimum focal distance of camera lens and maximum focal distance respectively；

If camera lens is zoom lens, also need to determine the focal length sampled point FL of numerical value from small to large₁, FL₂..., FL_k..., FL_K；Wherein k=1~K, FL₁And FL_KIt is the minimum focus and maximum focal length of camera lens respectively；

Preferably, the focal distance sampled point and focal length sampled point use the sampled point in camera lens calibration process； Following document is refer on camera lens demarcation：[1]Duane C B.Close-range camera calibration[J] .Photogram.Eng.Remote Sens, 1971,37：855-866. and [2] Zhang Z.Flexible camera Calibration by viewing a plane from unknown orientations [C] //Computer Vision, 1999.The Proceedings of the Seventh IEEE International Conference on.IEEE, 1999,1：666-673.

Focal distance choosing method：It is placed on the rotation section of the servo-motor control system of the regulation focus of camera lens (such as [0,1]) J-1 sections are divided into, common J end points, these corresponding end points are focal distance sampling point value；J typically chooses 10-30 Between integer.

The choosing method of focal length sampled point：It is placed on the rotation section of the servo-motor control system focused of camera lens K-1 sections are divided into (such as [0,1]), common K end points, these corresponding end points are focal length sampling point value；K is typically according to camera lens Zooming range is suitably chosen.

S3. camera inner parameter corresponding to each focal distance sampled point is obtained by data processing equipment and distortion is joined Number；The camera lens inner parameter and lens distortion parameter are obtained by camera lens calibration process；

S4. servo-motor control system sends the focal length and focal distance information of camera lens to data processing equipment, works as focusing Distance is in j-th of sampled point FD_jPlace, adjustment camera position enable the mark point blur-free imaging on background screen；

If camera lens is zoom lens, when focal distance takes j-th of focal distance sampled point FD_jAnd focal length is in kth Individual sampled point FL_kDuring place, adjustment camera position enables the mark point blur-free imaging on background screen；

S5. passed using video camera posture external trace device such as optictracking device or mechanical arm to data processing equipment Pass the positional information under its current state；Including to make world coordinate system surround its X-axis, Y-axis and Z respectively successively after translation The rotation Eulerian angles overlapped after axle rotation with the customized coordinate system of video camera posture external trace device, and video camera posture Position coordinates of the external trace device under world coordinate system；

The optictracking device such as total powerstation etc.；

S6. data processing equipment utilizes the world coordinates of N number of mark point of S1 acquisitions, mark point in video camera imager coordinate The camera lens inner parameter and lens distortion parameter that picpointed coordinate and S3 under system obtain, obtain camera coordinates system and generation Spin matrix and the video camera centre of perspectivity between boundary's coordinate system are in the translation vector of world coordinate system, i.e., video camera is in the world Attitude information under coordinate system；

Preferably, video camera imaging coordinate system origin is set in field of view center.

S7. video camera posture external trace device provides current under the current state that data processing equipment is obtained using S5 Attitude information of the video camera tried to achieve in positional information, and S6 under world coordinate system, try to achieve video camera amendment demarcation information and The angle of visual field；

S8. if camera lens is tight shot：Focal distance is adjusted, to each focal distance sampled point FD_jPerform step Rapid S4~S7, until traveling through all focal distance sampled points, obtain the amendment demarcation letter corresponding to each focal distance sampled point Breath and the angle of visual field, data processing equipment establish the look-up table LUT1 of focal distance-amendment demarcation information-angle of visual field；

If camera lens is zoom lens：Focal distance and focal length are adjusted, to each focal distance sampled point FD_jWith it is every Individual focal length sampled point FL_kStep S4~S7 is performed, until traveling through all focal distance sampled points and focal length sampled point, is obtained each Amendment demarcation information and the angle of visual field, data processing equipment corresponding to focal distance sampled point and focal length sampled point establish focusing From the look-up table LUT2 of-focal length-amendment demarcation information-angle of visual field；

S9. if camera lens is tight shot：The look-up table that image rendering engine is established according to data processing equipment LUT1, corresponding amendment demarcation information and the angle of visual field are obtained by focal distance.

If camera lens is zoom lens：The look-up table that image rendering engine is established according to data processing equipment LUT2, corresponding amendment demarcation information and the angle of visual field are obtained by focal distance and focal length.

It goes for tight shot to the camera position amendment calibration system being related in the present invention, is equally applicable to become Zoom lens, illustrate this hair by taking the camera position amendment calibration system with tight shot and zoom lens as an example respectively here The technical scheme of the bright camera position amendment scaling method：

First, tight shot (see accompanying drawing 2)

S1. the world coordinates of mark point is obtained：

The world coordinates A of N number of mark point on utilization space measuring apparatus measurement background screen₁(x₁, y₁, z₁) ..., A_N(x_N, y_N, z_N), N number of mark point comprises at least 3 not collinear mark points；The mark point coordinates is the home position of mark point And the mark point is respectively positioned in the picture of video camera collection；Coordinate of wherein i-th of the mark point under world coordinate system be A_i(x_i, y_i, z_i), i=1~N；

S2. focal distance sampled point is determined：

By servo-motor control system, the focal distance of numerical value from small to large is determined according to camera lens calibration process Sampled point FD₁, FD₂..., FD_j..., FD_J(j=1~J), FD₁And FD_JIt is the minimum focal distance of camera lens and maximum focusing respectively Distance；

S3. camera inner parameter and distortion parameter corresponding to each focal distance sampled point are obtained and is recorded, institute State camera lens inner parameter and lens distortion parameter is obtained by camera lens calibration process；

Specifically, for j-th of focal distance sampled point FD_j, corresponding camera lens inner parameter is：f_xj, f_yj, c_xj, c_yj, wherein：

f_xj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith photography The ratio between horizontal width dx of each unit of machine imager, i.e.,

f_yj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith photography The ratio between vertical height dy of each unit of machine imager, i.e.,

Preferably, video camera imager described herein is CCD or CMOS.

c_xj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, with the level at imaging surface center partially The pixel count of shifting；

c_yj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, it is vertical with imaging surface center partially The pixel count of shifting；

