iccv iccv2013 iccv2013-87 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Martin Schiegg, Philipp Hanslovsky, Bernhard X. Kausler, Lars Hufnagel, Fred A. Hamprecht
Abstract: The quality of any tracking-by-assignment hinges on the accuracy of the foregoing target detection / segmentation step. In many kinds of images, errors in this first stage are unavoidable. These errors then propagate to, and corrupt, the tracking result. Our main contribution is the first probabilistic graphical model that can explicitly account for over- and undersegmentation errors even when the number of tracking targets is unknown and when they may divide, as in cell cultures. The tracking model we present implements global consistency constraints for the number of targets comprised by each detection and is solved to global optimality on reasonably large 2D+t and 3D+t datasets. In addition, we empirically demonstrate the effectiveness of a postprocessing that allows to establish target identity even across occlusion / undersegmentation. The usefulness and efficiency of this new tracking method is demonstrated on three different and challenging 2D+t and 3D+t datasets from developmental biology.
Reference: text
sentIndex sentText sentNum sentScore
1 These errors then propagate to, and corrupt, the tracking result. [sent-8, score-0.218]
2 Our main contribution is the first probabilistic graphical model that can explicitly account for over- and undersegmentation errors even when the number of tracking targets is unknown and when they may divide, as in cell cultures. [sent-9, score-0.851]
3 The tracking model we present implements global consistency constraints for the number of targets comprised by each detection and is solved to global optimality on reasonably large 2D+t and 3D+t datasets. [sent-10, score-0.449]
4 The usefulness and efficiency of this new tracking method is demonstrated on three different and challenging 2D+t and 3D+t datasets from developmental biology. [sent-12, score-0.211]
5 Introduction The tracking of multiple dividing targets is a challenging computer vision problem and has useful application e. [sent-14, score-0.351]
6 Due to the occurrence of object divisions at any time, the number of targets for each time step is unknown even if user-specified for a subset of frames. [sent-17, score-0.325]
7 Multi-object tracking in general may be implemented as a two-step pipeline consisting of a detection/segmentation step and a data association or assignment/tracking step [18]. [sent-18, score-0.224]
8 Such approaches, however, are obviously susceptible to errors in the detection step which are propagated to the tracking model and typically cannot be corrected downstream. [sent-19, score-0.341]
9 Therefore, the ultimate goal of data association tracking is European Molecular Biology Laboratory (EMBL) 69117 Heidelberg, Germany hufnage l embl . [sent-20, score-0.3]
10 Right: Excerpt of the proposed factor graph showing the three detection variables for the connected component at time t: Red variables are indicators for a division event. [sent-23, score-0.58]
11 The other variables, taken together, represent the number of targets covered by a detection but they can also represent the other depicted scenarios such as disappearance or “demerging”. [sent-24, score-0.269]
12 to address detection and data association jointly such that both steps can maximally benefit from each other and information can be propagated from more to less obvious parts of 2928 Figure 2: Tiny excerpt of dataset B with its almost indistinguishable objects. [sent-27, score-0.233]
13 Due to low contrast, multiple cells are segmented as only one connected component (undersegmentation) as pointed out in the middle row. [sent-29, score-0.178]
14 Our tracking model (bottom row) can handle such errors and preserves the target identities as indicated by colors (see the three previously merged cells in t = 52) by fitting the correct number of Gaussians (ellipses) to detections containing multiple objects. [sent-30, score-0.669]
15 Furthermore, the proposed factor graph can handle false detections (oversegmentation) as indicated by the black detection in frame 42 (bottom row). [sent-31, score-0.473]
16 There are first approaches addressing joint detection and tracking [16, 17], but none of them has been extended to deal with dividing objects. [sent-33, score-0.366]
17 Given that the tracking of multiple dividing objects already is an NP-hard problem [14] in itself, joint detection and assignment is harder still. [sent-34, score-0.453]
18 As a first step into this direction, we propose a model that handles detection errors explicitly in the tracking step and can even correct most of them. [sent-35, score-0.346]
19 1 and can be categorized into over- and undersegmentation errors occurring due to low contrast or noise in the images. [sent-37, score-0.258]
20 Oversegmentation may result in false detections whereas undersegmentation could lead to the appearance and vanishing of tracks or to accidental track merging. [sent-40, score-0.483]
21 In this context, the divisibility of the objects is particularly challenging since demerging due to previous merging must be distinguished from object division. [sent-41, score-0.214]
22 Note that we will differentiate between object division and object demerging throughout the paper. [sent-42, score-0.288]
23 We present the first method which explicitly models all of the potential segmentation errors outlined above in one probabilistic graphical model. [sent-43, score-0.246]
24 The proposed factor graph models conservation laws for the number of objects contained in each detection to ensure global consistency of the solution. [sent-44, score-0.783]
25 In this way, temporarily merged targets can be resolved under identity preservation even for objects which are merged during longer sequences. [sent-48, score-0.538]
26 We commence with the review of prior art and propose the tracking framework and particularly the construction of the factor graph in Sec. [sent-53, score-0.321]
