cvpr cvpr2013 cvpr2013-224 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Ahmed T. Kamal, Jay A. Farrell, Amit K. Roy-Chowdhury
Abstract: Due to their high fault-tolerance, ease of installation and scalability to large networks, distributed algorithms have recently gained immense popularity in the sensor networks community, especially in computer vision. Multitarget tracking in a camera network is one of the fundamental problems in this domain. Distributed estimation algorithms work by exchanging information between sensors that are communication neighbors. Since most cameras are directional sensors, it is often the case that neighboring sensors may not be sensing the same target. Such sensors that do not have information about a target are termed as “naive ” with respect to that target. In this paper, we propose consensus-based distributed multi-target tracking algorithms in a camera network that are designed to address this issue of naivety. The estimation errors in tracking and data association, as well as the effect of naivety, are jointly addressed leading to the development of an informationweighted consensus algorithm, which we term as the Multitarget Information Consensus (MTIC) algorithm. The incorporation of the probabilistic data association mecha- nism makes the MTIC algorithm very robust to false measurements/clutter. Experimental analysis is provided to support the theoretical results.
Reference: text
sentIndex sentText sentNum sentScore
1 edu l Abstract Due to their high fault-tolerance, ease of installation and scalability to large networks, distributed algorithms have recently gained immense popularity in the sensor networks community, especially in computer vision. [sent-6, score-0.469]
2 Multitarget tracking in a camera network is one of the fundamental problems in this domain. [sent-7, score-0.311]
3 Distributed estimation algorithms work by exchanging information between sensors that are communication neighbors. [sent-8, score-0.246]
4 Such sensors that do not have information about a target are termed as “naive ” with respect to that target. [sent-10, score-0.264]
5 In this paper, we propose consensus-based distributed multi-target tracking algorithms in a camera network that are designed to address this issue of naivety. [sent-11, score-0.554]
6 The estimation errors in tracking and data association, as well as the effect of naivety, are jointly addressed leading to the development of an informationweighted consensus algorithm, which we term as the Multitarget Information Consensus (MTIC) algorithm. [sent-12, score-0.464]
7 The incorporation of the probabilistic data association mecha- nism makes the MTIC algorithm very robust to false measurements/clutter. [sent-13, score-0.23]
8 Multiple sensors can cover more area, provide views from different angles and the fusion of all their measurements may lead to robust scene understanding. [sent-17, score-0.254]
9 For example, C1 gets direct measurements about T1 which it shares with its immediate network neighbor, C2 . [sent-28, score-0.264]
10 To motivate the core contribution of this work, we first describe the inter- distributed1 relationship between distributed estimation and camera networks. [sent-37, score-0.342]
11 Most of the work in distributed tracking has been in the multi-agent systems community [7]. [sent-38, score-0.366]
12 The methods there assume that each target can be viewed by each sensor which may not be true for many application scenarios, especially for a camera network (see Fig. [sent-39, score-0.466]
13 This limits the 1We use the term distributed to mean that each camera processes its own data and arrives at a final solution through negotiations with its neighbors; there is no central processor. [sent-41, score-0.306]
14 The term distributed has been also used in computer vision to refer to a camera network that is distributed over a wide area but where the processing is centralized. [sent-42, score-0.674]
15 In this paper, our goal is to design a distributed multi-target tracking scheme which is suited for such sensors with limited field-of-view (FOV). [sent-44, score-0.465]
16 A distributed multi-target tracking problem can be divided into three sub-problems, namely, distributed information fusion, data association (measurement to track association) and dynamic state estimation. [sent-45, score-0.98]
17 Among many types of distributed information fusion approaches, consensus algorithms [7] are schemes where each node, corrects its own state using information only from its network neighbors. [sent-46, score-0.885]
18 By iteratively doing so, each node can individually compute a global function of the prior state and measurement infor- mation of all the nodes (e. [sent-47, score-0.479]
