CN106327515B - A kind of motion target tracking method based on 2DPCA - Google Patents
A kind of motion target tracking method based on 2DPCA Download PDFInfo
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Abstract
The present invention proposes a kind of new motion target tracking method based on 2DPCA under Particle filtering theory frame.Firstly, establishing moving target characteristic model using 2DPCA；Secondly, obtaining posterior probability required for motion target tracking；Finally, realizing the tracking of moving target.The present invention overcomes traditional PCA methods to extract covariance matrix difficulty, computationally intensive problem, improves the precision of moving target feature extraction, reduces the motion target tracking time, improves the accuracy of tracking, has stronger robustness.
Description
Technical field
The invention belongs to computer vision processing technology fields, and in particular to a kind of motion target tracking based on 2DPCA
Method.
Background technique
Motion target tracking technology has extensive practical application in computer vision field, such as in vision monitoring, reality
When traffic flow monitoring, human-computer interaction etc., motion target tracking technology all plays a crucial role.Moving target with
The key of track technology is to solve two problems: the foundation of target signature model and the tenacious tracking of target.PCA(Principal
Component Analysis, principal component analysis) method as a kind of feature extraction and analysis method, is often used in target spy
Levy the foundation of model.Moving target feature is modeled using PCA method, although can more completely retain moving target
Main component feature, but PCA method is based on one-dimensional vector, and the first two dimensional image by input is needed before extracting principal component
Sequence is converted into one-dimensional row vector or a dimensional vector.Since the image resolution ratio of input is generally large and video sequence frame
Number is more, when two dimensional image is converted to one-dimensional vector, it usually needs a huge vector space, therefore often occupy
The more memory space of Target Tracking System.Further, since the rank of matrix is larger, and very for trained sample size
It is few, therefore it is very difficult to calculate covariance matrix required when PCA feature extraction, carried out after obtaining covariance matrix feature to
It is also required to devote a tremendous amount of time when amount and characteristic value operation, to increase the motion target tracking time.
For the these problems for overcoming PCA method to occur, 2DPCA (Two-dimensional Principal
Component Analysis, two-dimensional principal component analysis) method is suggested.The operation of this method is directly based upon two dimensional image square
Battle array, do not need to convert two dimensional image to one-dimensional vector when extracting feature vector, therefore the covariance matrix size of image and
Image it is of same size.Compared with PCA method, covariance matrix reduces the feature vector much finally obtained also than the side PCA
Method obtains more accurate, and operation time also greatly reduces.2DPCA is applied to motion target tracking, calculation amount can be reduced,
Improve the accuracy of tracking.
Summary of the invention
It is an object of the invention to propose a kind of motion target tracking method based on 2DPCA, traditional side PCA is overcome
Method extracts covariance matrix difficulty, computationally intensive problem, improves the precision of moving target feature extraction, reduces movement mesh
The mark tracking time, the accuracy of tracking is improved, there is stronger robustness.
In order to solve the above technical problem, the present invention provides a kind of motion target tracking methods based on 2DPCA, using such as
Method shown in formula (1) calculates moving target posterior probability needed for motion target tracking process, to realize movement mesh
Mark tracking,
In formula (1), p (At|Zt) it is the moving target posterior probability that acquisition is calculated under Particle filtering theory frame；AtFor t
The subgraph matrix at moment；Zt=(xt,yt,st,rt,θt,λt) it is intended to indicate that the two dimensional affine of the dbjective state of t moment is joined
It counts, wherein xtFor the direction x offset, ytFor the direction y offset, stFor target scale scale, rtFor target aspect ratio, θtFor target
Rotate angle, λtFor target tilt angle；For weight factor；||·||FIndicate Frobenius norm；
In formula (1), Xt={ Xi, i=1 ..., d } and it is one in the image array that t moment size is w × d, XiIndicate one
The column vector of a w dimension；AtThe subgraph matrix for being h × w for t moment size, the subgraph matrix is by XtImage array obtains；
(·)TThe transposition of representing matrix；For projection centre, wherein For the average value of subimage sequence, definition
As shown in formula (2):
In formula (2), AiFor the arbitrary frame image in subimage sequence, m is subimage sequence frame number；
In formula (1),Part can use dtIt represents, for indicating subspace distance.
