cvpr cvpr2013 cvpr2013-285 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Junseok Kwon, Kyoung Mu Lee
Abstract: We propose a novel tracking algorithm that robustly tracks the target by finding the state which minimizes uncertainty of the likelihood at current state. The uncertainty of the likelihood is estimated by obtaining the gap between the lower and upper bounds of the likelihood. By minimizing the gap between the two bounds, our method finds the confident and reliable state of the target. In the paper, the state that gives the Minimum Uncertainty Gap (MUG) between likelihood bounds is shown to be more reliable than the state which gives the maximum likelihood only, especially when there are severe illumination changes, occlusions, and pose variations. A rigorous derivation of the lower and upper bounds of the likelihood for the visual tracking problem is provided to address this issue. Additionally, an efficient inference algorithm using Interacting Markov Chain Monte Carlo is presented to find the best state that maximizes the average of the lower and upper bounds of the likelihood and minimizes the gap between two bounds simultaneously. Experimental results demonstrate that our method successfully tracks the target in realistic videos and outperforms conventional tracking methods.
Reference: text
sentIndex sentText sentNum sentScore
1 Abstract We propose a novel tracking algorithm that robustly tracks the target by finding the state which minimizes uncertainty of the likelihood at current state. [sent-2, score-1.243]
2 The uncertainty of the likelihood is estimated by obtaining the gap between the lower and upper bounds of the likelihood. [sent-3, score-1.07]
3 By minimizing the gap between the two bounds, our method finds the confident and reliable state of the target. [sent-4, score-0.472]
4 In the paper, the state that gives the Minimum Uncertainty Gap (MUG) between likelihood bounds is shown to be more reliable than the state which gives the maximum likelihood only, especially when there are severe illumination changes, occlusions, and pose variations. [sent-5, score-1.293]
5 A rigorous derivation of the lower and upper bounds of the likelihood for the visual tracking problem is provided to address this issue. [sent-6, score-1.008]
6 Additionally, an efficient inference algorithm using Interacting Markov Chain Monte Carlo is presented to find the best state that maximizes the average of the lower and upper bounds of the likelihood and minimizes the gap between two bounds simultaneously. [sent-7, score-1.701]
7 Experimental results demonstrate that our method successfully tracks the target in realistic videos and outperforms conventional tracking methods. [sent-8, score-0.606]
8 Introduction The objective of the tracking problem is to track the target accurately in the real environments [3, 5, 6, 8, 9, 11, 13, 15, 21, 3 1, 35, 36]. [sent-10, score-0.536]
9 For robust tracking, most conventional tracking methods formulate the tracking problem by the Bayesian framework [10, 20, 18, 26, 27, 28, 33, 34]. [sent-11, score-0.525]
10 In the Bayesian tracking approach, the goal of the tracking problem is to find the best state, which maximizes the posterior probability p(Xt |Y1:t). [sent-12, score-0.575]
11 To obtain the MAP state, the method searches for the state that maximizes the likelihood p(Yt |Xt), which is near the previous state as a prior. [sent-14, score-0.792]
12 In this case, |thXe likelihood is typically calculated by measuring the similarity between the observation Yt at the state Xt and . [sent-15, score-0.434]
13 (c) How our method efficiently employs infinite number of target models? [sent-137, score-0.282]
14 (a) The likelihood bounds (uncertainty) are formed inevitably in real tracking situations due to different target models that are employed via different updating strategies during the tracking process. [sent-140, score-1.327]
15 (b) A large gap between the upper and lower bounds indicates that the corresponding state gives very different answers (likelihoods) depending on the target models used (red and blue), although the average likelihood obtained by using set of all target models (green) is high. [sent-141, score-1.692]
16 That means the likelihood estimation over that state is uncertain and unreliable. [sent-142, score-0.459]
17 So, our method tries to find the state that has minimum gap (uncertainty), which gives consistent answers (likelihoods), regardless of the target models. [sent-143, score-0.721]
18 And by maximizing the average likelihood bound at the same time, our method gets the state, which confidently maximizes the likelihood. [sent-144, score-0.417]