For j-th of focal distance sampled point FD_j, corresponding camera lens distortions parameter is：k_1j, k_2j, k_3j, p_1jWith p_2j, wherein k_1j, k_2j, k_3jIt is FD for focal distance_jWhen radial distortion parameter, wherein k_3jFor selected parameter, when camera lens is flake K is used during camera lens_1j, k_2j, k_3jThese three radial distortion parameters, when camera lens is non-fish eye lens, k_3j=0, i.e. other camera lenses Use k_1j, k_2jThis two radial distortion parameter；p_1j, p_2jIt is FD for focal distance_jWhen tangential distortion parameter；

Also, obtain each focal distance FD_jUnder internal reference matrix M_jFor：

S4. when focal distance takes j-th of focal distance sampled point FD_jWhen, adjustment camera position causes on background screen Mark point being capable of blur-free imaging；

S5. data processing equipment obtains the current location of video camera posture external trace device such as optictracking device transmission Information [θ_xj, θ_yj, θ_zj, T_xj, T_yj, T_zj].Wherein [θ_xj, θ_yj, θ_zj] it is world coordinate system is surrounded respectively successively after translation The rotation Eulerian angles overlapped after X-axis, Y-axis and Z axis rotation with the customized coordinate system of video camera posture external trace device, [T_xj, T_yj, T_zj] it is position coordinates of the video camera posture external trace device under world coordinate system, by video camera posture external trace The current location information that equipment provides is expressed as matrix form：

Here

T_Ij=[T_xj T_yj T_zj]^T

0=[0,0,0]；

S6. sat using the picture point of the world coordinates of the S1 N number of mark points obtained, mark point under video camera imaging coordinate system The camera lens inner parameter and lens distortion parameter that mark and S3 are obtained, are obtained between camera coordinates system and world coordinate system Spin matrix R_pjAnd the video camera centre of perspectivity is in the translation vector T of world coordinate system_pj, i.e., video camera is in world coordinate system Under attitude information；

Preferably, current focal distance is FD_jWhen, obtain the spin moment between camera coordinates system and world coordinate system Battle array R_pj, the video camera centre of perspectivity world coordinate system translation vector T_pj, attitude matrix H of the video camera under world coordinate system_pj Method be：

According to the picpointed coordinate of i-th of mark pointAnd current focal distance FD_jUnder lens distortion ginseng Number, obtain the picpointed coordinate (x ' of i-th of mark point after correction_ij, y '_ij)：

Wherein if camera lens is non-fish eye lens, k_3j=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ij, y '_ij) it Between relation be expressed as：

Wherein λ_jReferred to as scale factor,

Spin matrix R wherein between camera coordinates system and world coordinate system_pjFor orthogonal matrix, T_pjIt is saturating for video camera Depending on center world coordinate system translation vector：

Pass through the world coordinates (x of formula (1) (2) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x′_ij, y '_ij), obtain matrix O_j=λ_j[R_pj, T_pj] and attitude information of the video camera under world coordinate systemWhereinTo make world coordinate system surround X respectively successively after translation The rotation Eulerian angles overlapped after axle, Y-axis and Z axis rotation with camera coordinates system,Had an X-rayed for video camera Translation vector of the center under world coordinate system；

Again because matrix R_pjIt is unit orthogonal matrix, has：

λ_j=1/ | | O_j(：, 1) | |；

Wherein O_j(：, 1) and it is matrix O_jThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjAnd the video camera centre of perspectivity In the translation vector T of world coordinate system_pj, attitude information of the video camera under world coordinate system is expressed as matrix H_pj：

S7. the current location information that video camera posture external trace device provides under the current state obtained using S5, and Attitude information of the video camera tried to achieve in S6 under world coordinate system, try to achieve video camera amendment demarcation information and the angle of visual field；

S7.1 calculates video camera attitude rectification matrix first.Calculate video camera attitude rectification matrix and mainly utilize video camera With the consistency of the relative position relation of optictracking device, constant relative position relation here is the effective of once mounting Phase, optictracking device is reinstalled, it is necessary to be re-scaled to camera position.Following formula can be utilized to calculate when calculating to take the photograph Shadow machine attitude rectification matrix H_j：

S7.2 is by video camera attitude rectification matrix H_jIt is transformed to correct quaternary number (θ_j, n_xj, n_yj, n_zj) and translation vector T_j：

The calculating video camera attitude rectification matrix H obtained due to formula (5)_jIt is 4 × 4 matrix, it is not easy to store, and And be also not easy to carry out interpolation calculation in subsequent arithmetic, therefore, it is necessary to transform it into the form for being easy to storage and computing.

The video camera attitude rectification matrix H_jIt is 4 × 4 matrix, its live part is H_j(1：3,1：4), i.e. H_jBefore Three rows, by H_j(1：3,1：4) it is expressed as form：

H_j(1：3,1：4)=[R_j, T_j]；

Wherein spin matrix R_jFor 3 × 3 real number matrix, translation vector T_j=[t_xj, t_yj, t_zj]^TFor 3-dimensional column vector；

Due to spin matrix R_jCan mutually it be changed with quaternary number, therefore by spin matrix R_jAmendment is converted to according to following formula Quaternary number (θ_j, n_xj, n_yj, n_zj)：

HereFor 3-dimensional row vector.

HereFor 3-dimensional row vector；

Thus storage R_jAmendment quaternary number (θ need to only be stored_j, n_xj, n_yj, n_zj), therefore video camera attitude rectification matrix H_jBe converted to video camera amendment demarcation information (θ_j, n_xj, n_yj, n_zj, t_xj, t_yj, t_zj)；Wherein correct quaternary number and translation vector It is collectively referred to as amendment demarcation information.

S7.3 calculates camera coverage angle：When focal distance is FD_jWhen, camera coverage angle α is calculated according to following formula_j：

Wherein W, H are the width of video camera, high-resolution.

S8. focal distance is adjusted, to each focal distance sampled point FD_jStep S4~S7 is performed, it is all right until traveling through Defocus distance sampled point, obtain the amendment demarcation information (θ corresponding to each focal distance sampled point_j, n_xj, n_yj, n_zj, t_xj, t_yj, t_zj) and angle of visual field α_j, establish the look-up table LUT1 that information-angle of visual field is demarcated in focal distance-amendment；

S9. export LUT1 and focal distance is passed through according to the look-up table LUT1 to image rendering engine, image rendering engine Obtain corresponding amendment demarcation information and the angle of visual field.

