CN107452036B - A kind of optical tracker pose calculation method of global optimum - Google Patents
A kind of optical tracker pose calculation method of global optimum Download PDFInfo
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- CN107452036B CN107452036B CN201710545644.2A CN201710545644A CN107452036B CN 107452036 B CN107452036 B CN 107452036B CN 201710545644 A CN201710545644 A CN 201710545644A CN 107452036 B CN107452036 B CN 107452036B
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/70—Determining position or orientation of objects or cameras
- G06T7/73—Determining position or orientation of objects or cameras using feature-based methods
- G06T7/75—Determining position or orientation of objects or cameras using feature-based methods involving models
Abstract
The invention discloses a kind of optical tracker pose calculation methods of global optimum, improve the pose calculation method of traditional tracker, the mathematical model based on global optimization thought is used, use space point and the corresponding relationship of picture point construct system of linear equations, it does not need to calculate pose of the tracker relative to single base station, it does not need to carry out pose data fusion yet, it can be with direct solution tracker global optimum pose；This method does not limit base station number, the information (even if the corresponding points lazy weight of this base station calculates pose with independent) for taking full advantage of all base station corresponding points, greatly reduces the minimum of computation condition (corresponding points amount threshold is reduced to all base stations by any one base station at least 5 groups of corresponding points and has 4 groups of corresponding points altogether) of tracker pose；In addition, can get the pose fusion results of global optimum, and result is more accurate, robustness is stronger when multiple receivers and tracker foundation contact.
Description
Technical field
The invention belongs to tracking and positioning technical fields, and in particular to a kind of optical tracker pose calculating side of global optimum
Method can be used for the application field that motion capture, surgical navigational, virtual reality etc. need optical tracking to position.
Background technique
HTC VIVE system is made of transmitter base station and photoreceiver, the capable of emitting periodicity light signal of transmitter to
Track region is scanned, and after receiver receives the scanning signal of transmitter, converts optical signals to digital signal, to obtain
Image coordinate of the receiver relative to transmitter, after a certain number of receivers are scanned, using computer vision algorithms make
Obtain the spatial pose of the rigid body of receiver composition.
HTC VIVE is gathered around there are two transmitter scanning base station (being equivalent to two video cameras), when calculating pose, needs one
At least five sensor points are closed by some base station scans to the pose that could be calculated between tracker and the base station on a tracker
System, tracker are blocked situation due to the variation of self-position angle there may be operative sensor in use, therefore it is required that
A fairly large number of sensor points must be laid on tracker, to guarantee still there are at least 5 when operative sensor point is blocked
Sensor points can receive base station scanning signal.Sensor points are more, and the volume of tracker is bigger, are unfavorable for the small-sized of tracker
Change.In addition, the method that HTC VIVE system when carrying out pose fusion, has used weighting ellipse fitting, this method is required more
Strictly, it needs to know the relative pose between each base station and tracker, and the pose data for being only applicable to two base stations are melted
It closes, when base station (video camera) is more, without the ability of pose data global optimization.
Summary of the invention
In view of this, passing through the object of the present invention is to provide a kind of optical tracker pose calculation method of global optimum
The pose calculation method for improving traditional tracker, relaxes tracker pose design conditions, i.e., arbitrarily individually connects cannot calculate
When receiving device and tracker pose, tracker pose meter only can be completed with the limited information between tracker and multiple receivers
It calculates.
