iccv iccv2013 iccv2013-230 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Aleksandr V. Segal, Ian Reid
Abstract: We propose a novel parametrization of the data association problem for multi-target tracking. In our formulation, the number of targets is implicitly inferred together with the data association, effectively solving data association and model selection as a single inference problem. The novel formulation allows us to interpret data association and tracking as a single Switching Linear Dynamical System (SLDS). We compute an approximate posterior solution to this problem using a dynamic programming/message passing technique. This inference-based approach allows us to incorporate richer probabilistic models into the tracking system. In particular, we incorporate inference over inliers/outliers and track termination times into the system. We evaluate our approach on publicly available datasets and demonstrate results competitive with, and in some cases exceeding the state of the art.
Reference: text
sentIndex sentText sentNum sentScore
1 uk Abstract We propose a novel parametrization of the data association problem for multi-target tracking. [sent-5, score-0.499]
2 In our formulation, the number of targets is implicitly inferred together with the data association, effectively solving data association and model selection as a single inference problem. [sent-6, score-0.521]
3 The novel formulation allows us to interpret data association and tracking as a single Switching Linear Dynamical System (SLDS). [sent-7, score-0.608]
4 This inference-based approach allows us to incorporate richer probabilistic models into the tracking system. [sent-9, score-0.336]
5 In particular, we incorporate inference over inliers/outliers and track termination times into the system. [sent-10, score-0.309]
6 Introduction Multi-target tracking is an important, but stubborn problem in Computer Vision as well as many related fields (notably robotics). [sent-13, score-0.238]
7 The first is the combinatorial space of possible associations between the observations and objects being tracked, and the second is model selection over the number of existing tracks. [sent-17, score-0.189]
8 In this paper we propose Latent Data Association as an alternative parametrization of the data association problem where the number of underlying target tracks is implicit in the data association. [sent-18, score-0.75]
9 We treat the new parametrization as a special case of a Switching Linear Dynamical System (SLDS) [19], and perform approximate inference using a Ian Reid Department of Computer Science, University of Adelaide i . [sent-19, score-0.191]
10 Nodes are numbered within each time slice and colored based on their global track membership. [sent-25, score-0.206]
11 Each node represents a single latent track state together with any observations (if they exist). [sent-26, score-0.634]
12 By treating multi-target tracking as an approximate hybrid inference problem, more complex reasoning about object classification can be incorporated into the same algorithm used for data association and tracking. [sent-28, score-0.67]
13 This is accomplished by adding discrete object category 2904 variables into the tracking model. [sent-30, score-0.385]
14 Using this model allows the classification and tracking problem to be naturally combined into a single system where statistical relationships between target motion (tracking) and target identity (detection and classification) can be exploited. [sent-32, score-0.455]
15 Previous Work Classical approaches to multi-target tracking were pioneered decades ago assuming point-like targets such as radar returns. [sent-34, score-0.372]
16 Most of these were progressive variations and generalizations of single target tracking in a cluttered environment. [sent-35, score-0.329]
17 The Probabilistic Data Association Filter (PDAF) [5] only deals with a single target at a time, but introduced the notion of soft data association based on a weighted mixture of measurements. [sent-36, score-0.461]
18 The Multiple Hypothesis Tracker (MHT) [22] keeps a list of all possible data association hypotheses and the resulting filter outputs for each target. [sent-38, score-0.408]
19 This technique re-frames multi-target tracking as the fusion of an object detector [10, 11, 21] with data association. [sent-40, score-0.297]
20 In contrast to classical methods focusing on radar data with point measurements, TBD literature has focused on tracking objects in video sequences. [sent-41, score-0.335]
21 The tracking question is formulated as linking compatible detections on the grid into consistent trajectories. [sent-44, score-0.349]
22 Berclaz et al [7] form a sparse graph over every hypothetical discrete object locations. [sent-45, score-0.205]
23 it is not easy to combine with a moving sensor platform) and forces a compromise between accuracy and the size of the tracking area. [sent-50, score-0.238]
24 All continuous variables are treated as such and smoothing of the output trajectories is done implicitly via the motion model without any postprocessing. [sent-52, score-0.189]
25 In this case, the set of discrete detections is partitioned into tracks without explicitly enumerating what happens to the target in between successive detections. [sent-54, score-0.439]
26 Jiang et al [14] formulates data association as a Linear Program (LP) over the sparse graph of detections. [sent-55, score-0.453]
27 Monte Carlo based approaches represent the distribution over the state space as a set of discrete samples. [sent-58, score-0.189]
28 In the case of Particle Filters (PF), these samples are manipulated so that their distribution tracks the posterior of the filter. [sent-60, score-0.245]
29 The JPDAF can be implemented as a PF [24, 25] in order to track people from a mobile platform using 2D laser range data. [sent-61, score-0.206]