For distance dt, subgraph AtAbout dtPosterior probabilityGaussian distributed model, definition such as formula (3)
It is shown:
In formula (3), I is a unit matrix, and ε is Gaussian noise；N () indicates Gaussian distribution model；
In formula (1),Part can use dwIt represents, for indicating the projecting in subspace of subspace
The distance of the heart.For distance dw, subgraph AtAbout dwPosterior probabilityGaussian distributed model, definition
As shown in formula (4):
In formula (4), N () indicates Gaussian distribution model；Σ indicates XtEigenmatrix；Diagonal element in matrix Σ is
Matrix XtCharacteristic value；
Further, in object tracking process, when the subgraph traced into is accumulated to certain amount, need to subgraph into
Row updates.If original set of sub-images is Ut={ Ai, i=1 ..., m }, the set of sub-images of accumulation is Ot={ Bi, i=
1 ..., 5 }, then updated set of sub-images
Compared with prior art, the present invention its remarkable advantage is: (1) present invention is using 2DPCA method to the son of image
Spatial signature vectors extract, and since 2DPCA is based on two dimensional image matrix, thus do not need in advance when extracting feature vector
A vector is converted by image, but directly constructs image covariance matrix, original image square using original image matrix
The feature vector of battle array is used to extract feature, to reduce operand；In addition, obtaining the covariance matrix ratio side PCA using 2DPCA
Method is more accurate, and the time for extracting feature vector also greatly reduces；(2) present invention obtains moving target using particle filter method
Dynamic model, the posterior probability of moving target obtained by 2DPCA method, and the moving target characteristic model based on 2DPCA is fixed
The two dimensional affine parameter of each moment target of justice, the problems such as capable of preferably overcoming target deformation, it is ensured that target following
Accuracy.
Detailed description of the invention
Fig. 1 is the motion target tracking method general flow chart the present invention is based on 2DPCA.
Fig. 2 is that the present invention is based on the motion target tracking method processes of 2DPCA to scheme in detail.
Fig. 3 is the comparison result figure of the method for the present invention Yu IVT method, L1T method and VTD method.
Specific embodiment
One, basic thought of the present invention
The present invention proposes a kind of motion target tracking method based on 2DPCA, base under Particle filtering theory frame
Present principles are:
Firstly, establishing moving target characteristic model using 2DPCA；
Then, posterior probability required for motion target tracking is obtained；
Finally, realizing the tracking to moving target according to the moving target posterior probability of acquisition.
Two, the concept of 2DPCA (two-dimensional principal component analysis)
Define Xt={ Xi, i=1 ..., d } and it is w × d image array in moment t, w is the line number of matrix, and d is
Matrix column number, X in the matrixiIndicate the column vector of w dimension；Define AtFor h × w subgraph matrix in moment t,
H is the line number of matrix, and d is matrix column number；Define YtIndicate subgraph matrix AtProjection properties matrix, then about XtLine
Property transformation as shown in formula (1):
Yt=AtXt (1)
Define YtCovariance matrix SxMark be total divergence J (Xt), by maximizing this total divergence criterion, it will be able to
Find optimal projecting direction XtSo that the vector Y after projectiontIt separates.Total divergence J (Xt) as shown in formula (2):
J(Xt)=tr (Sx) (2)
In formula (2), SxFor YtCovariance matrix, definition is as shown in formula (3):
Sx=E [(Yt-E(Yt))(Yt-E(Yt))T]
=E [(AtXt-E(AtXt))(AtXt-E(AtXt))T] (3)
=E [[(At-E(At))Xt][(At-E(At))Xt]T]
In formula (3), E () indicates expectation, ()TThe transposition of representing matrix；
In formula (2), tr (Sx) representing matrix SxMark, definition is as shown in formula (4):
Define Ut={ Ai, i=1 ..., m } it is m frame subgraph AiThe sequence of composition, then the covariance matrix G of subgrapht
As shown in formula (5):
Gt=E [(At-E(At))T(At-E(At))] (5)
In formula (5), GtIt is the nonnegative matrix of a w × w.
Define subimage sequence Ut={ Ai, i=1 ..., m average value A such as formula (6) shown in:
According to formula (5) and formula (6), the covariance matrix G of subgraph is obtainedtEquivalent representation such as formula (7) institute
Show:
Criterion formula (7) obtains formula (8) and formula (9):
According to formula (8) and formula (9), enable:
To the X in formula (10)tPartial derivative is sought, formula (11) are obtained:
In formula (11),Indicate F to XtLocal derviation；Solution formula (11) obtains formula (12):
GtXt=λ Xt (12)
In formula (12), XtIndicate that optimal axis of projection, λ indicate characteristic value.
By formula (12) it is found that optimal axis of projection is covariance matrix GtThe corresponding feature vector of maximum eigenvalue λ.It is logical
Often, an optimal axis of projection is inadequate, and therefore, selection corresponds to maximum preceding d mutually orthogonal unit characters of characteristic value
Vector is indicated as shown in formula (13) as optimal axis of projection:
In formula (13), max () expression is maximized；Arg () indicates orthogonal.