19 (c) The proposed method only compares two target models with observations while utilizing the infinite number of target models, which generate lower and upper bounds of the likelihood. [sent-145, score-1.032]
20 In this case, the MAP estimation assumes that the best state produces the highest likelihood score near by the previous state. [sent-148, score-0.434]
21 However, in the real-world scenario, this as- sumption is not valid unless the target model Mt is always correct. [sent-149, score-0.276]
22 In practice, the target model is easily corrupted and distorted during the online update. [sent-150, score-0.295]
23 To deal with severe appearance changes, many tracking algorithms evolve the target model with online update. [sent-151, score-0.6]
24 Our method successfully tracks the target using the MUG estimation, whereas the conventional methods fail to track it using the MAP estimation. [sent-177, score-0.398]
25 The MUG estimation finds the true state A of the target because the gap between the likelihood bounds in State A is smaller than that in State B. [sent-178, score-1.294]
26 tracking error, the target model includes more background and becomes erroneous as time goes on. [sent-180, score-0.501]
27 This drift phenomenon frequently occurs even though the methods find the optimal MAP state because of the noisy target model. [sent-182, score-0.528]
28 According to this fundamental inherent problem, the conventional MAP-based tracking approach need to be reconsidered. [sent-183, score-0.282]
29 Thus, in this paper, we redefine the goal oftracking problem as to find the best state that maximizes the average bound of the likelihood and, at the same time, minimizes the gap between bounds of the likelihood. [sent-184, score-1.288]
30 Note that in general tracking problem, the upper and lower bounds or the uncertainties of the likelihoods are naturally formed since many different likelihoods are made by different target models that are the reference appearances of the target. [sent-186, score-1.135]
31 The different target models are usually constructed due to the different updating strategies during the tracking process [23]. [sent-187, score-0.501]
32 Specially when there exist severe occlusions, illumination changes, and so on, the likelihood uncertainty becomes larger, as empirically demonstrated in Fig. [sent-188, score-0.42]
33 This is because the distractors such as occlusions and illumination changes usually make the target models to be much different with each other. [sent-190, score-0.392]
34 Since the different likelihoods can be generated by different target models, obtaining the likelihood bounds is the same as considering all possible target models that could be constructed. [sent-191, score-1.158]
35 Using the likelihood bounds, the proposed method can find the good target state because it implicitly covers all possible appearance changes of the target with all possible target models. [sent-192, score-1.265]
36 1(b), the large gap between the upper and lower bounds indicates that the corresponding state can have either a very good likelihood or a very bad likelihood depending on the employed target model. [sent-194, score-1.634]
37 In this case, the likelihood estimation over the state is easily affected by the noisy target models and the estimated likelihood is uncertain and not reliable. [sent-195, score-0.942]
38 Hence, by minimizing the gap between the two likelihood bounds, the proposed method can find the confident state of the target. [sent-196, score-0.654]
39 MUG is also affected by aforementioned distractors (outliers) in the target model. [sent-197, score-0.308]
40 To measure the confidence of the likelihood, our method estimates the lower and upper bounds of the likelihood, minimizes the gap between the bounds, and accurately tracks the target, as shown in Fig. [sent-202, score-0.888]
41 In tracking methods using multiple target models, the VTS tracker [19] tracked the target successfully with the visual tracker sampler framework. [sent-204, score-0.946]
42 The MIL tracker [2] solved the ambiguity of the target appearance using multiple instances of the target model and robustly tracked the target with the online multiple instance learning algorithm. [sent-205, score-0.965]
43 Compared with these works which utilized a relatively small number of target models, our method implicitly employs all possible target models with the likelihood bounds. [sent-206, score-0.765]
44 In tracking methods with the likelihood bound, the L1BPR tracker [24] proposed an efficient L1 tracker with the Bounded Particle Re-sampling (BPR) technique which considers the upper bound of the likelihood. [sent-207, score-0.808]
45 Our method utilizes the likelihood bounds to measure uncertainty of the likelihood and enhances the accuracy of visual tracking. [sent-209, score-0.959]