19 The important fact is that consensus is reached without all-to-all communication; thus consensus based frameworks do not require any specific communication network topology and are generally applicable to any arbitrary, connected network. [sent-50, score-0.845]
20 The consensus estimates asymptotically converge to the global result. [sent-51, score-0.331]
21 Due to the simplicity and robustness of consensus algorithms, they have been used in many applications, including estimation problems in sensor networks (e. [sent-53, score-0.529]
22 In a distributed multi-target tracking scheme, each node may need to maintain a state estimate of each target even though it is not directly observing the target, since the nodes will need to collaborate with each other. [sent-56, score-0.807]
23 Each node gets measurements of the targets and must associate the measurements to the appropriate target’s track. [sent-57, score-0.449]
24 In a consensusbased scheme, each node maintains its own copy of the state estimates of all the targets which makes consensus-based approaches inherently appropriate for our problem. [sent-58, score-0.367]
25 We call a node ‘naive’ about a target when there are no measurements of that target available in its local neighborhood (consisting of the node and its immediate network neighbors). [sent-62, score-0.816]
26 In such a situation, in a consensus-based framework, due to limited local observability and limited number of consensus iterations, the naive node has access to less information about the target’s state. [sent-63, score-0.56]
27 A well-known consensus-based scheme for distributed state estimation is the Kalman Consensus Filter (KCF) [6]. [sent-64, score-0.393]
28 Moreover, the cross-covariance terms between the state estimates at different nodes were not incorporated in the estimation process in KCF as they are usually hard to compute in a distributed environment. [sent-68, score-0.47]
29 Recently, the Information-weighted Consensus Filter (ICF) [5] was proposed to address the issues with both naivety and optimality for the distributed state estimation problem. [sent-70, score-0.56]
30 For a multi-target tracking problem, the data association and the tracking steps are highly inter-dependent. [sent-72, score-0.476]
31 The performance of tracking will affect the performance of data association and vice-versa. [sent-73, score-0.353]
32 Thus, an integrated distributed tracking and data association solution is required where the uncertainty from the tracker can be incorporated in the data association process and vice-versa. [sent-74, score-0.855]
33 As distributed solutions are usually applied to low-power wireless sensor networks where the computational and communication power is limited, the JPDAF scheme will be utilized in the proposed distributed multi-target tracking framework. [sent-78, score-0.881]
34 The main contribution of this paper is the tight integration of data association with state-of-the-art distributed single target tracking methods, taking special care of the issue of naivety, and demonstration of its performance in the case of a camera network. [sent-79, score-0.797]
35 For example, in [4], a centralized approach for tracking in a multi-camera setup was proposed where the cam- eras were distributed spatially over a large area. [sent-89, score-0.483]
36 However, in this paper, we deal with the distributed multi-target tracking problem where there is no centralized server, the processing is distributed over all the camera nodes and no target hand-off strategy is required. [sent-91, score-0.978]
37 Various methods for distributed multi-target tracking have been proposed in the sensor-networks literature. [sent-92, score-0.366]
38 In [3], a solution to the dis222444000422 tributed data association problem was proposed by means of the message passing algorithm based on graphical models in which iterative, parallel exchange of information among the nodes viewing the same target was required. [sent-93, score-0.446]
39 In [8, 10, 11], the distributed multi-target tracking schemes did not account for naivety or the presence of cross-correlation between the estimates at different nodes. [sent-95, score-0.559]
40 Problem Formulation Consider a sensor network with NC sensors. [sent-100, score-0.265]
41 The set of nodes having direct communication channel with node Ci (sharing an edge with Ci) is represented by Ni. [sent-109, score-0.273]
42 The state of the jth target is represented by the vector xj ∈ Rp. [sent-115, score-0.302]
43 For example, for a tracking application in a camera ∈ne Rtwork, xj might be a vector containing ground plane position and velocity components. [sent-116, score-0.236]
