英---基于李群正态分布的粒子滤波算法的视频目标跟踪

1、Tracking Video Target via Particle Filtering on theLie Group Normal Distribution GE Huilin, ZHU ZhiyuAbstract: Most existing video target tracking algorithm based on particle filtering are in Euclidean space. While video target tracking occurs in complex environments, it is very difficult to guarant

2、ee the tracking effect. This paper describes the covariance descriptor to represent the object image region, and describes the geometric deformation of the object image region by an affiiie transformation. The affine transformation matrix is one element of the Lie group. We directly implement the vi

3、deo tracking system state lies in a low dimensional manifold, and make full use of state space of intrinsic geometrical characteristic,the manifold of optimization algorithm to solve Riemami mean value s studied. By constructing Lie group normal distribution as the optimal importance function for ex

4、tracting state sample. This paper proposes particle filtering on the Lie group with optimal importance fimctions, which provides a kind of new train of thought for improving efficiency and robustness of the tracking algorithm. The simulation experiments show that in the case of object scale size cha

5、nging, rotating, etc. geometric deformation light intensity changing > target occlusion and fast motion situation, the proposed Lie group particle filtering algorithm can still realize target tracking well and impore the real-time performance of the system.Key word: Target tracking, particle filt

6、ering, covariance matrix. Lie group normal distribution0、 IntroductionVideo tracking combines image processing, pattern recognition, artificial intelligence, automatic control and computer if 1 dry fields such as advanced technology, is the key technology to realize intelligent monitoring, and in mi

7、litary visual guidance, video surveillance, robot vision navigation, medical diagnosis and has a wide application in such aspects as weather analysis 1-2.Particle filter in recent years, won a wide application in video tracking, become one of the main research direction of video target tracking 3-4.

8、 Although particle filter can be applied to all nonlinear non-gaussian systems, not limited by noise properties, but for high-dimensional system for tracking, also will encounter "dimension disaster" problem.Through manifold learning to obtain the particle filter, this paper analyses the i

9、mportance of the probability density function of the general options, makes the nonlinear model of the choice of importance probability density function not mainly rely on the system state model. The optimization algorithm based on the theory of lie groups, build Li Qunzheng distribution based on li

10、e group index mapping, and the importance Li Qunzheng distribution is expressed as function of particle sampling. Video tracking, the observation noise covariance is likely to be unknown and time-varying, or when using the covariance matrix to express the image of the target area 5-6, in the image m

11、atching, need to compute the difference of two covariance matrix of image region, because of the covariance is a positive definite matrix, all the positive definite matrix form a Riemannian manifold, so at this point with the method of the European space tracking no longer suitable for 7, must use o

12、f space differential geometry properties of positive definite matrix, structure more efficient algorithm. How to make full use of intrinsic geometric structure of target motion, the differential geometry.1, Li qun manifold particle filter This article projective transformation are used to indicate t

13、he visual target tracking in image scaling, translation, deformation change, such as application of differential geometry mathematical tools, the image of the projective transformation into matrix lie group structure, the target of the projective change projective transformation is applied to repres

14、ent the visual target tracking in image scaling, translation, deformation change, such as application of differential geometry mathematical tools, the image of the projective transformation matrix constructed as li qun, the target of the projective transformation parameters as state variables, set u

15、p the state transfer model on the lie group. Applications are considered on the optimization algorithm are studied of the mean, realize the state estimation1.1 The projective transformation is expressed as li qunIn visual target tracking, target template to show interest. If by looking for the metho

16、d of template matching and target tracking target in the image frames, the target geometrical deformation can be expressed as a projective transformation, while 2 d projective transformation matrix is an element of lie groups.Projective transformation model of moving targets with matrix is expressed

17、 as , A total ofeight parameters, including A is second-order reversible matrix, said the scale of the target changes suchas deformation, namely 𝐸1𝐸6, T is translation vector, ,V,1-𝑇 is infinite linear projection. The projective transformation group of regularization, the det

18、erminant value of unit 1, and get special linear group SL (3, R), namely, li qun subgroup of G. Lie algebra of SL (3 R) base vector as follows:1.2 State model As shown in figure 1 is an embedded in the 2 d to 3 d European space manifold G,figure 𝑇𝑥 said in tangent space, it is consid