46 In sampling based tracking methods, the particle filter [12] handled the non-Gaussianity of the target distribution in the tracking problems. [sent-210, score-0.821]
47 However, our method uses the samples to obtain the state that minimizes the uncertainty of the target distribution, whereas the samples in the other methods are used to obtain the maximum of the target distribution. [sent-214, score-0.956]
48 The second contribution is a rigorous derivation of the lower and upper bounds of the likelihood in the visual tracking problem. [sent-217, score-1.008]
49 Although the bounds of the likelihood are obtained based on [14], applying those bounds into the visual tracking problem directly is not trivial since proper and careful 222333555644 designs of the parameter γ and the distribution q are needed for the visual tracking problem. [sent-218, score-1.476]
50 In this work, γ and q are designed as the hyper parameter of the likelihood and the prior distribution of a target model, respectively. [sent-219, score-0.563]
51 Our method constructs two chains and inferences the best state on the chains using the IMCMC method in [19]. [sent-221, score-0.407]
52 In the first chain, the proposed method finds the state that maximizes the average bound (mean of the lower and upper bounds) of the likelihood. [sent-222, score-0.602]
53 In the second chain, the method searches for the state that minimizes the gap between two likelihood bounds. [sent-223, score-0.798]
54 These chains communicate with each other to obtain the best state that maximizes the average bound and minimizes the gap between bounds at the same time. [sent-224, score-1.162]
55 In (1), our method finds the state that maximizes the average bound [pu (Yt |Xt) + pl (Yt |Xt)] and minimizes the gap between bounds,| X[pu (Yt |Xt) − pl (Yt |Xt)], at the same time. [sent-227, score-0.802]
56 To obtain the MUG state, we need to estimate the lower and upper bounds of the likelihood. [sent-229, score-0.516]
57 As aforementioned, the main cause of the tracking failures is the noisy target models. [sent-239, score-0.501]
58 Therefore, our method integrates out the target model θ in (2) and estimates the log marginal likelihood: ? [sent-240, score-0.282]
59 XTo approximate the integral numerically, we obtain the mathematical lower (Jensen’s inequality) and mathematical upper bounds (Gibbs’ inequality) of the marginal likelihood based on [14]. [sent-243, score-0.765]
60 Θp(θ|Yt,Xt)lnpq((Yθ|tγ,,θX|Xt)t)dθ, (4) where q(θ|γ, Xt) is the prior distribution ofthe target model θw ahnerde γ (isθ t|γhe, hyper parameter of the distribution. [sent-246, score-0.338]
61 Because θ is marginalized out in (3)(4), the lower and upper bounds of the likelihood is the function of Xt and γ, which are a state and a parameter, respectively. [sent-247, score-0.95]
62 Then, the goal of our method is to find both the best state and parameter, which reduce gap between the likelihood bounds. [sent-248, score-0.635]
63 , I{n our method, the parameter is not set empirically but is obtained analytically to maximize the lower bound in (3) and to minimize the upper bound in (4). [sent-250, score-0.39]
64 In addition, it prevents the best state with the minimum uncertainty gap from having a low likelihood score. [sent-256, score-0.791]
65 Our method simultaneously searches states that minimize uncertainty of the likelihood estimation by decreasing the numerator in (1). [sent-257, score-0.445]
66 Then, the method can avoid outliers which have a large uncertainty gap, even though they have high likelihood scores. [sent-258, score-0.371]
67 Learning γu for the Upper Bound We learn the best parameter γu which minimizes the upper bound (4): γu= argmin lnpu(Yt |Xt, γ). [sent-263, score-0.339]
68 imum of the upper bound of the likelihood at the state Xt in (4) is estimated based on [14]: lnpu(Yt|Xt,γu) ≈Z1i=? [sent-312, score-0.644]
69 Learning γl for the Lower Bound We learn the best parameter γl which maximizes the lower bound in (3): γl= argmax lnpl (Yt |Xt, γ). [sent-316, score-0.388]
70 (11) 1 To find the parameter γl = (μl , σl) that satisfies (10), the quasi-optimized lower bound is estimated by Stochastic Approximation Monte Carlo (SAMC) in [22] to define the recursive approximation of the solution of ddγ lnpl (Yt |Xt, γ) = 0. [sent-323, score-0.321]
71 Then, the final estimate of the lower bound at the state Xt in (3) is estimated based on [14]: lnpl(Yt|Xt,γl) ≈Z1i=? [sent-334, score-0.363]
72 The first chain frequently accepts the state that maximizes the average likelihood bound. [sent-339, score-0.666]
73 The second frequently accepts the state that minimizes the gap between the bounds. [sent-340, score-0.578]