44 The state dynamics of target Tj are modeled as xj(t + 1) = Φxj(t) + γj(t). [sent-117, score-0.252]
45 At time t, e(at)ch is sensor Ci, depending on its FOV and the location of the targets, gets li(t) measurements denoted as {zin}lni=(t1). [sent-119, score-0.251]
46 Under the hypothesis that the observation zin is generated from Tj, it is assumed that zin was generated by the following observation model zin = Hijxij + νij. [sent-121, score-0.264]
47 Each node also maintains a prior/predicted state estimate (and its covariance for each target. [sent-124, score-0.299]
48 Throughout this paper, the inverse of the state covariance matrix (information/precision matrix) will be used and denoted as = We assume that the initial prior state estimate and information matrix is available to each node for each target upon its detection. [sent-125, score-0.615]
49 , , find the state estimate for each target at each node by using the prior and measurement information available in the entire network in a distributed fashion. [sent-128, score-0.961]
50 A critical step in this process is association of measurements with targets, which is the topic of this paper. [sent-129, score-0.341]
51 Average consensus Average consensus [7] is a popular distributed algorithm to compute the arithmetic mean of some values {ai}iN=C1 . [sent-133, score-0.853]
52 InP average consensus algorithm, each node initializes its consPensus state as ai (0) = ai and iteratively communicates with its neighbors and updates its own state information. [sent-138, score-0.771]
53 At the beginning of iteration k, a node Ci sends its previous state ai (k −1) to its immediate network neighbors Ci0 ∈ Ni and also(k kr−ec1ei)v teos t hse im neighbors’ previous istgahtebso ai0 (k ∈− 1 N). [sent-139, score-0.455]
54 i0X∈Ni(ai0(k − 1) − ai(k − 1)) = A(ai (k − 1)) (3) Here A(ai) is a shorthand mathematical operator for a single step aof average consensus (defined as the above). [sent-142, score-0.305]
55 The average consensus algorithm can be used to compute the average of vectors and matrices by applying it to their individual elements separately. [sent-144, score-0.305]
56 Average consensus assumes all agents have an estimate for all elements of a and that all estimates are of equal accuracy and uncorrelated. [sent-149, score-0.331]
57 These distributed estimation frameworks have been applied in various fields including camera networks for distributed implementations of 3-D point triangulation, pose estimation [12], and action recognition [11]. [sent-152, score-0.695]
58 The average consensus algorithm is applicable only for a static parameter estimation problem. [sent-153, score-0.341]
59 Kalman Consensus Filter The Kalman Consensus Filter (KCF) [6] is a popular distributed dynamic state estimation framework. [sent-157, score-0.393]
60 KCF utilizes the average consensus algorithm to average the state estimates over different nodes at each time step. [sent-158, score-0.496]
61 Information Weighted Consensus In [5], the Information-weighted Consensus Filter (ICF) algorithm was proposed, which is a distributed state estimation framework that accounts for the naivety issue and can achieve optimal performance equivalent to a centralized solution. [sent-176, score-0.677]
62 Thus a node which has less information about a target’s state is given less weight in the overall estimation process. [sent-180, score-0.315]
63 Multi-target data association The KCF and the ICF algorithms assume that the data association (which measurement belongs to which target) is known. [sent-183, score-0.599]
64 For a realistic multi-target state estimation problem, solving data association is itself a challenging problem even in the centralized case. [sent-184, score-0.497]
65 Here we briefly review the Joint Probabilistic Data Association Filter (JPDAF) [1] algorithm which is the starting point of the proposed multisensor multi-target distributed tracking algorithm. [sent-185, score-0.399]
66 The JPDAF is a single sensor algorithm, thus the sensor index iis unnecessary and will be dropped. [sent-186, score-0.28]
67 A double superscript zjn is required for the hypothesis that measurement zn is associated with target Tj . [sent-187, score-0.379]
68 The Kalman gain Kj, mean measurement yj and mean measurement innovation y˜j for target Tj are defined as Kj = yj = Pj−HjT(Sj)−1, (12) Xl Xβjnzn, (13) nX= X1 Xl y˜j = Xβjn z˜jn = yj − (1 − βj0)Hj xˆj−. [sent-190, score-0.596]
69 This will then be used in the next section to derive the distributed multi-target tracking algorithm. [sent-204, score-0.366]
70 (18), Jj− xˆj−is the weighted prior information and uj + βj0Uj ˆxj−is the weighted measurement information (taking data association uncertainty βj0 into account). [sent-219, score-0.543]