Three, the related notion of the motion target tracking based on IVT algorithm
For target in the motion state of t moment, two dimensional affine parameter Ζ can be usedt=(xt,yt,st,rt,θt,λt)
It indicates；Wherein xtFor the direction x offset, ytFor the direction y offset, stFor target scale scale, rtFor target aspect ratio, θtFor mesh
Mark rotation angle, λtFor target tilt angle.The two dimensional affine parameter Xt=(xt,yt,st,rt,θt,λt) it is detailed in document
(R.Szeliski:Computer Vision:Algorithms and Applications.Springer.(2010))。
Using IVT algorithm (Incremental Learning for Robust Visual Tracking
Algorithm, the robustness Vision Tracking based on incremental learning) pursuit movement target, needed for moving target posteriority
Shown in probability such as formula (14):
In formula (14),For weight factor；||·||FIndicate Frobenius norm；AtFor in moment t subgraph square
Battle array.(Incremental Learning for Robust Visual Tracking Algorithm, is based on the IVT algorithm
The robustness Vision Tracking of incremental learning) be detailed in document ([Ross D A, Lim J, Lin R S, et al.:
Incremental learning for robust visual tracking[J].International Journal of
Computer Vision.(2008)77(1-3):125-141.])。
Four, the related notion of the 2DPCA motion target tracking based on particle filter
Target Tracking Problem may be considered a hidden markov chain problem, for subimage sequence Ut={ Ai,i
=1 ..., m }, motion state Z of the target in t momenttHave by bayesian theory to draw a conclusion:
p(Zt|At)∝p(At|Zt)∫p(Zt|Zt-1)p(Zt-1|At-1)dZt-1 (15)
In formula (15), p (At|Zt) it is observation model, p (Zt|Zt-1) it is dynamic model.
1, dynamic model p (Zt|Zt-1)
Dynamic model p (Zt|Zt-1) spatially use Brownian Motion Model, motion state Z of the target in t momenttPass through
Motion state Z of the target at the t-1 momentt-1Gaussian Profile obtain, indicate as shown in formula (16):
In formula (16), N () indicates Gaussian distribution model；For a diagonal covariance
Matrix, diagonal element are each two dimensional affine parameter Ζt=(xt,yt,st,rt,θt,λt) variance.
2, observation model p (At|Zt)
Define subimage sequence Ut={ Ai, i=1 ..., m average value A such as formula (17) shown in:
For according to target t moment motion state ZtA determining subgraph At, define it and pass through projection vector square
Battle array XtProjection centre after projection isWherein
Subgraph AtPosterior probability p (At|Zt) subgraph A can be expressed astTo subgraph spatial reference point away from
From the distance can be decomposed into subspace distance dtWith the distance d for projecting to subspace center of subspacew。
For subspace distance dt, subgraph AtAbout dtPosterior probabilityGaussian distributed model,
Definition is as shown in formula (18):
In formula (18), I is a unit matrix, and ε is Gaussian noise；N () indicates Gaussian distribution model；
For distance dw, subgraph AtAbout dwPosterior probabilityGaussian distributed model, definition is such as
Shown in formula (19):
In formula (19), N () indicates Gaussian distribution model；Σ indicates XtEigenmatrix；Diagonal element in matrix Σ
It is matrix XtCharacteristic value.
Convolution (18) and formula (19), obtain subgraph AtPosterior probability p (At|Zt), it indicates such as formula (20) institute
Show:
Five, the concept of moving target characteristic model
Define yt=AtXtIndicate subgraph AtPass through XtMapping obtains yt, and ytGaussian distributed, i.e. yt~N (u, L),
Wherein, L is diagonal matrix.Then subspace image AtIt can indicate are as follows:
In formula (21),For Gaussian noise, meetI is a unit matrix.Convolution (20) and
Formula (21), then subgraph AtMoving target characteristic model p (At) can indicate are as follows:
Six, the concept of the posterior probability of the 2DPCA motion target tracking based on particle filter
Logarithm is taken to obtain formula (23) simultaneously on formula (22) equal sign both sides:
In formula (23), multinomialIt is partially indicated with c, multinomialPart indicates that multinomial c is a constant, therefore log [p (A with lt)]
Value determined by multinomial l.Formula (23) is equivalent to formula (24):
Shown in Sherman-Morrison-Woodbury formula such as formula (25):
(A-uvT)-1=A-1+A-1u(1-vTA-1u)-1vTA-1 (25)
According to formula (25), in formula (24)It can be with equivalent representation are as follows:
And because are as follows:
In formula (27), D is a diagonal matrix, Dii=Lii+σ2, then formula (26) can be of equal value are as follows:
Formula (28) are substituted into formula (23), available:
In formula (29), multinomial c is a constant, therefore log [p (At)] by multinomial l1It determines, then:
Therefore moving target characteristic model p (A is obtainedt) posterior probability p (At|Zt) are as follows:
Seven, a process of the method for the present invention is executed
Step 1, chooses the moving target in image sequence in first frame image manually, and with indicating that symbol logo comes out,
Such as outlined the moving target in first frame image with red squares frame, as reference target.