74 At the proposal step, a new state is proposed by the proposal density function. [sent-343, score-0.275]
75 Given the proposed state, each chain decides whether the state is accepted or not with the acceptance ratio in the acceptance step: ap1= min? [sent-345, score-0.357]
76 132495)w1h03762i(c84 ) MCIVTFRAGTMILVTSMTTMUG the chain finds the state that maximizes the average bound and minimizes the gap between two bounds simultaneously. [sent-354, score-1.184]
77 The best state in IMCMC is obtained by employing two chains, in which one chain only searches for the state that maximizes the average bound and the other only searches for the state that minimizes the gap between two bounds. [sent-355, score-1.321]
78 As indicated in Table 2, using two chains shows better tracking performance because the tracking methods using a single chain get trapped in local optima more frequently as the target distribution becomes complex. [sent-357, score-0.977]
79 The target distribution is complex because the different two types of the likelihood distribution are mixed in a single distribution. [sent-358, score-0.529]
80 Our method divides a complex distribution into two simple ones using IMCMC, where two distributions describe the average bound and the gap between two bounds, respectively. [sent-359, score-0.327]
81 Our method was robust to the geometric appearance changes of the non-rigid target in diving, high-jump, and skater; the occlusions in bird1, and woman; and the motion blur in bird2. [sent-364, score-0.359]
82 In this paper, we wanted to demonstrate that our method can produce better tracking results by utilizing a very simple likelihood function and its lower and upper bounds. [sent-365, score-0.626]
83 The tracking performance of our method can be further enhanced if more advanced likelihood functions are employed. [sent-367, score-0.468]
84 Additionally, with the simple likelihood function, our method produced more accurate tracking results than other state-of-the-art methods, where they are robust to the pose variations, occlusions, and illumination changes. [sent-368, score-0.494]
85 5, the tracking performance under the severe occlusions and background clutters was tested. [sent-422, score-0.328]
86 When the sequence contained several appearance changes of the target at the same time, our method robustly tracked the target over time, while other tracking methods frequently missed the targets. [sent-423, score-0.917]
87 The tracking results of MIL drifted into the background when the aforementioned changes transformed the target appearance into a different one. [sent-424, score-0.58]
88 Our method overcame this problem and successfully tracked the target by evaluating the target configuration with several likelihoods. [sent-425, score-0.573]
89 6, our method did not miss the target in all frames, although the sequences include the severe geometric appearance changes of the target. [sent-427, score-0.356]
90 On the other hand, MIL and VTS frequently failed to track the target when the target was severely deformed. [sent-428, score-0.584]
91 Our method was more efficient than VTS in terms of the computational cost because it utilized two likelihoods only for evaluating the configuration by estimating the lower and upper bounds of the likelihood. [sent-429, score-0.575]
92 Conclusion In this paper, we propose a novel tracking framework that tracks the target robustly by finding the best state of the target, which minimizes the gap between the lower and upper bounds of the likelihood. [sent-431, score-1.607]
93 Obtaining the likelihood bounds is the same as considering all possible target models during the tracking process. [sent-432, score-1.084]
94 Therefore, our method finds the good state of the target by reflecting pearance changes of the target. [sent-433, score-0.546]
95 all possible ap- The experimental results demonstrate that our method outperforms the conventional tracking methods using the MAP and ML estimation. [sent-434, score-0.282]
96 The method also shows better tracking performances than those of the state-of-the-art tracking methods when there are illumination, occlusions, and deformation. [sent-435, score-0.486]
97 Tracking results with lower and upper bounds of the likelihood obtained by MUG. [sent-668, score-0.741]
98 Yellow and red curves represent lower and upper bounds of the likelihood over time in MUG, respectively. [sent-670, score-0.741]
99 Green curve represents gap between the bounds over time in MUG. [sent-671, score-0.559]
100 MCMC-based particle filtering for tracking a variable number of interacting targets. [sent-703, score-0.321]
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