1 focal distance of table-amendment demarcation information-angle of visual field look-up table LUT1 form

When camera lens are tight shot, image generation engine is being obtained using look-up table LUT1 according to focal distance It is not every because the focal distance sampled point recorded in look-up table LUT1 is limited when corresponding amendment demarcation information and the angle of visual field The focal distance of secondary selection is all precisely the focal distance of sample point.For the focal distance at non-sampled point, can use The mode of interpolation arithmetic obtains amendment demarcation information corresponding to its, due to correcting quaternary number, translation vector and the angle of visual field its number It is different to learn characteristic, therefore in order to reach more accurate interpolation arithmetic effect, different interpolation algorithms can be respectively adopted.It is specific next Say, the amendment quaternary number demarcated for amendment in information enters row interpolation, translation vector (t using SLERP interpolation methods_x, t_y, t_z) Using linear interpolation, the angle of visual field uses linear interpolation, or other forms to enter row interpolation.

Wherein, preferably, the method for entering row interpolation to amendment quaternary number using SLERP algorithms is as follows：

If FD_j＜ FD ＜ FD_j+1, video camera is in focal distance FD_jAnd FD_j+1The video camera attitude rectification matrix at place is respectively H_jAnd H_j+1, its spin matrix is respectively R_jAnd R_j+1, spin matrix is expressed as to correct quaternary numberWithWhen then for currently practical focal distance FD Amendment quaternary number q calculated by following formula：

HereIt is q_jIt is inverse,

It is possible thereby in the case where focal distance is any value, corresponding amendment demarcation information and the angle of visual field are obtained.

2nd, zoom lens (see accompanying drawing 3)

For the camera position amendment calibration system using zoom lens, the change except needing consideration focal distance, The change of focal length should also be considered simultaneously, the amendment mark under each focal distance sampled point, focal length sampled point should be obtained respectively Information and the angle of visual field are determined, referring specifically to Fig. 3：

S1. the world coordinates of mark point is obtained：

N number of mark point A on utilization space measuring apparatus measurement background screen₁..., A_NWorld coordinate system under coordinate A₁ (x₁, y₁, z₁) ..., A_N(x_N, y_N, z_N), N number of mark point comprises at least 3 not collinear mark points；The mark point is sat It is designated as the home position of mark point and the mark point is respectively positioned in the picture of video camera collection；Wherein i-th of mark point exists Coordinate under world coordinate system is A_i(x_i, y_i, z_i), i=1~N；

S2. focal distance sampled point and focal length sampled point are determined：

By servo-motor control system, the focal distance of numerical value from small to large is determined according to camera lens calibration process Sampled point FD₁, FD₂..., FD_j..., FD_J(j=1~J), FD₁And FD_JIt is the minimum focal distance of camera lens and maximum focusing respectively Distance；In addition, determine the focal length sampled point FL of numerical value from small to large₁, FL₂..., FL_k..., FL_K(k=1~K), FL₁And FL_KPoint It is not the minimum focus and maximum focal length of camera lens.

S3. it is abnormal that camera lens inner parameter and camera lens corresponding to each focal distance sampled point and focal length sampled point are obtained Variable element is simultaneously recorded, and the camera lens inner parameter and lens distortion parameter are obtained by camera lens calibration process；

Preferably, for j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding video camera mirror Head inner parameter be：f_xjk, f_yjk, c_xjk, c_yjk, wherein：

f_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the emergent pupil of camera lens and camera lens optical axis intersection point to imaging surface away from From f_jkThe ratio between with the horizontal width dx of each unit of imager, i.e.,

f_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the emergent pupil of camera lens and camera lens optical axis intersection point to imaging surface away from From f_jkThe ratio between with the vertical height dy of each unit of imager, i.e.,

c_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface, the water with imaging surface center The pixel count of flat skew；

c_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface, with hanging down for imaging surface center The pixel count directly offset；

For j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding camera lens distortions ginseng Number is：k_1jk, k_2jk, k_3jk, p_1jkAnd p_2jk, wherein k_1jk, k_2jkAnd k_3jkIt is FD for focal distance_jAnd focal length is FL_kWhen radial direction it is abnormal Variable element, wherein k_3jkFor selected parameter, k is used when camera lens is fish eye lens_1jk, k_2jkAnd k_3jkThese three radial distortions are joined Number；When camera lens is non-fish eye lens, k_3jk=0, i.e. other camera lenses only use k_1jk, k_2jkThe two radial distortion parameters；p_1jk, p_2jkIt is FD for focal distance_jAnd focal length is FL_kWhen tangential distortion parameter；

And obtain each focal distance FD_jWith focal length FL_kUnder internal reference matrix be M_jk：

S4. when focal distance takes j-th of focal distance sampled point FD_jAnd focal length is in k-th of sampled point FL_kDuring place, adjustment is taken the photograph Put the mark point blur-free imaging enabled on background screen in shadow seat in the plane；

S5. obtain current state under video camera posture external trace device such as optictracking device or mechanical arm transmission work as Front position information [θ_xjk, θ_yjk, θ_zjk, T_xjk, T_yjk, T_zjk].Wherein [θ_xjk, θ_yjk, θ_zjk] it is to make world coordinate system after translation The rotation overlapped respectively after X-axis, Y-axis and Z axis rotation with the customized coordinate system of video camera posture external trace device successively Turn Eulerian angles, [T_xjk, T_yjk, T_zjk] it is position coordinates of the video camera posture external trace device under world coordinate system；Will photography The current location information that machine posture external trace device provides is expressed as matrix form：

Here

T_Ijk=[T_xjk T_yjk T_zjk]^T

0=[0,0,0]

S6. sat using the picture point of the world coordinates of the S1 N number of mark points obtained, mark point under video camera imaging coordinate system The camera lens inner parameter and lens distortion parameter that mark and S3 are obtained, are obtained between camera coordinates system and world coordinate system Spin matrix R_pjkAnd the video camera centre of perspectivity is in the translation vector T of world coordinate system_pjk, i.e., video camera is in world coordinate system Under attitude information；

Current focal distance is FD_jAnd current focus is FL_kWhen, obtain between camera coordinates system and world coordinate system Spin matrix R_pjk, the video camera centre of perspectivity world coordinate system translation vector T_pjk, appearance of the video camera under world coordinate system State matrix H_pjkMethod be：

According to current focal distance FD_jWith current focus FL_kThe picpointed coordinate of lower i-th of mark pointAnd Lens distortion parameter obtains the picpointed coordinate (x ' after its correction_ijk, y '_ijk)：

Wherein if camera lens is non-fish eye lens, k_3jk=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ijk, y '_ijk) it Between relation be expressed as：