A kind of optical tracker pose calculation method of global optimum of the invention, comprising:
Step 1 is directed to each sensor, determines that it can receive the transmitter of signal, by a sensor and its energy
A transmitter for receiving signal receives combination as a transmitting, traverses all the sensors, counts all transmittings and connects
Combined number is received, and is denoted as N；
Step 2 receives combination for any one transmitting, enables sensor serial number j therein, transmitter serial number is expressed as
i；Then determine three-dimensional coordinate of j-th of sensor under itself rigid body coordinate systemDetermine that j-th of sensor can be received at it
To the two dimensional image coordinate in i-th of transmitter of signalThen it establishes and is received in combination in correspondence with each other about the transmitting
Effective equation group of three-dimensional space point and two-dimensional image point:
Wherein, pi1、pi2、pi3And pi4It indicates between sensor rigid body coordinate system and the image coordinate system of i-th of transmitter
Projection relation matrix PiIn element；aij=[0, -1, vij]T, bij=[1,0 ,-uij]T, wherein uijAnd vijRespectively indicate two dimension
Image coordinateIn two change in coordinate axis direction coordinate； Wherein,Indicate that sensor rigid body coordinate system is transformed into transmitter coordinate
The spin matrix of system,Indicate that sensor rigid body coordinate system is transformed into the translation matrix of transmitter coordinate system；
Step 3 emits to receive to combine for each and establishes equation group shown in a formula (1), and N number of transmitting receives combination
N number of equation group is obtained, the system of linear equations of 2N dimension is consequently formed；
The line style equation group that step 3 is formed is rewritten into following form by step 4:
AX=B (2)
Wherein A is the matrix of 2N × 12,
The column vector that X is 12 × 1, X=[r11, r12, r13, t1, r21, r22, r23, t2, r31, r32, r33, t3]T；
B is the column vector of 2N × 1,
Step 5, as 4≤N≤5, formula (2) is solved method particularly includes:
9 elements are extracted in X and obtain spin matrix R, are indicated are as follows:
R=fR(X)
And spin matrix R is made to be unitary matrice, meet RR-1=I and R-1=RT, I be 3 × 3 unit matrix；
Then following optimization problem is converted by Solving Linear problem shown in formula (2):
s.t.fR(X)fR(X)T- I=0
That is: meetingConstraint condition under, make
The X being minimized is optimal solution, realizes that pose resolves；
As N >=6, formula (2) is solved using analytic method, obtains X, realizes that pose resolves.
In the step 5, the optimization problem is solved using Levenberg-Marquardt algorithm.
The invention has the following beneficial effects:
Present invention improves over the pose calculation methods of traditional tracker, have used the mathematical modulo based on global optimization thought
The corresponding relationship of type, use space point and picture point constructs system of linear equations, does not need to calculate tracker relative to single base station
Pose, do not need yet carry out pose data fusion, can be with direct solution tracker global optimum pose；This method does not limit base
It stands quantity, takes full advantage of the information of all base station corresponding points (even if the corresponding points lazy weight of this base station calculates position with independent
Appearance), the minimum of computation condition of tracker pose is greatly reduced (by corresponding points amount threshold by least 5 groups of any one base station
Corresponding points are reduced to all base stations and have 4 groups of corresponding points altogether)；In addition, can get when multiple receivers and tracker foundation contact
The pose fusion results of global optimum, and result is more accurate, robustness is stronger.
Detailed description of the invention
Fig. 1 is existing HTC VIVE system pie graph；
Difference of the Fig. 2 for the method for the present invention and the method for HTC VIVE during processing.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
As shown in Figure 1, HTC VIVE system includes 1 Helmet Mounted Display and 2 handles.On Helmet Mounted Display and handle
Dozens of photoreceiver is installed, when the infrared light scanning signal when base station is received by a certain number of receivers, can be counted
The spatial position for calculating Helmet Mounted Display and handle, to realize the posture tracking of user.