Step 2 initializes and empties subimage sequence Ut={ Ai, i=1 ..., m }.
Step 3 judges n > n for the n-th frame image of inputth(nthFor the frame number threshold value of setting).If meeting n >
nth, five are thened follow the steps, step 4 is otherwise executed.
Step 4, using IVT method (Incremental Learning for Robust Visual Tracking
Algorithm, the robustness Vision Tracking based on incremental learning) pursuit movement target [Ross D A, Lim J, Lin R
S,et al.:Incremental learning for robust visual tracking[J].International
Journal of Computer Vision.(2008)77(1-3):125-141.]。
Step 5, after required moving target during the calculating motion target tracking of method shown in formula (31)
Probability is tested, to realize the tracking of moving target.
Step 6, return step three.
Beneficial effects of the present invention can be further illustrated by following experiment:
For the embodiment of the present invention using Matlab2012b as experiment porch, input image sequence is " dudek ", and every frame image is big
Small is 480 × 720, amounts to 150 frames.Choosing face is that moving target is tracked, from the 100th frame to the 110th frame, moving target
It is blocked, disappearance is blocked to moving target after the 110th frame.
This experiment compares the method for the present invention and existing IVT method, L1T method and VTD method.Using square
For root error (RMS) as foundation is compared, calculation formula such as formula (32) is shown:
Wherein, RD indicates that tracking result pixel value, TD indicate true pixel values.Comparison result is as shown in Figure 3.From Fig. 3
As can be seen that in the tracking initial stage, IVT method, actual value that L1T method and the method for the invention track and true
Less than 5 pixels of the root-mean-square error of value, but after partial occlusion, the root-mean-square error of the method for the invention is less than existing
Other algorithms, it is seen that using this method carry out motion target tracking have certain advantage.
The L1T method is detailed in document (Mei X, and Ling H:Robust visual tracking using L1
minimization[C].Computer Vision,2009IEEE 12th International Conference on.
IEEE.(2009):1436-1443.)。
The VTD method is detailed in document (J.Kwon and K.Lee.Visual tracking decomposition.
In CVPR,pages 1269–1276,2010.)。
Claims (1)
1. a kind of motion target tracking method based on 2DPCA, which is characterized in that obtained using the method as shown in formula (1)
Moving target posterior probability needed for motion target tracking process, thus realize motion target tracking,
In formula (1), p (At|Zt) it is the moving target posterior probability obtained under Particle filtering theory frame；AtFor the son of t moment
Image array；Zt=(xt,yt,st,rt,θt,λt) be intended to indicate that t moment dbjective state two dimensional affine parameter, wherein xtFor
The direction x offset, ytFor the direction y offset, stFor target scale scale, rtFor target aspect ratio, θtAngle, λ are rotated for targett
For target tilt angle；For weight factor；| | | | indicate Frobenius norm；
In formula (1), Xt={ Xi, i=1 ..., d } and it is one in the image array that t moment size is w × d, XiIndicate a w dimension
Column vector；AtThe subgraph matrix for being h × w for t moment size, the subgraph matrix is by image array XtIt obtains；(·)TTable
Show the transposition of matrix；For projection centre, wherein For the average value of subimage sequence, definition such as formula (2)
It is shown:
In formula (2), AiFor the arbitrary frame image in subimage sequence, m is subimage sequence frame number.
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| CN103473790A (en) * | 2013-08-29 | 2013-12-25 | 西北工业大学 | Online target tracking method based on increment bilateral two-dimensional principal component analysis (Bi-2DPCA) learning and sparse representation |
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Non-Patent Citations (3)
| Title |
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| Object Tracking via 2DPCA and l1-Regularization;Dong Wang etal;《IEEE SIGNAL PROCESSING LETTERS》;20121130;第19卷(第11期);第711-714页 |
| Two-Dimensional PCA:A New Approach to Appearance-Based Face Representation and Recognition;Jian Yang etal;《IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE》;20040131;第26卷(第1期);第131-137页 |
| 基于2DPCA和稀疏表示的目标跟踪算法;曹晓丽 等;《中国包装工业》;20141231;第78-82页 |
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