19、ered on the tangent plane at point X.Tangent space can be seen as the points on the manifold on the manifold a set of allowable speed of the movement. Solid arrow said tangent at point x.Are considered on the distance between two points by which the length of the curve between two points, said has t

20、he shortest distance curve is geodesics are considered on the geodesic line length is intrinsic distance. For each tangent 𝑇𝑥,there is a only starts at point x, with initial velocity geodesic.Index mapping EXP𝑋, mapping a to the end of the geodesics on the manifold.Figure 1 m

21、anifold and its tangent plane at point xSelect target projective transformation parameters as the state of the system, state vector, the goal of the use X𝑘said k time, Z1：k= Z1， Z2， Z𝑘 said until k moment of the observed image sequence, in order to obtain li qun manifold on system dy

22、namic model of state vector should be left unchanged on the lie group G vector (vector) in tangent space, with V𝑘 said from k - 1 hour observation images Z𝑘1 to k time observation of image motion speed between velocity (image), rammed by a transfer model for:Including the 𝜂&#

23、119896;1 expression random noise. 1.3 The observation model In the video tracking box using covariance descriptor to represent the image of the target area. The target area of covariance matrix can be expressed as:Including the 1.4 Riemann average weighted particles Because of the space geometric st

24、ructure and the change of measure, the average European space to solve method is no longer suitable for li qun, it involves manifold of constrained optimization problems,in analogy to the European space optimization algorithm, the research on the application of manifold optimization algorithms to so

25、lve Riemann averages, realize the state estimation According to differential geometry knowledge, complete Riemannian manifold M on the point set of the average of x1，x2，x𝑛 are defined as:Where d (y, x𝑖) for M on Riemann geodesic distance function.2, Based on the importance of Li Qunz

26、heng distribution function is selectedThis paper by giving the Riemannian metric Riemannian manifold, and then use digital characteristics of manifold optimization algorithm, and constructs the special linear Li Qunzheng distribution. 2.1 SL (3, R) of Riemann mean and covariance matrix algorithm Rie

27、mann average by the formula (4), by definition on Riemannian manifold function outside the coordinates of the Taylor expansion, and combined with the gradient type: Can get a Riemannian manifold average gradient descent algorithm is: For the covariance matrix, design a SL (3 R) to map: f：XSL(3,R)

28、19877;6Due to the SL (3 R) every point on the X can be expressed as the linear combination of the base (1), notice the matrix trace is zero, can simply choose mapping for:So, experience covariance matrix is:2.2 Li qun normal distributionIn the above Riemann average algorithm, using li qun logarithmi

29、c mapping instead of Riemann logarithmic mapping, can according to the optimization algorithm, it is concluded that the mean call accordingly to build distribution based on lie group index mapping Li Qunzheng distribution, namely:3, The particle filter algorithm based on Liqun group of normal distri

30、butionLi qun normal distribution particle filter algorithm steps are as follows: S1: initialization: particle sets *𝑥0𝑖+𝑖=1𝑁𝑠generated by the prior probability P (x0) that all weight of examples1𝑁𝑠S2: importance sampling: according to the formu

31、la (12) along the optimal importance function sampling particles S3: importance weights calculation: according to the observation likelihood function of the model(𝑦𝑘|𝑋𝑘(𝑖) calculate the particle weight and normalized.S4: if necessary for resampling.S5: calcula

32、te the Riemann average particle, according to the formula (4) the system state estimationS6: return to S2, iterative computation.4, Test and analysisThis paper designed the 5 set of simulation experiments, in li qun particle filter algorithm, six li qun affine parameters set the standard deviation a

33、s (0.05, 0.02, 0.05, 0.02, 5, 5), in the covariance estimation value 𝜎cov is 0.96.In each set of experiments comparing the results of different tracking algorithms are given respectively.Again by tracking the time, and the algorithm error, effective number of particles and a series of measur

34、es, fully illustrates the li qun manifold particle filter algorithm is proposed in this paper in all kinds of complicated cases, can achieve stable tracking. The experiment a rubik's cube in the video from far to near move and rotate.The following for li qun particle filter tracking, European sp

35、ace particle filter tracker for FPF.On the left in figure 2 are ZPF tracking results, the right of VPF tracking results.127 frames and frame 127 video target deformation under the condition of rotation and size, VPF red box lost accuracy.This is because the FPF algorithm is the parameter space as a