30 Khan et al [15] use a Markov Chain Monte Carlo (MCMC) based particle filter to incorporate motion priors over target interactions. [sent-62, score-0.345]
31 Breitenstein et al [9] introduce the Detector Confidence Particle Filter (DCPF) to directly incorporate detector scores as a measure of confidence. [sent-63, score-0.183]
32 MCMC can also be used as an independent tracking algorithm by sampling over the joint posterior of the whole problem. [sent-65, score-0.323]
33 Recently, Benfold et al [6] proposed a real-time global MCMC strategy which simply ignores the continuous state variables of the targets and samples directly over groupings of observations. [sent-67, score-0.387]
34 This has the disadvantage of losing the latent/hidden state space of the targets and so requires postprocessing to recover smooth trajectories. [sent-68, score-0.194]
35 Andriyenko et al [3, 4] formulate tracking as a direct optimization problems over splines, and in the latter case discrete track labels. [sent-69, score-0.611]
36 We assume a fixed number of tracks and attempt to simultaneously find the target trajectories and the data association of observations to targets. [sent-78, score-0.775]
37 Depending on =the problem, each} }ob asnedrv tati doenn zti gco tuimld ei. [sent-86, score-0.205]
38 follows the trajectory Xm = The data association problem is classically formulated as finding a correspondence between the targets and observations at each point in time. [sent-96, score-0.569]
39 In this notation, di(t) = j ∈ {1, , M} indicates that the observation zi(t) is associated with the jth target, with the constraint that dDis(tc)r = · · · no two observations can be assigned to the same target. [sent-101, score-0.185]
40 While the classical approach attempts to assign observations to previously existing tracks, Latent Data Association starts by assuming that each detection is its own track (of length 1) with a permanently associated hidden state variable. [sent-119, score-0.473]
41 The problem of tracking then becomes a question of linking these singleton tracks into longer trajectories. [sent-120, score-0.443]
42 We do this by assigning each track at time t as the continuation of some track at t 1. [sent-121, score-0.412]
43 We refer to this form of data association as latteimnte eb tec −au 1s. [sent-124, score-0.37]
44 e W Wthee rdeifsecrr teote t hviasria fobrlmes now ctao natssroolc aiastsiooncia atsio lan-s between adjacent latent state variables. [sent-125, score-0.205]
45 Figure 1 illustrates this parametrization with the tracks being spliced between t = 3 and t = 4. [sent-126, score-0.289]
46 To define this model formally, we define a node as the set of hidden state variables associated with some track at a specific time instance, as well as any observations of this state. [sent-127, score-0.597]
47 For n = (t, i), we define xti as the unobserved state variables of the node and zti as the observations (if present). [sent-130, score-0.898]
48 − The binary indication matrix Li(tj) is used to control the Li(tj) latent data associations at time t; setting = 1 corresponds to linking node (t, i) with node (t 1, j). [sent-131, score-0.45]
49 In order to ensure track continuations are always onet? [sent-134, score-0.206]
50 This parametrization of the problem subsumes standard data association as well as model selection over the number of tracks; any number of tracks and any data association can be represented with a suitable value for L = {L(t)}. [sent-143, score-1.029]
51 By fixing the set of latent data association indicators, we partition the nodes into independent tracks. [sent-144, score-0.534]
52 Each observation zti is generated from the associated target state xti according to an observation model, P(zti |xti). [sent-146, score-0.853]
53 (5) If we assume linear motion and observation models, the model forms an SLDS [19] where the discrete L(t) variables control the relationships between continuous variables in the Markov Chain. [sent-149, score-0.367]
54 This SLDS can be used to implicitly 2906 (a) Classical data association Figure 2. [sent-150, score-0.37]
55 trolled by the data association variables D(t) or latent data association variables L(t) Dashed lines represent dependencies con- respectively. [sent-152, score-0.966]
56 solve the data association problem together with model selection over the number of targets. [sent-153, score-0.37]
57 For a node (t, i), we define prti as the index of the previous node (at t−1) in the same track and nxti as the index ofthe next node t(a−t 1t )+in 1th). [sent-160, score-0.545]
58 The forward and backward messages respectively can then be defined recursively as →μti(xti) =? [sent-162, score-0.189]
59 This quantity can be efficiently retrieved from any node along the track as mti=? [sent-167, score-0.319]
60 X −→μt−1,j· P(zti|xti) · P(xti|xt−1,j) ·←μ −t+1,nxti (12) Note that mtij is the hypothetical value of mti if we had torn the node (t, i) from its current assignment and attached it to node (t 1, j) instead. [sent-174, score-0.48]
61 11 does not affect any of the forward messages before time t or any of the backward messages after time t these only depend on values of for t? [sent-176, score-0.286]
62 We use the messages { −→μt−1 } and } to update L(t) , and subsequently use {the new avnadlue { of L(}t) t oto u compute the forward messages { −→μt}. [sent-181, score-0.244]
63 11 8: add virtual nodes at t 9: for all n = (t, i) do 10: update forward message −μ →ti using Eq. [sent-195, score-0.25]
64 Approximate message passing procedure used for inference in the forward direction. [sent-197, score-0.277]
65 Pedestrian Tracking by Detection with Latent Data Association Up to this point we have described the Latent Data Association parametrization and inference algorithm in general terms. [sent-199, score-0.191]