Wherein λ_jkReferred to as scale factor,

Spin matrix R wherein between camera coordinates system and world coordinate system_pjkFor orthogonal matrix, T_pjkIt is saturating for video camera Depending on center world coordinate system translation vector：

Pass through the world coordinates (x of formula (3) (4) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x′_ijk, y '_ijk), obtain matrix O_jk=λ_jk[R_pjk, T_pjk] and attitude information of the video camera under world coordinate systemWhereinFor make world coordinate system after translation successively The rotation Eulerian angles overlapped respectively after X-axis, Y-axis and Z axis rotation with camera coordinates system, For translation vector of the video camera centre of perspectivity under world coordinate system；

Because matrix R_pjkIt is unit orthogonal matrix, has：

λ_jk=1/ | | O_jk(：, 1) | |；

Wherein O_jk(：, 1) and it is matrix O_jkThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjkAnd the video camera centre of perspectivity In the translation vector T of world coordinate system_pjk, attitude information of the video camera under world coordinate system is expressed as matrix H_pjk：

S7. the current location information that video camera posture external trace device provides under the current state obtained using S5, and Attitude information of the video camera tried to achieve in S6 under world coordinate system, try to achieve video camera amendment demarcation information and the angle of visual field；

S7.1 calculates video camera attitude rectification matrix：

It is mainly to utilize the relative position relation of video camera and optictracking device to calculate video camera attitude rectification matrix Consistency, it is the term of validity of once mounting that relative position relation here is constant, reinstalls optictracking device, it is necessary to taking the photograph The positioning of shadow machine is re-scaled.Formula (6) can be utilized to calculate video camera attitude rectification matrix H when calculating_jk。

Wherein

S7.2 is by video camera attitude rectification matrix H_jkIt is transformed to correct quaternary number (θ_jk, n_xjk, n_yjk, n_zjk) and translation vector T_jk：

The calculating video camera attitude rectification matrix H obtained due to formula (6)_jkIt is 4 × 4 matrix, it is not easy to store, and And be also not easy to carry out interpolation calculation in subsequent arithmetic, therefore, it is necessary to transform it into the form for being easy to storage and computing.

The video camera attitude rectification matrix H_jkIt is 4 × 4 matrix, its live part is H_jk(1：3,1：4), i.e. H_jk's First three rows, by H_jk(1：3,1：4) it is expressed as form：

H_jk(1：3,1：4)=[R_jk, T_jk],

Wherein spin matrix R_jkFor 3 × 3 real number matrix, translation vector T_jk=[t_xjk, t_yjk, t_zjk]^TFor 3-dimensional column vector；

Due to spin matrix R_jkCan mutually it be changed with quaternary number, by spin matrix R_jkAmendment four is converted to according to following formula First number (θ_jk, n_xjk, n_yjk, n_zjk)：

HereFor 3-dimensional row vector.

Thus storage R_jkOnly need to store (θ_jk, n_xjk, n_yjk, n_zjk), therefore video camera attitude rectification matrix H_jkConversion Information (θ is demarcated for video camera amendment_jk, n_xjk, n_yjk, n_zjk, t_xjk, t_yjk, t_zjk)；Wherein correct quaternary number and translation vector is collectively referred to as Information is demarcated for amendment.

S7.3 calculates camera coverage angle：When focal distance is FD_j, focal length FL_kWhen, camera coverage angle α_jkUnder Face formula is calculated：

Wherein W, H are the width of video camera, high-resolution.

S8. focal distance and focal length are adjusted, to each focal distance sampled point FD_jWith each focal length sampled point FL_kPerform step Rapid S4~S7, until traveling through all focal distance sampled points and focal length sampled point, obtain each focal distance sampled point and focal length Amendment demarcation information and the angle of visual field corresponding to sampled point, establish looking into for focal distance-focal length-amendment demarcation information-angle of visual field Look for table LUT2；Form example is shown in Table 2；

Specifically, focal length priority principle can be taken, i.e., focal distance is first fixed, for each under the focal distance Focal length sampled point repeats S4~S7, then adjusts focal distance, repeats above-mentioned steps, until traversal travels through all focal distances Sampled point, step S4~S7 thus is performed to each focal distance sampled point and focal length sampled point, obtain amendment four corresponding to it First number (θ, n_x, n_y, n_z), translation vector (t_x, t_y, t_z) and angle of visual field α.

S9. export LUT and generate engine to image, be easy to image generation engine to be obtained according to focal distance and focal length corresponding The amendment demarcation information and angle of visual field.

2 focal lengths of table-focal distance-amendment demarcation information-angle of visual field look-up table LUT2 form

In the case of camera lens is zoom lens, image is generated engine and focused using look-up table LUT2 according to current When distance and focal length obtain corresponding amendment demarcation information and the angle of visual field, due to the focal distance sampling recorded in look-up table LUT2 Point and focal length sampled point are limited, and the focal distance not chosen every time, focal length are all precisely focal distance and Jiao of sample point Away from.For the focal distance at non-sampled point and focal length (such as when actual focal distance FD does not adopt in any one focal distance Sampling point FD_jPlace, or real focal length FL is not in any one focal distance sampled point FL_kPlace, or when actual focal distance FD not In any one focal distance sampled point FD_jPlace and real focal length FL is not also in any one focal distance sampled point FL_k Place), amendment demarcation information corresponding to its can be obtained using interpolation arithmetic by the way of, due to amendment quaternary number, translation vector with And its mathematical characteristic of the angle of visual field is different, therefore in order to reach more accurate interpolation arithmetic effect, different insert can be respectively adopted Value-based algorithm.Specifically, amendment quaternary number enters row interpolation, translation vector T using SLERP interpolation methods_jk=[t_xjk, t_yjk, t_zjk ]^TUsing linear interpolation, the angle of visual field uses linear interpolation, or other forms to enter row interpolation.

