Real Time Tracking via Sparse Representation

Transcription

1 203 8th International Conference on Communications an Networing in China (CHINACOM) Real Time Tracing via Sparse Representation Hong-Mei Zhang, Xian-Sui Wei, Tao Huang 2, Yan He, Xiang-Li Zhang, JinYe School of Information an Communication Guilin University of Electronic Technology, st Jin-Ji Roa, Guilin, China 2 Wuzhou University, 82 st Ming-Fu Three Roa, Wuzhou, China uuhao3@26.com Abstract the L tracer gains robustness by casting tracing as a problem of sparse approximation in a particle filter framewor. Unfortunately, the particle filter an norm minimization lea to a large amount of calculation as a result that the L tracer cannot achieve real-time tracing. The aim of this paper is to evelop a new tracer which not only runs in real time but also has a better robustness than L tracer via sparse representation. In our propose algorithm, caniate targets are sample in the region of interest(roi) to increase the tracing spee. Moreover, base on the bloc orthogonal matching pursuit(bomp), a very fast solver is evelope to solve the problem of norm minimization to improve tracing spee an accuracy. We conuct extensive experiment to valiate an compare the performance of the BOMP algorithms against six popular -minimization solvers in ifferent challenging sequences. We also implement great experiment to valiate the high computational efficiency an tracing accuracy of our propose tracer compare with four alternative state-of-the-art tracers in six challenging sequences. Keywors-L tracer; particle filter; spares representation; ROI; BOMP I. INTRODUCTION Object tracing has been an active research irection in the computer vision as it is wiely applie in the vieo surveillance, intelligent robot, an transportation system an so on. Despite the great number of algorithms have been propose, object tracing remains a challenging problem ue to appearance change cause by pose, illumination, occlusion an others. Some tracing algorithms have been propose in recent years[,2,3,4,5]. Recently, sparse representation has been use in the L tracer that an object is expresse by a spare linear combination of target an trivial templates[6,7,8]. L tracer is base on the particle filter framewor. It emonstrates promising robustness compare with many exiting tracers in various tracing environments. However, L tracer has a rather high computation complexity, this limits its applications in real-time scenarios. The spee bottlenec is the solver to norm minimization. Bao et al.[9] an Li et al.[0] further exten the L tracer by using the Accelerate Proximal Graient algorithm(apg) an orthogonal matching pursuit algorithm(omp) for solving the optimization problems efficiently. However, these improve algorithms still have a high computation complexity as they are base on the particle filter framewor. Inspire by the L tracer using spare representation, we propose a real-time tracing algorithm via spare representation(rttsr). This paper aims at eveloping a more robust tracing algorithm which runs in real time. Specifically, the caniate targets are sample in the region of interest at a new frame, each target caniate is sparsely represente in the space spanne by target templates an trivial templates. The sparsity is achieve by solving a norm minimization problem. Then the caniate target with the smallest projection error is taen as the tracing result. The target template is upate accoring to the tracing result. The main components of our tracing algorithm are shown by Fig.. There are two ey contributions of our wor. One is that we proposes a very fast metho that is boc orthogonal matching pursuit(bomp)[] to solve the norm minimization problem with improve tracing accuracy an spee. The other more significant contribution is that the caniate targets are sample in the region of interest rather than uner the Particle Filter framewor to improve the tracing spee. Our propose algorithm runs at real-time an performs favorably against state-of-the-art tracers on challenging sequences in terms of accuracy, while achieves higher efficiency compare with L tracer. The rest of the paper is organize as follows: relate wors are summarize in Section 2. In Section 3, the propose RTTSR algorithm is presente. Experimental results are reporte in Section 4. Finally, we conclue this paper in Section 5. II. RELATED WORK A. Sparse Representation The global appearance of one object uner ifferent illumination an viewpoint conitions is nown lie approximately in a low imensional subspace[2]. Given n target template set T [ t,...,t ] R where each template n t i R columns is stace to form a D vector, a tracing target y R approximately lies in the linear span of T, y Ta e [ T,I,-I][ a, e, e ] T Ax, st.. x 0 () + - n Where e is the error vector, a ( a, a,, an ) R is the n n target coefficient vector, I R is the unit matrix. e+ R, e- R represent a positive trivial coefficient vector an a negative trivial coefficient vector respectively, ( n 2 ) A [ T,I,-I ] R is the over complete ictionary, T n 2 x = [a,e R +,e-] is a non-negative coefficient vector. x can be achieve via solving the following minimization problem with nonnegative constraints: norm Supporte by the National Natural Science Founation, China(No ); GuangXi Sci.&Tech. Development Founation(GKG2807-2C)Guangxi Key Lab of Wireless Wieban an Communication &Signal Processing(PF207X.) IEEE