If three-dimensional coordinate of j-th of photosensitive sensor under world coordinate system is X on trackerwj=[xj, yj, zj]T,
Corresponding image coordinate is x in i-th of transmitter base stationij=[uij, vij]T, then according to projection imaging principle, XwjWith xij's
Relationship meets following formula:
Wherein j=1,2 ... J, J are number of sensors；For coordinate Xwj
And xijHomogeneous coordinates expression form (herein if not illustrating withIndicate the homogeneous coordinates of A), Pi=Ki[Rci
|Tci] be i-th transmitter projection matrix, KiFor Intrinsic Matrix, RciFor spin matrix, TciFor translation matrix, they are
It can be obtained by initial alignment.RciAnd TciThree-dimensional point coordinate can be described from world coordinate system to i-th of transmitter base station coordinate
The transformation of system, if three-dimensional coordinate of the sensor points under i-th of transmitter base station coordinate system is Xcij, then XcijWith XwjRelationship
As shown in formula (2):
Xcij=RciXwj+Tci (2)
If three-dimensional coordinate of the sensor points in the case where tracking rigid body local coordinate system is Xrj, according to projection imaging principle,
The imaging model that similar formula (1) can be obtained, as shown in formula (3):
Wherein Rri、TriDescribe change of the three-dimensional point from tracking rigid body local coordinate system to i-th of transmitter base station coordinate system
It changes, as shown in formula (4):
Xcij=RriXrj+Tri (4)
In conjunction with formula (2) and (4) available XwjWith XrjBetween transformational relation, as shown in formula (5):
Wherein R and T is pose of the tracker in world coordinate system.Due to RciAnd TciIt immobilizes, and is initially marking
Determining the stage has obtained, therefore only needs to calculate R in real time in useriWith TriThe three-dimensional position of tracker can be obtained according to formula (5)
Appearance.Formula (3) are returned to, due to KiFor known calibration data, therefore it need to only know that several groups are correspondingIt can seek
Rri、Tri.In situation known to this Intrinsic Matrix, with n spatial point image point estimation position for video camera corresponding with them
The method of appearance, i.e. spin matrix and translation matrix, referred to as PnP (perspective-n-point) problem, it can be divided into two
The case where class, one kind is 3≤n≤5, another kind of the case where being n >=6.The research focus of first kind PnP problem is the problem that determines
For real solution at most up to how many, conclusion includes: that P3P problem is up to 4 solutions；When 4 control points are coplanar, P4P problem has only
One solution, and when 4 control points are non-coplanar, P4P problem is up to 4 solutions；P5P problem can have up to two solutions.Second class
PnP problem can use DLT (Direct Linear Transform) method linear solution.It can about being discussed in detail for PnP problem
With bibliography [1] ([1] Wu Y, Hu Z.PnP Problem Revisited [J] .Journal of Mathematical
Imaging and Vision, 2006,24 (1): 131-141), which is not described herein again.
HTC VIVE system is gathered around there are two base station, for a tracker, if first base station has taken on tracker
p1The image coordinate of a sensor, second base station have taken p2The image coordinate of a sensor, then HTC VIVE system is wanted
It asks and works as p1>=5 or p2When >=5, the pose of the tracker can be just calculated.Work as p1>=5 and p2When >=5, two base stations can be respective
The spatial pose of tracker is obtained according to formula (5), R can be denoted as respectively1、T1、R2、T2.It needs to obtain two base stations at this time
Pose data are merged, and to obtain, precision is higher, the stronger tracker pose of robustness.The pose fusion that HTC VIVE is used
Shown in algorithm such as formula (6):
Wherein Slerp () is spherical linear interpolating function (referring to document [2] https: //en.wikipedia.org/
Wiki/Slerp), α is coefficient, shown in calculation method such as formula (7):
α=p1/(p1+p2) (7)
The pose fusion method as shown in formula (6) is only applicable to the fusion of two pose data, works as base station number
Amount will be unable to carry out pose fusion using formula (6) when being greater than 2.
Pose calculation method proposed by the present invention is not limited to the case where only there are two base stations, it is suitable for any amount base
Stand (or video camera) the case where.J-th of sensor points of simultaneous formula (1) and formula (5) available tracker are in rigid body
Three-dimensional coordinate under local coordinate systemTo the image coordinate of i-th of base station imaging planeProjection relation, following institute
Show:
Formula (8) is equivalent to the form of formula (9):
WhereinForAntisymmetric matrix, ifThen have:
IfThen have It is available to bring M into formula (9):
IfPi=[pi1, pi2, pi3, pi4], and enableWherein
By CijIt brings into formula (11), available unknown number is three equations of R and T:
Since formula (13) describes the homogeneous coordinate transformation degenerated, wherein only 2 equations are independent, therefore only select
The first two equation in modus ponens (13) is for solving R and T.Due toThereforeBring formula into
(13) it is obtained in the first two equation:
Enable aij=[0, -1, vij]T, bij=[1,0 ,-uij]T, and will be in formula (12)WithIt brings into formula (14),
It obtains:
The both members of formula (15) are taken into transposition, are obtained:
Formula (16) is one group of corresponding three-dimensional space point and effective equation group that two-dimensional image point generates, when there are N groups
When such corresponding points, formula (16) can be rewritten into the system of linear equations of standard, and as shown in formula (17), wherein A is 2N × 12
Matrix, the column vector that X is 12 × 1, B are the column vector of 2N × 1.