66 To this end we describe the observation and state space models for both 2D and 3D tracking, as well as extensions to handle false positive detections and track length priors. [sent-201, score-0.452]
67 Since every detection now corresponds to a track, outliers must correspond to outlier tracks, leading to an extra discrete state variable, cti ∈ {pedestrian, outlier}, representing the target class. [sent-204, score-0.461]
68 The pedestrian detectors we use are discriminative, so no generative model exists to explain the observations based on the target class. [sent-207, score-0.307]
69 In practice, a lot of information is contained in the missing detections a track with very few detections is more likely to be an outlier than one with many consistent detections. [sent-229, score-0.436]
70 To incorporate this negative information, we include detector failure into the observation model. [sent-230, score-0.175]
71 The indicator variable mti = 1is used to denote a missing observation at node n = (t, i). [sent-231, score-0.337]
72 In this case n is a virtual node and the zti and sti observation variables are ignored. [sent-232, score-0.563]
73 Because of the detector failure model, we cannot assume a track continues on indefinitely after its last observation doing so would imply a very large number of missing observations and make all tracks likely to be outliers. [sent-235, score-0.645]
74 Instead, we give each target track a fixed probability of terminating at every time instance after its last observation. [sent-236, score-0.336]
75 We introduce the indicator variable eti to mark that the track has ended. [sent-237, score-0.28]
76 If eti = 1, we require that mti = 1; once a track ends, it cannot have any additional observations. [sent-239, score-0.394]
77 9 do not depend on the Markov chain being continuous; analogous equations hold for a discrete chain if the marginalization integrals are replaced with sums. [sent-247, score-0.176]
78 We run discrete message passing over eti and cti and compute the track log-likelihood of the data by adding the log-likelihoods obtained from Eq. [sent-248, score-0.647]
79 11 with the cost of each assignment based on the combined track loglikelihood. [sent-251, score-0.253]
80 Evaluation Experimental validation was performed using four publicly available video sequences comprising over 1200 frames from two standard pedestrian tracking datasets (TUD [1] and PETS’09 [12]). [sent-253, score-0.344]
81 2D tracking was used for the TUD datasets and 3D tracking for the PETS sequence. [sent-254, score-0.476]
82 We ran 2D tracking on TUD-Stadtmitte despite the available camera calibration because the oblique viewing angle makes accurate estimation of ground plane positions difficult. [sent-255, score-0.238]
83 Raw detections, ground truth annotations, and tracking area specifications provided by Andriyenko et al [4] were used for all evaluations. [sent-256, score-0.321]
84 Results are presented in terms of the CLEAR MOT [8] metrics for tracking performance and precision-recall curves for classification accuracy. [sent-257, score-0.238]
85 In the 2D case, the continuous state space is composed of the bounding box center and the log of the dimensions. [sent-261, score-0.191]
86 Both the position, p, and logdimensions, d, have an associated velocity ( p˙ and resulting in an 8D state space: (px , py, dx , dy , p˙ x , p˙ y, d˙x , d˙y). [sent-263, score-0.232]
87 We again use a constant-velocity model for the ground plane position, but assume the dimensions follow a random walk with no velocity (unlike in the 2D tracking case, we expect the 3D dimensions to stay relatively constant). [sent-284, score-0.387]
88 Because our system keeps track of object sizes as well as location, the size of the bounding boxes output by the detector vs the size of the labeled ground truth plays an important role in the performance of the system. [sent-316, score-0.304]
89 In this case we assumed average 3D pedestrian dimensions and projected these into 2D bounding boxes. [sent-329, score-0.196]
90 These curves are possible because of the probabilistic nature of our approach where each output has an associated posterior pedestrian vs outlier probability. [sent-338, score-0.311]
91 While these figures convey the quantitative measures of performance, we encourage the reader to view the supplementary material to observe the qualitative tracking behavior and performance. [sent-339, score-0.238]
92 Conclusions and Future Work This paper has proposed a novel parametrization of the data association problem for multi-target tracking that has a number of very useful properties. [sent-341, score-0.737]
93 The key idea behind our formulation is the proposal to perform latent data association, in which we seek associations between latent state variables over time. [sent-342, score-0.447]
94 (6785VT609PiewI12D46–8)9SM1–87TF4512M–368 1 evaluated by PETS’09 workshop 2 cropped to tracking region of Andriyenko et al [3, 4] 3 our own 2D evaluations using authors’ provided output data 4 results as published by authors Table 1. [sent-362, score-0.404]
95 Sonar tracking of multiple targets using joint probabilistic data association. [sent-431, score-0.384]
96 An mcmc-based particle filter for tracking multiple interacting targets. [sent-443, score-0.333]
97 Coupled object detection and tracking from static cameras and moving vehicles. [sent-451, score-0.238]
98 Markov chain monte carlo [21] [22] [23] [24] [25] data association for general multiple-target tracking problems. [sent-474, score-0.767]
99 Gmcp-tracker: Global multi-object tracking using generalized minimum clique graphs. [sent-492, score-0.238]
100 Monte carlo filtering for multi target tracking and data association. [sent-507, score-0.385]
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