2 Upate the target templats Region of Interest Target templatstrivial templates... e e Sparse Representation Caiate Targets Figure. Main component of our tracing algorithm min x st.. y = Ax, x 0 (2) x The formula(2) is also well nown as the basis pursuit enoising problem with a scalar weight : 2 min y - Ax + a st.. x 0 (3) 2 2 Where a is the control coefficient. We gain the tracing result by fining the smallest resiual after projecting on the target template subspace. The tracing result y is chosen by y arg min y y yta (4) 2 B. Template Upate The object is trace through the vieo by extracting a template from the first frame an fining the object of interest in successive frames. Intuitively, object appearance remains the same only for a certain perio of time, but eventually the template is no longer an accurate moel of the object appearance. If we o not upate the template, the template coul not capture the appearance variations ue to illumination or pose changes. In orer to ensure the stability of tracing, we nee to upate the target template. The main iea of template upating is that the least similarity template is upate as the new current tracing result. The weight of new temple is initialize by the mean value of all weights to prevent tracing rift. The upating in our approach inclues three operations: template replacement, template upating, an weight upating. The specific process of template upate scheme is summarize in the literature [6]. C. L Tracer III. REAL-TIME TRACKING VIA SPARSE REPRESENTATION A. Fast Restructing Algorithm Xue et al.[6,7,8] propose a L Tracer tracing metho by using preconitione conjugate graients algorithm (PCG) as reconstruction algorithm, but computational complexity result in the low efficiency of tracing. This paper consiers a faster reconstruction algorithm: bloc sparse orthogonal matching pursuit algorithm (BOMP)[]. The special sparse signal ----Bloc-Sparse signals that exhibit aitional structure in the form of the nonzero coefficients occurring in clusters was present. Such signals often appear in the practical applications, for example, image processing. Elar et al.[] firstly efine two separate notions of coherence about Bloc-Sparse signals: sub-coherence an bloc-coherence. Base on this, the bloc-version of orthogonal matching pursuit (OMP), calle BOMP, was propose an the theoretical framewor of compresses sensing about Bloc-Sparse signals was establishe. BOMP algorithm taes full avantage of the bloc sparse structure characteristics of the signal, provies significant improvement of accuracy an spee against traitional algorithms. The bloc-sparse signal x is escribe as follows: T T T x x [] x [2]... x [ N] T T p Where x [] i R for i=, N an T enotes transpose. The vector x is calle bloc- sparse if x T [] i has non-zero Eucliean norm for at most inices. If p=, the vector x reuce to the conventional sparse signal. BOMP can be summarize as: ) Initialization: Let the resiual r 0 y, the iteration counter = an the inex set E0 be the empty set. 2) Sensing step: Fin the bloc inex i by solving T the optimization i arg max Φ [ ir ] 2. Then, E E i 3) Upate of the resiual: i r I Φ Φ y, ( ) p E E where I p is the ientity matrix of size Kp Kp, ΦE is a set of blocs Φ Φ[i ] Φ[i ] E pseuo-inverse. an enotes the 4) Increment: Set = +, an return to step (2) if K. 725