AX=B
X=[r11, r12, r13, t1, r21, r22, r23, t2, r31, r32, r33, t3]T (17)
Thus the present invention will seek tracker pose R, T conversion to solve system of linear equations problem shown in formula (17).
The dimension for noticing unknown number X is 12, therefore as N >=6, the equation can pass through X=A+The mode of B seeks analytic solutions, A+For A
Generalized inverse.As 4≤N≤5, equation AX=B owes fixed, has multiple solutions, but can pass through the alternative manner of increase constraint condition
It solves.Due to whole elements of the spin matrix R in X comprising tracker, therefore can be rotated by extracting 9 elements in X
Matrix R, process function representation shown in formula (18):
R=fR(X) (18)
Because spin matrix R is unitary matrice (i.e. unit orthogonal matrix), meet RR-1=I and R-1=RT, I be 3 × 3 unit
Matrix, therefore available constraint condition: RRT=I, i.e. RRT- I=0.It is possible thereby to by Solving Linear shown in formula (17)
Problem is converted into following optimization problem:
Optimization problem shown in formula (19) can be by solution by iterative method, and a kind of common method is Levenberg-
Marquardt algorithm, details can refer to document [3] (Mor é J J.The Levenberg-Marquardt algorithm:
Implementation and theory[J].Lecture Notes in Mathematics,1978,630:105-116)。
The step of present invention seeks tracker pose is summarized below:
Step 1. utilizes three-dimensional coordinate of a certain sensor points under rigid body local coordinate system on trackerIt is right with its
The two dimensional image coordinate for some base station answered2 effective equation groups are obtained according to formula (8)-(16) process.
Step 2. is had each group of sensor three-dimensional point image coordinate point corresponding with its according to the method for Step 1
Equation group is imitated, then all equation groups are formed into the system of linear equations shaped like AX=B according to formula (17).
Step 3. selects different calculation methods according to the difference of corresponding points quantity N.Analytic method X=A is used as N >=6+B is solved, and is solved as 4≤N≤5 using optimal method shown in formula (19).
The present invention calculates the three-dimensional pose of tracker from the angle of global optimization, and the representative of typical method at present
HTC VIVE system is compared, and the method for the present invention relaxes tracker pose design conditions, while when base station number being supported to be more than 2
Pose data fusion, the more accurate robust of calculated result.Fig. 2 compared the method for the present invention and HTC VIVE method processed
Difference in journey.
As can be seen that HTC VIVE uses the calculation method based on distributed thought, need individually to calculate tracker
It is merged relative to the pose of each base station, then by them.The present invention is not examined based on the calculation method of global optimization thought
Consider pose of the tracker relative to each base station, only is used for its corresponding points information to construct system of linear equations, it is linear by solving
Equation group obtains global optimum's pose of tracker, does not need data fusion.
As an example it is assumed that being denoted as p by the sensor points quantity that i-th of base station takes on a trackeri, i=1,
Base station number (is denoted as M here) by 2 ..., M, and for HTC VIVE system M=2, it must satisfy at least one piWhen >=5,
Tracker pose can be calculated.Work as p1>=5 and p2When >=5, it calculates pose of the tracker relative to two base stations, need using
Formula (6) carries out the fusion of pose data to obtain final result.For the present invention, the number M of base station is unrestricted, only
It needs to meetThe pose of tracker can be calculated, this greatly reduces the condition of pose calculating.Such as work as p1=2,
p1=2, p2When=2, HTC VIVE system cannot calculate pose, and the method for the present invention can calculate pose.For another example work as p1=5,
p2When=3, HTC VIVE system can only calculate pose of the tracker relative to base station 1, and pose of the tracker relative to base station 2
Since corresponding points lazy weight can not calculate, this is equivalent to 3 groups of corresponding points information for wasting base station 2.The method of the present invention according to
Formula (16) and (17), can be all of all corresponding points information, therefore calculated result is by more accurate robust.Lower 1 compared
The performance difference of the method for the present invention and HTC VIVE method.