Wherein, preferably, the method for entering row interpolation to amendment quaternary number using SLERP algorithms is as follows：

If 1. FD_j＜ FD ＜ FD_j+1And FL_k＜ FL ＜ FL_k+1, i.e., when actual focal distance FD is not in any one focusing From sampled point FD_jPlace, and real focal length FL is not also in any one focal length sampled point FL_kPlace, using with its closest to focusing Distance and focal length sampled point combination (FD_j, FL_k), (FD_j, FL_k+1), (FD_j+1, FL_k), (FD_j+1, FL_k+1) corresponding to amendment four First number q_{J, k}, q_{J, k+1}, q_{J+1, k}, q_{J+1, k+1}, enter row interpolation according to the following formula, then for currently practical focal distance FD and actual Jiao Away from for FL when amendment quaternary number q_{L, d}Calculated by following formula：

Wherein：

If 2. FD_j＜ FD ＜ FD_j+1, FL=FL_kWhen, i.e., when actual focal distance FD does not sample in any one focal distance Point FD_jPlace and real focal length FL is focal length sampled point FL_kWhen, using with its closest to focal distance sampled point combine (FD_j, FL_k), (FD_j+1, FL_k) corresponding to amendment quaternary number information q_{J, k}, q_{J+1, k}, enter row interpolation according to the following formula, then for currently practical Focal distance FD and real focal length are FL_kWhen amendment quaternary number q_{L, d}Calculated by following formula

Wherein

If 3. FD=FD_j, FL_k＜ FL ＜ FL_k+1When, i.e., actual focal distance FD is focal distance sampled point FD_jIt is and actual Focal length FL is not in any one focal length sampled point FL_kDuring place, using with its closest to focal length sampled point combine (FD_j, FL_k), (FD_j, FL_k+1) corresponding to amendment quaternary number information q_{J, k}, q_{J, k+1}, enter row interpolation according to the following formula, then for currently practical focusing Distance FD_jAnd amendment quaternary number q when real focal length is FL_{L, d}Calculated by following formula：

Wherein

It is possible thereby in the case where focal distance and focal length are any value, corresponding amendment demarcation is obtained with interpolation by tabling look-up Information and the angle of visual field.

The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any Be familiar with the people of the technology disclosed herein technical scope in, it will be appreciated that the conversion and replacement expected, should all cover at this Within the scope of invention, therefore, protection scope of the present invention should be defined by the protection domain of claims.

Claims (12)

1. a kind of camera position amendment scaling method, it is characterised in that comprise the following steps：

S1. N number of mark point A on background screen is obtained₁..., A_NCoordinate under world coordinate system：A₁(x₁, y₁, z₁) ..., A_N (x_N, y_N, z_N), wherein coordinate of i-th of mark point under world coordinate system is A_i(x_i, y_i, z_i), i=1~N；N number of mark Note point comprises at least 3 not collinear mark points；Home position and the mark point of the mark point coordinates for mark point It is respectively positioned in the picture of video camera collection；

S2. the focal distance sampled point FD of numerical value from small to large is determined₁, FD₂..., FD_j..., FD_J；Wherein j=1~J, FD₁With FD_JIt is the minimum focal distance of camera lens and maximum focal distance respectively；

If camera lens is zoom lens, also need to determine the focal length sampled point FL of numerical value from small to large₁, FL₂..., FL_k..., FL_K；Wherein k=1~K, FL₁And FL_KIt is the minimum focus and maximum focal length of camera lens respectively；

If S3. camera lens is tight shot, each focal distance sampled point FD is obtained_jJoin inside corresponding camera lens Number and lens distortion parameter；

If camera lens is zoom lens, each focal distance sampled point FD is obtained_jWith each focal length sampled point FL_kIt is corresponding Camera lens inner parameter and lens distortion parameter；

The camera lens inner parameter and lens distortion parameter are obtained by camera lens calibration process；

If S4. camera lens is tight shot, when focal distance takes j-th of focal distance sampled point FD_jWhen, adjust video camera Position enables the mark point blur-free imaging on background screen；

If camera lens is zoom lens, when focal distance takes j-th of focal distance sampled point FD_jAnd focal length is in k-th of sampling Point FL_kDuring place, adjustment camera position enables the mark point blur-free imaging on background screen；

S5. the current location information that video camera posture external trace device provides under current state is obtained, including to sit the world Mark system is self-defined with video camera posture external trace device after its X-axis, Y-axis and Z axis rotation respectively successively after translation The rotation Eulerian angles that overlap of coordinate system, and position coordinates of the video camera posture external trace device under world coordinate system；

S6. using the S1 N number of mark points obtained picpointed coordinate under video camera imaging coordinate system of world coordinates, mark point and The camera lens inner parameter and lens distortion parameter that S3 is obtained, obtain the rotation between camera coordinates system and world coordinate system Torque battle array and the video camera centre of perspectivity are in the translation vector of world coordinate system, i.e. posture letter of the video camera under world coordinate system Breath；

S7. the current location information that video camera posture external trace device provides under the current state obtained using S5, and in S6 Attitude information of the video camera tried to achieve under world coordinate system, try to achieve video camera amendment demarcation information and the angle of visual field；

S8. if camera lens is tight shot：Focal distance is adjusted, to each focal distance sampled point FD_jExecution step S4~ S7, until traveling through all focal distance sampled points, obtain the demarcation information of the amendment corresponding to each focal distance sampled point and regard Rink corner, establish the look-up table LUT1 of focal distance-amendment demarcation information-angle of visual field；

If camera lens is zoom lens：Focal distance and focal length are adjusted, to each focal distance sampled point FD_jWith each Jiao Away from sampled point FL_kStep S4~S7 is performed, until traveling through all focal distance sampled points and focal length sampled point, obtains each focusing Amendment demarcation information and the angle of visual field corresponding to distance sample and focal length sampled point, establish focal distance-focal length-amendment demarcation The look-up table LUT2 of information-angle of visual field；

S9. if camera lens is tight shot：Then according to the look-up table LUT1, corresponding amendment is obtained by focal distance Demarcate information and the angle of visual field；

If camera lens is zoom lens：Then according to the look-up table LUT2, obtained by focal distance and focal length corresponding Amendment demarcation information and the angle of visual field.