3 B. Sampling Metho of Caniate Targets The sampling metho for caniate targets of L Tracer is base on the Particle Filter framewor. It is a time-consuming process because it nees to preict the state of particles, upate weight of particles, an re-sample of particles. Fortunately, we propose a new sampling metho is base on the region of interest for caniate targets to improve the spee. Specifically, we let R( x, y, w, h) enote the location of image patch. The scale subjects to Gauss istribution. For each new frame, we crop out a set of caniate targets: r T ( x, y, w, h) : ( x, y) r ; ( w, h) ~ N( w, h,,,0) (5) t t t w h Where t is the center of the tracing result at (t-)th frame. N() is Gauss istribution. ( wt, ht ) is the scale of the tracing result at (t-)th frame. ( w, h) is the variance of scale(we assume it is fixe). We assume that the location of the caniate targets is equally liely to appear within a raius r of the tracer result location at (t-)th frame: p( x, y) if ( x, y) r t N (6) 0 otherwise Where N is the sum of pixel in the region of interest at (t-)th frame. C. Propose Tracing Algorithm The basic iea of our tracing algorithm is that each of caniate target is sample in the region of interest at a new frame, each of caniate target caniate is sparsely represente in the space spanne by target templates an trivial templates, an sparsity is achieve by solving an norm minimization problem using bloc sparse orthogonal matching pursuit algorithm (BOMP)[].Then the caniate target with the smallest projection error is taen as the tracing result. The target templates are upate accoring to the tracing target result. Our tracing algorithm can be summarize as: Algorithm : Real Time Tracing via Sparse Representation Input: Current frame F t ; Template set tii n T ; Set sample raius r ; Set variance of scale (, ) ; begin. Get caniate targets via (5); w h 2. Targets caniate is sparsely represent by template T; en Output: 3. Get x via solving (2) with BOMP; 4. Chosen the tracing result via (4); Tracing result; Upate target templates T; IV. EXPERIMENT A. Experiment Setup The raius of region of interest is set to r 20,the variance of scale is set to w h.4 an about 600 samples are generate. All the algorithms are run on a PC with 2.0GHZ qua-core CPU an 2G memory. B. Compare with Six Fast min Solvers With Real Visual Data In this case, we valiate an benchmar the performance of BOMP algorithms against an extensive list of six state-of-the-art min solvers on the vieo sequence Car4 an Face. The other algorithms involve in the comparison are A Fast Iterative Soft-Thresholing Algorithm(FISTA)[3], Homotopy[4], OMP[0], BOMP[], Augmente Lagrangian Metho(ALM)[5], PCG[6], Approximate Message Passing(AMP)[7]. All algorithms use MATLAB language to realize an all experiments are performe in MATALAB. TABLE.The average tracing error an frame rate for the Car4 vieo sequence. The error is measure using the Eucliian istance of two center points. The first time is shown in bol. Average error Average frame rate FISTA Homotopy OMP BOMP ALM APG AMP TABLE 2.The average tracing error an frame rate for the Face vieo sequence. The error is measure as the same as in the TABLE.The first time is shown in bol. Average error Average frame rate FISTA Homotopy OMP BOMP ALM APG AMP

4 (a) Davi inoor (b) Car4 (c) Face () Sylv (e) Girl (f) Oneleaveshop The average tracing error an frame rate of the test methos for the Car4 vieo sequence an the Face vieo sequence are reporte in Table an Table2 (the lowest average tracing error an the highest frame rate value among the seven are highlighte). Accoring to the TABLE an TABLE 2, we consier the BOMP algorithm outperform other min solvers in terms of both accuracy an robustness in the object tracing. Ours L-PCG IVT MIL OAB Figure 2. Tracing results of ifferent algorithms for ifferent sequences C. Qualitative Comparison with Other Methos The performance of our propose tracing algorithm is evaluate on six publicly available vieo sequences name Davi inoor, Car4, Face, Girl, Sylv, Oneleaveshop an compare with four latest state-of-the-art tracers inclue L-APG[9](it is the latest state-of-the-art L Tracer which uses APG to solve the norm minimization problem), Incremental Visual Tracing(IVT)[4], Multiple Instance Learning(MIL)[3], Online AaBoost(OAB)[8]. The Fig.3 727

5 Figure 3. The tracing error for each test sequence TABLE 3. The average tracing error which were measure as the same as in the TABLE. The first time is shown in bol. Ours OAB MIL IVT L-APG Davi inoor Car Face Sylv Girl Oneleaveshop AVE shows the tracing error for each test sequence with ifferent tracers. The average tracing errors for each test sequence with ifferent tracers are shown in TABLE 3. For the Davi inoor sequence shown in Fig. 2(a), both of the illumination an the pose of the target change graually. Our tracing algorithm, IVT an MIL can trac the target well, while other tracers lose the target while the pose of the person change. For the car4 sequence shown in Fig. 2(b), a vehicle unergoes rastic illumination changes as it passes beneath a brige. Our tracing algorithm, IVT an L-PCG can trac the target well, while other tracers lose the target after the car goes through the brige. For the Face sequence shown in Fig. 2(c), the target uner the occlusion an pose change. Only our tracing algorithm can trac the target through the all sequence. Other tracers trac rifting from the target when the man s face is severely occlue by the boo. Fig. 2() shows the results on the sequence sylv, where a moving animal oll is unergoing challenging pose variations, lighting change an scale variations. Our tracing algorithm, OAB an MIL can trac the target well an our tracing algorithm achieves best performance, while other tracers eventually lose the target after 60th frame as a result of rastic pose an illumination change. Results on the sequence girl are shown in Fig. 2(e), where the woman is unergoing challenging pose rastic variations an scale variations. Only our tracing algorithm can trac the target well though all the sequence, while other tracers trac rifting the target as a result of rastic pose. Results on the sequence Oneleaveshop are shown in Fig. 2(f), only OAB rift to the man when he occlues the target ue to his similar appearance as target. Other tracers can trac the target uring the entire sequence. D. Efficiency Comparison with L-APG The Efficiency of our propose tracing algorithm is evaluate on six publicly available vieo sequences compare with L-APG. For comparison, the two tracing algorithms use MATLAB language to realize. The TABLE 4 shows that our tracing algorithm achieves a real-time spee that is up to 3 times faster than that of the L-APG. V. CONCLUSION In summary, base on the sparse representation technology, a real-time tracing is propose via sparse representation with improve tracing accuracy. Specifically, the caniate targets are ranom sample in the region of interest to increase the tracing spee. Moreover, on the basis of the boc orthogonal matching pursuit(bomp), a very fast 728