36、whole, can not be fully reliable estimates of the number of particles were observed.Tracking precision, and to the left of the LPF algorithm for combining the geometry deformation parameter space, the continuous variation before frame parameters is established between li qun space structure, improve

37、 the tracking accuracy and robustness of the algorithm. Figure 2 Rubik's cube size and attitude change tracking results compared Experiment 2 car has blocked video target sequence, as shown in figure 3, when vehicle movement to the bushes keep out, to keep out the object can only perform forecas

38、t operation, to maintain the original hypothesis condition, importance and use state transition as a function of li qun particle filter algorithm can keep good tracking robustness.When the car has blocked VPF algorithm for tracking the target must be happened after migration, and LPF flat algorithm

39、is still able to auto target accurately positioning. Figure 3 Car has sheltered tracking results compared In order to further illustrate lie groups are considered on the superiority of particle filter tracker, table 1 shows the two tracker tracking error and time.Where N said particle number, take 2

40、00 and 600 respectively, Err. said the mean error, Time said the average Time per frame matching, the unit for seconds.The table 1 shows that when N = 200, the average error of VPF is six times the LPF.Selection, however, as the population increases, when N = 600, LPF, on average, each frame matchin

41、g time is slower than the VPF.The experimental results show that compared with European space particle filter tracking, tracking accuracy of particle filter tracker based on lie groups had a significant bureau, and real-time tracking is also improved.Experiment three figure 4 said the light change &

42、quot;1" toys for tracking, the optimal importance function on the left is li qun tracker tracking results, the right to state transition density tracker tracking results.When 1 "toys" move to 611 frames, intensity of illumination suddenly dimmed, the tracker is still on the left Figur

43、e 4 target illumination change tracking results comparedExperiments four in view of the taking lens movement and speed quickly, similar to the vigorous exercise goals happen in video sequences.By the assumption of the smooth movement state transition model is difficult to predict the movement of the

44、 brush pot.Because the mechanical model also assumes that smooth the movement of the time interval between an infinitesimal, so you need to select Li Qunzheng distribution as importance function.Tracking results as shown in figure 5, for "brush pot" series, originally accurate tracking is

45、degraded state transition density, especially when the object frame in the 211th and 300th frame fast movement, yellow Li Qunzheng distribution on the left track frame is quite accurate.Figure 5 shots mobile tracking results more quickly Experiment five in order to further demonstrate the target mot

46、ion state of severe cases Li Qunzheng importance distribution function of the advantages of the tracker figure 6 for tracking suddenly accelerated motion "toys 2", the results show that the optimal importance lie group function tracker in all rectangular box is very keen to track objects.T

47、oys in the 209th frame 2 sudden changes in motion state, the use function of the optimal importance still can track objects and state transition density tracker is completely lost track the target.Similarly, in order to further illustrate the tracker based on importance Li Qunzheng distribution func

48、tion of tracking efficiency, with the average number of particles 𝑁eff as evaluation index, two tracker tracking is presented in table 2, all the frames, the value of the average number of particlesFigure 6 target mobile tracking results more quicklyCan be seen from the results in table 2, a

49、lthough the two kinds of particle filter tracker has chosen the same particle number 400, but li qun optimal importance function tracker Neff more obvious than state transition density tracker, show that the tracking efficiency of the former than the latter.5, Conclusion This paper puts forward a ki

50、nd of lie groups are considered on particle filter algorithm, and applied to the video target tracking. Through affine lie group, make full use of the projective transformation parameter lie group structure, directly on the low dimensional manifold sampling implementation status, reduce the dimensio

51、n of target tracking system, the calculation sample average Riemann manifold, get system state estimation, help to solve the problem of particle degradation, improve the tracking precision, real time and robustness of the algorithm.Li Qunzheng distribution were obtained through the manifold learning

52、, as the importance function, makes the nonlinear model of the choice of importance probability density function not mainly rely on the system state model.The superiority of this algorithm is analyzed by comparing the experiment, the effectiveness of the method is verified by the experiments.Referen

53、ces1 Zhou S K, Chellappa R, Moghaddam B. Visual tracking andrecognition using appearance adaptive models in particlefilters J. IEEE Transaction on Image Processing, 2004,13(11): 1491-1506。2 Sheng X H, Hu Y H. Distributed particle filters for wirelesssensor network target trackingC. ICASSP，05. Philadelphia:2005, 4(2): 845-848