The performance comparison of 1 the method for the present invention of table and HTC VIVE method
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (2)
1. a kind of optical tracker pose calculation method characterized by comprising
Step 1 is directed to each sensor, determines that it can receive the transmitter of signal, a sensor can be received with it
A transmitter to signal receives combination as a transmitting, traverses all the sensors, counts all transmitting reception groups
Number is closed, and is denoted as N；
Step 2 receives combination for any one transmitting, enables sensor serial number j therein, transmitter serial number is expressed as i；Then
Determine three-dimensional coordinate of j-th of sensor under itself rigid body coordinate systemDetermine that j-th of sensor can receive letter at it
Number i-th of transmitter in two dimensional image coordinateThen the three-dimensional received in combination in correspondence with each other about the transmitting is established
Effective equation group of spatial point and two-dimensional image point:
Wherein, pi1、pi2、pi3And pi4Indicate the projection between sensor rigid body coordinate system and the image coordinate system of i-th of transmitter
Relational matrix PiIn element；aij=[0, -1, vij]T, bij=[1,0 ,-uij]T, wherein uijAnd vijRespectively indicate two dimensional image
CoordinateIn two change in coordinate axis direction coordinate；Wherein,Indicate that sensor rigid body coordinate system is transformed into the spin matrix of transmitter coordinate system,Indicate that sensor rigid body coordinate system is transformed into the translation matrix of transmitter coordinate system；
Step 3 emits to receive to combine for each and establishes equation group shown in a formula (1), and N number of transmitting reception is combined to obtain the final product
To N number of equation group, the system of linear equations of 2N dimension is consequently formed；
The line style equation group that step 3 is formed is rewritten into following form by step 4:
AX=B (2)
Wherein A is the matrix of 2N × 12,
The column vector that X is 12 × 1, X=[r11,r12,r13,t1,r21,r22,r23,t2,r31,r32,r33,t3]T；
B is the column vector of 2N × 1,
Step 5, as 4≤N≤5, formula (2) is solved method particularly includes:
9 elements are extracted in X and obtain spin matrix R, are indicated are as follows:
R=fR(X)
And spin matrix R is made to be unitary matrice, meet RR-1=I and R-1=RT, I be 3 × 3 unit matrix；
Then following optimization problem is converted by Solving Linear problem shown in formula (2):
That is: meeting s.t.fR(X)fR(X)TUnder the constraint condition of-I=0, makeIt takes most
The X of small value is optimal solution, realizes that pose resolves；
As N >=6, formula (2) is solved using analytic method, obtains X, realizes that pose resolves.
2. a kind of optical tracker pose calculation method as described in claim 1, which is characterized in that in the step 5, use
Levenberg-Marquardt algorithm solves the optimization problem.
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| CN108333579A (en) * | 2018-02-08 | 2018-07-27 | 高强 | A kind of system and method for the light sensation equipment dense deployment based on Vive Lighthouse |
| CN108765498B (en) | 2018-05-30 | 2019-08-23 | 百度在线网络技术（北京）有限公司 | Monocular vision tracking, device and storage medium |
| CN109032329B (en) * | 2018-05-31 | 2021-06-29 | 中国人民解放军军事科学院国防科技创新研究院 | Space consistency keeping method for multi-person augmented reality interaction |
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| CN101750012A (en) * | 2008-12-19 | 2010-06-23 | 中国科学院沈阳自动化研究所 | Device for measuring six-dimensional position poses of object |
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| CN106908764A (en) * | 2017-01-13 | 2017-06-30 | 北京理工大学 | A kind of multiple target optical tracking method |
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| CN101750012A (en) * | 2008-12-19 | 2010-06-23 | 中国科学院沈阳自动化研究所 | Device for measuring six-dimensional position poses of object |
| CN104484523A (en) * | 2014-12-12 | 2015-04-01 | 西安交通大学 | Equipment and method for realizing augmented reality induced maintenance system |
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Inventor after: Bao Yihua Inventor after: Weng Dongdong Inventor after: Li Dong Inventor after: Hu Xiang Inventor before: Weng Dongdong Inventor before: Li Dong Inventor before: Hu Xiang |