A kind of 2. camera position amendment scaling method according to claim 1, it is characterised in that in step S3,

(1) when camera lens is tight shot：

For j-th of focal distance sampled point FD_j, corresponding camera lens inner parameter is：f_xj, f_yj, c_xj, c_yj, wherein：

f_xj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith video camera into The ratio between horizontal width dx as each unit of instrument, i.e.,

f_yj：Expression focal distance is FD_jWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jWith video camera into The ratio between vertical height dy as each unit of instrument, i.e.,

c_xj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, with the horizontal-shift at imaging surface center Pixel count；

c_yj：Expression focal distance is FD_jWhen, the optical axis of camera lens and the intersection point of imaging surface, with the vertical shift at imaging surface center Pixel count；

For j-th of focal distance sampled point FD_j, corresponding camera lens distortions parameter is：k_1j, k_2j, k_3j, p_1jAnd p_2j, its Middle k_1j, k_2j, k_3jIt is FD for focal distance_jWhen radial distortion parameter, wherein k_3jFor selected parameter, when camera lens is fish eye lens When use k_1j, k_2j, k_3jThese three radial distortion parameters, when camera lens is non-fish eye lens, k_3j=0, i.e. other camera lenses only use k_1j, k_2jThe two radial distortion parameters；p_1j, p_2jIt is FD for focal distance_jWhen tangential distortion parameter；

Also, obtain each focal distance FD_jUnder internal reference matrix M_jFor：

<mrow> <msub> <mi>M</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>f</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>c</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>f</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

(2) when camera lens is zoom lens：

For j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding camera lens inner parameter is： f_xjk, f_yjk, c_xjk, c_yjk, wherein：

f_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jk The ratio between with the horizontal width dx of each unit of imager, i.e.,

f_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the distance f of the emergent pupil and camera lens optical axis intersection point to imaging surface of camera lens_jk The ratio between with the vertical height dy of each unit of imager, i.e.,

c_xjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface is inclined with the level at imaging surface center The pixel count of shifting；

c_yjk：Expression focal distance is FD_j, focal length FL_kWhen, the intersection point of optical axis and imaging surface is vertical with imaging surface center inclined The pixel count of shifting；

For j-th of focal distance sampled point FD_jWith k-th of focal length sampled point FL_k, corresponding camera lens distortions parameter is： k_1jk, k_2jk, k_3jk, p_1jkAnd p_2jk, wherein k_1jk, k_2jkAnd k_3jkIt is FD for focal distance_jAnd focal length is FL_kWhen radial distortion ginseng Number, wherein k_3jkFor selected parameter, k is used when camera lens is fish eye lens_1jk, k_2jkAnd k_3jkThese three radial distortion parameters；When When camera lens is non-fish eye lens, k_3jk=0, i.e. other camera lenses only use k_1jk, k_2jkThe two radial distortion parameters；p_1jk, p_2jkFor Focal distance is FD_jAnd focal length is FL_kWhen tangential distortion parameter；

And obtain each focal distance FD_jWith focal length FL_kUnder internal reference matrix be M_jk：

<mrow> <msub> <mi>M</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>f</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>c</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>f</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>

A kind of 3. camera position amendment scaling method according to claim 2, it is characterised in that in step S5,

(1) when camera lens is tight shot：

The current location information that the video camera posture external trace device provides is [θ_xj, θ_yj, θ_zj, T_xj, T_yj, T_zj]；Wherein [θ_xj, θ_yj, θ_zj] for make world coordinate system after translation successively respectively around X-axis, Y-axis and Z axis rotation after with video camera posture The rotation Eulerian angles that the customized coordinate system of external trace device overlaps, [T_xj, T_yj, T_zj] set for video camera posture external trace The standby position coordinates under world coordinate system, by the current location information that video camera posture external trace device provides be expressed as Lower matrix form：

<mrow> <msub> <mi>H</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>T</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

Here

<mrow> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

T_Ij=[T_xj T_yj T_zj]^T

0=[0,0,0]；

(2) when camera lens is zoom lens：

Current location information [the θ that the video camera posture external trace device provides_xjk, θ_yjk, θ_zjk, T_xjk, T_yjk, T_zjk]；Its In [θ_xjk, θ_yjk, θ_zjk] for make world coordinate system after translation successively respectively around X-axis, Y-axis and Z axis rotation after with video camera The rotation Eulerian angles that the customized coordinate system of posture external trace device overlaps, [T_xjk, T_yjk, T_zjk] for outside video camera posture Position coordinates of the tracking equipment under world coordinate system；The current location information table that video camera posture external trace device is provided It is shown as following matrix form：

<mrow> <msub> <mi>H</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>T</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

Here

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

T_Ijk=[T_xjk T_yjk T_zjk]^T

0=[0,0,0].

A kind of 4. camera position amendment scaling method according to claim 3, it is characterised in that in step S6,

(1) when camera lens is tight shot：

Current focal distance is FD_jWhen, obtain the spin matrix R between camera coordinates system and world coordinate system_pj, video camera it is saturating Depending on center world coordinate system translation vector T_pj, attitude matrix H of the video camera under world coordinate system_pjMethod be：

According to the picpointed coordinate of i-th of mark pointAnd current focal distance FD_jUnder lens distortion parameter, obtain Picpointed coordinate (the x ' of i-th of mark point after correction_ij, y '_ij)：

<mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>4</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>3</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>6</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>4</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>3</mn> <mi>j</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>6</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow>

<mrow> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>

Wherein if camera lens is non-fish eye lens, k_3j=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ij, y '_ij) between relation It is expressed as：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

Wherein λ_jReferred to as scale factor,

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

Spin matrix R wherein between camera coordinates system and world coordinate system_pjFor orthogonal matrix, T_pjFor the video camera centre of perspectivity In the translation vector of world coordinate system：

<mrow> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> <mi>c</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>;</mo> </mrow>

Pass through the world coordinates (x of formula (1) (2) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x '_ij, y '_ij), Obtain matrix O_j=λ_j[R_pj, T_pj] and attitude information of the video camera under world coordinate system WhereinFor make world coordinate system after translation successively respectively around X-axis, Y-axis and Z axis rotation after with photography The rotation Eulerian angles that machine coordinate system overlaps,For translation of the video camera centre of perspectivity under world coordinate system Vector；

Again because matrix R_pjIt is unit orthogonal matrix, has：

λ_j=1/ | | O_j(：, 1) | |；

Wherein O_j(：, 1) and it is matrix O_jThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjAnd the video camera centre of perspectivity is alive The translation vector T of boundary's coordinate system_pj, attitude information of the video camera under world coordinate system is expressed as matrix H_pj：

<mrow> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

(2) when camera lens is zoom lens：

Current focal distance is FD_jAnd current focus is FL_kWhen, obtain the rotation between camera coordinates system and world coordinate system Matrix R_pjk, the video camera centre of perspectivity world coordinate system translation vector T_pjk, posture square of the video camera under world coordinate system Battle array H_pjkMethod be：