6 TABLE 4. The average frame rate for each test sequence Ours L-APG Davi inoor Car Face Sylv Girl Oneleaveshop solver is evelope to solve the resulting norm minimization problem to improve the tracing accuracy an spee. The experiments also valiate the great running time efficiency an tracing accuracy of our propose tracing algorithm. REFERENCES [] D. Comaniciu, V. Ramesh an P. Meer, Kernel-Base Object Tracing, IEEE Trans. Pattern Analysis an Machine Intelligence, vol. 25, no. 5, pp , May [2] D. Schulz, W. Burgar, D. Fox an A.B. Cremers, &lquo, Tracing Multiple Moving Targets with a Mobile Robot Using Particle Filters an Statistical Data Association, &rquo, IEEE Int'l Conf. Robotics an Automation, 200. [3] B. Babeno, M.-H. Yang an S. Belongie, Visual tracing with onlinemultiple instance learning, CVPR, pp , [4] D. Ross, J. Lim, R.-S. Lin, an M.-H. Yang, Incremental Learning for Robust Visual Tracing, Int'l J. Computer Vision, vol. 77, no., pp. 25-4, [5] H. Grabner, M. Grabner, H. Bischof, Real-time tracing via on-line boosting, Proc. BMVC, pp , [6] X. Mei, H. Ling, Robust visual tracing using l minimization, Proc. IEEE Int'l Conf. Computer Vision, [7] X. Mei, H. Ling, Y. Wu, E. Blasch an L. Bai, Minimum error boune efficient L tracer with occlusion etection, Proc. IEEE Int. Conf. CVPR, pp , 20. [8] X. Mei an H. Ling, Robust visual tracing an vehicle classification via sparse representation, IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no., pp , 20. [9] C. Bao, Y. Wu, H. Ling an H. Ji, Real time robust l tracer using accelerate proximal graientapproach, CVPR, pp , 202. [0] H. Li, C. Shen an Q. Shi, "Real-time visual tracing with compresse sensing," Proc. IEEE Int. Conf. CVPR, pp , 20. [] Y. C. Elar, P. Kuppinger an H. Bölcsei, Bloc-sparse signals: Uncertainty relations an efficient recovery, IEEE Trans. Signal Process., pp , 200. [2] K. Lee an D. Kriegman, &lquo, Online Learning of Probabilistic Appearance Manifols for Vieo-Base Recognition an Tracing, &rquo, Proc. IEEE Conf. Computer Vision an Pattern Recognition (CVPR), [3] A. Bec an M. Teboulle, A fast iterative shrinage-threshol algorithm for linear inverse problems, SIAM J. Imaging Sci., vol. 2, pp , [4] M. Osborne, B. Presnell an B. Turlach, A new approach to variable selection in least squares problems, IMA J. Numer. Anal., vol. 20, pp , [5] J. Yang, Y. Zhang, Alternating irection algorithms for l-problems in compressive sensing, SIAM journal on scientific computing, vol.33, pp , 20. [6] K. Koh, S.J. Kim, an S. Boy, An interior-point metho for large-scale l-regularize logistic regression, Journal of Machine learning research, vol. 8, no.8, pp , [7] D. L. Donoho, A. Malii an A. Montanari, Message-passing algorithms for compresse sensing, Proc. Nat. Aca. Sci., vol. 06, no. 45, pp , [8] H. Grabner, M. Grabner an H. Bischof, Real-Time Tracing via On-Line Boosting, Proc. British Machine Vision Conf., vol., 4-7, pp ,