71 To incorporate measurement information from an additional sensor, the weighted measurement information from that sensor has to be added to this summation. [sent-221, score-0.472]
72 This is a property of estimators in the information form for combining measurements from multiple sensors, when noise in those measurements is uncorrelated with each other, which we assume in this work. [sent-222, score-0.249]
73 Based on the data association results derived in the previous section and the ICF, we will now derive a distributed multitarget tracking algorithm. [sent-231, score-0.63]
74 Now, in a distributed system, each node will have its own prior information { ˆxij−, Jji−}. [sent-233, score-0.445]
75 However, consensus guarantees tihnfaot rtmhea tiinofnor {mˆ xation at }al. [sent-234, score-0.305]
76 Assuming that consensus was reached at the previous time step, the prior information at each node will be equal, i. [sent-237, score-0.507]
77 xˆji− (27) The three averaging terms in (25) and (26) can be computed in a distributed manner using the average consensus algorithm [7]. [sent-248, score-0.548]
78 Note that if a sensor does not get any measurement for Tj, i. [sent-250, score-0.279]
79 Comparison of KCF, ICF and MTIC We now compare the state estimation equations of KCF (38-39), ICF (40-41) and MTIC (42-43) for one particular target and a single consensus iteration step. [sent-255, score-0.593]
80 (40) (41) 222444000755 Algorithm Algorithm 1MTIC for target Tj at node Ci at time step t Input: ˆxij−(t), Jij−(t), Hij, Rij. [sent-281, score-0.276]
81 −1 KjiTJji−(30) 4) Initialize consensus data vij(0) Vij(0) (32) JNji−+ Gij ← (31) JNji−+ Uij ← Wij(0) uij+ JNji−+ βji0Uij! [sent-284, score-0.305]
82 xˆij− ← (33) 5) Perform average consensus (Sec. [sent-285, score-0.305]
83 This handles the issue with naivety as the innovation from a naive neighbor’s prior state will be given less weight. [sent-307, score-0.443]
84 The term ui, in (40) and (42) are not exactly the same, as ICF assumes perfect data association and computes ui from zij . [sent-309, score-0.306]
85 the appropriate measurement in MTIC, ui is computed Another difference between (40) and (42) is the term, A(βi0Ui xˆi− ), which is present in MTIC due to the reason that there is chance with probability βi0 that none of the measurements belong to the target, i. [sent-311, score-0.326]
86 , (41) and (43), are different for ICF and MTIC as the data association uncertainty is incorporated in Gi for MTIC. [sent-317, score-0.259]
87 This shows the tight integration of the data association and tracking steps in MTIC, as the uncertainty of one step is considered in the other. [sent-318, score-0.382]
88 In ICF-NN, the nearest observation zin is associated with a target Tj only if the target is predicted to be in Ci’s FOV. [sent-321, score-0.364]
89 We simulate a camera network with NC = 15 cameras monitoring an area containing NT = 3 targets roaming ran- × domly in a 500 500 area. [sent-325, score-0.277]
90 cAe dcii rncu sluacnht network topology with a degree of 2 (at each node) was chosen for the network connectivity. [sent-327, score-0.25]
91 If the ground truth state was within the FOV of a sensor, a measurement was generated from the ground truth track using the measurement model (2) with Ri = 100I2. [sent-337, score-0.392]
92 Total number of consensus iterations per measurement step, K, was set to 20. [sent-341, score-0.444]
93 False measurements (clutter) were generated at each node at each measurement step using a Poisson process with λ = 312. [sent-343, score-0.388]
94 Here, λ is the average number of false measurements per sensor per measurement step. [sent-344, score-0.39]
95 The average amount of clutter per sensor per measurement step, λ, was varied from 2516 to 8. [sent-357, score-0.351]
96 Thus, although the data association failed, the tracking error did not grow much. [sent-369, score-0.353]
97 Conclusion In this paper, we have proposed the Multi Target Information Consensus (MTIC) algorithm, which is a generalized consensus-based distributed multi-target tracking scheme applicable to a wide-variety of sensor networks. [sent-383, score-0.506]
98 MTIC handles the issues with naivety which makes it applicable to sensor networks where the sensors may have limited FOV (which is the case for a camera network). [sent-384, score-0.517]
99 Distributed data association for multi-target tracking in sensor networks. [sent-469, score-0.493]
100 Tracking and activity recognition through consensus in distributed camera networks. [sent-482, score-0.611]
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