According to current focal distance FD_jWith current focus FL_kThe picpointed coordinate of lower i-th of mark point And camera lens is abnormal Variable element obtains the picpointed coordinate (x ' after its correction_ijk, y '_ijk)：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>1</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>2</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>4</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>3</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>6</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>1</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>2</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>4</mn> </msup> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mn>3</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>6</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>

Wherein if camera lens is non-fish eye lens, k_3jk=0；

World coordinates (the x of i-th of mark point_i, y_i, z_i) picpointed coordinate (x ' after corresponding correction_ijk, y '_ijk) between close System is expressed as：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Wherein λ_jkReferred to as scale factor,

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>sin&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>cos&amp;theta;</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

Spin matrix R wherein between camera coordinates system and world coordinate system_pjkFor orthogonal matrix, T_pjkIn being had an X-rayed for video camera Translation vector of the heart in world coordinate system：

<mrow> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>T</mi> <mrow> <mi>z</mi> <mi>j</mi> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>

Pass through the world coordinates (x of formula (3) (4) and each mark point_i, y_i, z_i) and corresponding correction after picpointed coordinate (x '_ijk, y '_ijk), Obtain matrix O_jk=λ_jk[R_pjk, T_pjk] and attitude information of the video camera under world coordinate system WhereinTo make world coordinate system be surrounded respectively successively after translation after X-axis, Y-axis and Z axis rotate with taking the photograph The rotation Eulerian angles that shadow machine coordinate system overlaps,It is the video camera centre of perspectivity under world coordinate system Translation vector；

Because matrix R_pjkIt is unit orthogonal matrix, has：

λ_jk=1/ | | O_jk(：, 1) | |；

Wherein O_jk(：, 1) and it is matrix O_jkThe 1st row, | | | | represent vector Euclid norm；

According to the spin matrix R between the camera coordinates system of acquisition and world coordinate system_pjkAnd the video camera centre of perspectivity is alive The translation vector T of boundary's coordinate system_pjk, attitude information of the video camera under world coordinate system is expressed as matrix H_pjk：

<mrow> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> 5

5. a kind of camera position amendment scaling method according to claim 4, it is characterised in that step S7 includes following step Suddenly：

(1) when camera lens is tight shot：

S7.1 calculates video camera attitude rectification matrix H_j：

<mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msubsup> <mi>H</mi> <mrow> <mi>I</mi> <mi>j</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

S7.2 is by video camera attitude rectification matrix H_jIt is transformed to correct quaternary number (θ_j, n_xj, n_yj, n_zj) and translation vector T_j：

The video camera attitude rectification matrix H_jIt is 4 × 4 matrix, its live part is H_j(1: 3,1: 4), i.e. H_jFirst three rows, By H_j(1: 3,1: 4) be expressed as form：

H_j(1: 3,1: 4)=[R_j, T_j]；

Wherein spin matrix R_jFor 3 × 3 real number matrix, translation vector T_j=[t_xj, t_yj, t_zj]^TFor 3-dimensional column vector；

By spin matrix R_jAmendment quaternary number (θ is converted to according to following formula_j, n_xj, n_yj, n_zj)：

HereFor 3-dimensional row vector；

Thus storage R_jAmendment quaternary number (θ need to only be stored_j, n_xj, n_yj, n_zj), therefore video camera attitude rectification matrix H_jTurn It is changed to video camera amendment demarcation information (θ_j, n_xj, n_yj, n_zj, t_xj, t_yj, t_zj)；

S7.3 calculates camera coverage angle：When focal distance is FD_jWhen, camera coverage angle α is calculated according to following formula_j：

<mrow> <msub> <mi>&amp;alpha;</mi> <mi>j</mi> </msub> <mo>=</mo> <mn>2</mn> <mi>arctan</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mrow> <mfrac> <msup> <mi>W</mi> <mn>2</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <msup> <mi>H</mi> <mn>2</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> </mrow> </msqrt> </mrow> <mo>)</mo> </mrow> </mrow>

Wherein W, H are respectively the width of video camera, high-resolution；

(2) when camera lens is zoom lens：

S7.1 calculates video camera attitude rectification matrix H_jk：

<mrow> <msub> <mi>H</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msubsup> <mi>H</mi> <mrow> <mi>I</mi> <mi>j</mi> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

S7.2 is by video camera attitude rectification matrix H_jkIt is transformed to correct quaternary number (θ_jk, n_xjk, n_yjk, n_zjk) and translation vector T_jk：

The video camera attitude rectification matrix H_jkIt is 4 × 4 matrix, its live part is H_jk(1: 3,1: 4), i.e. H_jkFirst three OK, by H_jk(1: 3,1: 4) be expressed as form：

H_jk(1: 3,1: 4)=[R_jk, T_jk]；

Wherein spin matrix R_jkFor 3 × 3 real number matrix, translation vector T_jk=[t_xjk, t_yjk, t_zjk]^TFor 3-dimensional column vector；

By spin matrix R_jkAmendment quaternary number (θ is converted to according to following formula_jk, n_xjk, n_yjk, n_zjk)：

HereFor 3-dimensional row vector；

Thus storage R_jkAmendment quaternary number (θ need to only be stored_jk, n_xjk, n_yjk, n_zjk), therefore video camera attitude rectification matrix H_jkBe converted to video camera amendment demarcation information (θ_jk, n_xjk, n_yjk, n_zjk, t_xjk, t_yjk, t_zjk)；

S7.3 calculates camera coverage angle：When focal distance is FD_jAnd focal length is FL_kWhen, camera coverage angle is calculated according to following formula α_jk：

<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>arctan</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mrow> <mfrac> <msup> <mi>W</mi> <mn>2</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi>x</mi> <mi>j</mi> <mi>k</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <msup> <mi>H</mi> <mn>2</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi>y</mi> <mi>j</mi> <mi>k</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> </mrow> </msqrt> </mrow> <mo>)</mo> </mrow> </mrow>

Wherein W, H are respectively the width of video camera, high-resolution.

6. a kind of camera position amendment scaling method according to claim 5, it is characterised in that in step S9, work as reality Focal distance FD is not in any one focal distance sampled point FD_jPlace, or real focal length FL do not sample in any one focal length Point FL_kPlace, or when actual focal distance FD is not in any one focal distance sampled point FD_jPlace and real focal length FL are not yet In any one focal length sampled point FL_kDuring place, obtained by the way of following interpolation arithmetic amendment demarcation information corresponding to it and The angle of visual field：

Row interpolation is entered using SLERP interpolation methods for the amendment quaternary number that amendment is demarcated in information, translation vector is using three-dimensional Linear interpolation；The angle of visual field enters row interpolation using linear interpolation method.

A kind of 7. camera position amendment scaling method according to claim 6, it is characterised in that in step S9,

(1) when camera lens is tight shot：

When actual focal distance FD is not in any one focal distance sampled point FD_jPlace, using SLERP algorithms to correcting quaternary number The method for entering row interpolation is as follows：

If FD_j＜ FD ＜ FD_j+1, video camera is in focal distance FD_jAnd FD_j+1The video camera attitude rectification matrix at place is respectively H_jAnd H_j+1, Its spin matrix is respectively R_jAnd R_j+1, spin matrix is expressed as to correct quaternary numberWithAmendment quaternary number q when then for currently practical focal distance FD is by following formula meter Calculate：

<mrow> <mi>q</mi> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mi>j</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>t</mi> </msup> <mo>;</mo> </mrow>

HereIt is q_jIt is inverse,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>q</mi> <mi>j</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>cos&amp;theta;</mi> <mi>j</mi> </msub> <mo>,</mo> <mo>-</mo> <mover> <msub> <mi>n</mi> <mi>j</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <msub> <mi>sin&amp;theta;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </mtd> <mtd> <mrow> <mover> <msub> <mi>n</mi> <mi>j</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mrow> <mi>x</mi> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow> <mi>y</mi> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow> <mi>z</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>F</mi> <mi>D</mi> </mrow> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>FD</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>;</mo> </mrow>

(2) when camera lens is zoom lens：

When actual focal distance FD is not in any one focal distance sampled point FD_jPlace, or real focal length FL is not at any one Focal length sampled point FL_kPlace, or when actual focal distance FD is not in any one focal distance sampled point FD_jPlace and actual Jiao Away from FL also not in any one focal length sampled point FL_kDuring place, the method for row interpolation is entered such as to amendment quaternary number using SLERP algorithms Under：

If 1. FD_j＜ FD ＜ FD_j+1And FL_k＜ FL ＜ FL_k+1, i.e., when actual focal distance FD does not adopt in any one focal distance Sampling point FD_jPlace, and real focal length FL is not also in any one focal length sampled point FL_kPlace, using with its closest to focal distance (FD is combined with focal length sampled point_j, FL_k), (FD_j, FL_k+1), (FD_j+1, FL_k), (FD_j+1, FL_k+1) corresponding to amendment quaternary number q_{J, k}, q_{J, k+1}, q_{J+1, k}, q_{J+1, k+1}, enter row interpolation according to the following formula, be then for currently practical focal distance FD and real focal length Amendment quaternary number q during FL_{L, d}Calculated by following formula：

<mrow> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> </msup> </mrow>

<mrow> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> </msup> </mrow> 7

<mrow> <msub> <mi>q</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>d</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> </msup> </mrow>

Wherein：

<mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>F</mi> <mi>D</mi> </mrow> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>FD</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>;</mo> </mrow>

<mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>FL</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>FL</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>FL</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>;</mo> </mrow>

If 2. FD_j＜ FD ＜ FD_j+1, FL=FL_kWhen, i.e., when actual focal distance FD is not in any one focal distance sampled point FD_jPlace and real focal length FL is focal length sampled point FL_kWhen, using with its closest to focal distance sampled point combine (FD_j, FL_k), (FD_j+1, FL_k) corresponding to amendment quaternary number information q_{J, k}, q_{J+1, k}, enter row interpolation according to the following formula, then for currently practical Focal distance FD and amendment quaternary number q when real focal length is FL_{L, d}Calculated by following formula

<mrow> <msub> <mi>q</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>t</mi> </msup> </mrow>

Wherein

<mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>F</mi> <mi>D</mi> </mrow> <mrow> <msub> <mi>FD</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>FD</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>;</mo> </mrow>

If 3. FD=FD_j, FL_k＜ FL ＜ FL_k+1When, i.e., actual focal distance FD is focal distance sampled point FD_jAnd real focal length FL is not in any one focal length sampled point FL_kDuring place, using with its closest to focal length sampled point combine (FD_j, FL_k), (FD_j, FL_k+1) corresponding to amendment quaternary number information q_{J, k}, q_{J, k+1}, enter row interpolation according to the following formula, then for currently practical focal distance FD And amendment quaternary number q when real focal length is FL_{L, d}Calculated by following formula：

<mrow> <msub> <mi>q</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>r</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>t</mi> </msup> </mrow>

Wherein

<mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>FL</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <msub> <mi>FL</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>FL</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>.</mo> </mrow>

8. a kind of camera position amendment scaling method according to claim 1, it is characterised in that space measurement is used in S1 Equipment obtains N number of mark point A on background screen₁..., A_NCoordinate under world coordinate system.

9. any camera position amendment scaling method according to claim 1-5, it is characterised in that the video camera appearance State external trace device is optictracking device or mechanical arm.

A kind of 10. camera position amendment scaling method according to claim 1, it is characterised in that video camera imager coordinate It is that origin is set in field of view center.

11. a kind of camera position amendment scaling method according to claim 1, the focal distance sampled point and focal length Sampled point uses the sampled point taken in camera lens calibration process.

A kind of 12. camera position amendment calibration system, it is characterised in that including：Servo-motor control system, video camera, take the photograph Shadow machine posture external trace device, background screen, mark point, space measurement equipment, data processing equipment, image rendering engine；

Wherein, servo-motor control system is connected with video camera, for adjusting the focal length and focal distance of camera lens；Servo motor control System processed is also connected with data processing equipment, for sending the focal length and focal distance information of camera lens to data processing equipment, with Data processing equipment is calculated amendment demarcation information and the angle of visual field and establish look-up table；

Data processing equipment is also connected with video camera, for reading video stream data in real time；

Video camera posture external trace device is arranged at outside video camera, for the position by photogrammetric camera and video camera appearance The skew of state external trace device, estimate position and the attitude information of video camera；Video camera posture external trace device also with number It is connected according to processing equipment, for sending measurement data information；

At least three not conllinear mark point is set on background screen, and these mark point radiuses are identical, and color has with background screen Contrast；

Space measurement equipment and image rendering engine are connected with data processing equipment respectively, and space measurement equipment is used for measurement markers The world coordinates of point home position is simultaneously sent to data processing equipment, and image rendering engine is used to be established according to data processing equipment Look-up table obtain corresponding amendment demarcation information and the angle of visual field.