27 Related Work Existing tracking approaches can broadly be categorized into three: (i) space-time segmentation, (ii) state space models, and (iii) tracking-by-assignment. [sent-59, score-0.166]
28 Tracking-by-assignment gracefully handles multiple, and even dividing objects; on the downside, object properties such as object velocity need to be implemented using factors that are higher order in time. [sent-63, score-0.156]
29 The tracking of undersegmented objects was first described in [11] and soon extended to deal with fragmentation (false positive detections) [2]. [sent-65, score-0.391]
30 Furthermore, the authors in [8] account for both dividing objects and undersegmentation, and exploit local evidence in pairs of frames to find undersegmented objects. [sent-68, score-0.335]
31 The structure of our graphical model also builds on the network flow formulation in [19]. [sent-70, score-0.171]
32 Note, however, that allowing for object division no longer permits to do inference via an ordinary network flow computation as in [19]. [sent-71, score-0.235]
33 Instead, admitting divisions necessarily turns the problem into an integer flow problem with homologous arcs (i. [sent-72, score-0.288]
34 Moreover, the only model which handles the tracking of dividing objects in a global probabilistic framework is the graphical model presented in [5]. [sent-76, score-0.59]
35 While oversegmentation is addressed in terms of false detections, it cannot deal with undersegmentation such as merged objects. [sent-77, score-0.434]
36 Tracking Divisible Objects in spite of Overand Undersegmentation The purpose of this work is to track dividing objects based on an error-prone segmentation. [sent-79, score-0.201]
37 We therefore model data association in a probabilistic graphical model [6] where we explicitly handle over- and undersegmentation errors (cf. [sent-80, score-0.465]
38 ontraugsoitng Figure 3: Factor graph for one detection Xit with two incoming and two outgoing transition candidates: One detection Xit is represented by two multi-state variables, Vit and Ait, to allow for vanishing and appearance, respectively. [sent-84, score-0.421]
39 yH oebrjee, ctthse a brelac akss squares implement conservation laws, i. [sent-95, score-0.254]
40 In this way, each segmented region is assigned the number of objects it contains while conservation laws across subsequent detections guarantee global consistency. [sent-99, score-0.697]
41 Finally, each detection is partitioned into its inferred number of objects by fitting a Gaussian mixture model such that post-hoc linking yields identity preservation for temporarily merged targets. [sent-100, score-0.402]
42 It should be noted that we distinguish between the terms object and detection which denote one target and one connected component, respectively, where a detection may comprise multiple objects. [sent-101, score-0.234]
43 In the following, we describe our tracking workflow in detail for which a schematic overview is depicted in Fig. [sent-102, score-0.252]
44 , m} and a vanishing vari- In particular, each detection pearance able Vit Ait ∈ {0, . [sent-111, score-0.166]
45 they estimate the division probability and a probability mass function of the number of objects contained in each detection. [sent-125, score-0.309]
46 These potentials are then used in the proposed factor graph (cf. [sent-126, score-0.195]
47 3) to find a globally consistent tracking solution (here, tracks are indicated by colors). [sent-128, score-0.201]
48 The appearance and vanishing vari- ables of one detection are connected by ψdet (Ati, Vit , fit) = =⎪⎩⎧⎪ ⎪ ⎪⎨ ⎪− ∞−ln ,? [sent-132, score-0.228]
49 1): Vit = Ait = k indicates that Xit comprises k objects (and Xit is a false detection if k = 0); Vit = 0, Ait > 0 means that the object(s) in Xit is/are appearing in this time step (i. [sent-143, score-0.226]
50 Here, the design parameters wapp and wvan penalize spontaneous appearance and vanishing. [sent-146, score-0.236]
51 In our experiments, we deal with cell tracking and therefore utilize domain specific features for cell division. [sent-153, score-0.58]
52 Division nodes are only added if the respective detection has at least two potential successors in the next time frame and the score from the division detection classifier is above some small threshold. [sent-159, score-0.365]
53 The third category of random variables in the proposed graphical model, the transition variables Titj ∈ {0, . [sent-160, score-0.289]
54 Local evidence for pairs of detections Xit, Xjt+1 is injected by Pˆ(Titj= k | dtij) =⎧⎨e1x −p e? [sent-165, score-0.176]
55 For instance, the conservation law for the outgoing transitions of Xit is ψout(Ati, Titj0 , . [sent-184, score-0.286]
56 (3) Furtherm⎪⎩ore, since sparse objects may lead to isolated (sub-)paths in the graphical model, i. [sent-194, score-0.184]
57 paths where only one transition between two detections is possible, we sub- sume variables in such paths in tracklets and set their unary potential to the sum of the single detections’ unaries plus their transition potentials for each possible configuration. [sent-196, score-0.528]
58 Resolving Merged Objects The inferred result of the described factor graph yields the number of objects covered by one detection Xit and the number of objects Titj transferred between two detections Xit, Xjt+1 in adjacent time steps. [sent-210, score-0.625]
59 Identities of individual objects are amalgamated into a cluster whenever undersegmentation leads to seeming mergers. [sent-211, score-0.293]
60 Given the number ofobjects k contained in detection Xit, we fit a Gaussian mixture model with k normal distributions N(μl , Σl) of unknown weight πl to the connected componNen(tμ with pixels/voxels {x1, . [sent-213, score-0.179]
61 We modify this merger resolving factor graph by setting all Ait = Vit = 1, i. [sent-240, score-0.206]
62 This graphical model is again solved to global optimality and its solution hence preserves identities of objects, even for long sequences of merged objects. [sent-243, score-0.359]
63 Ctrioonss Correlation for Region Center Correc- Most tracking-by-assignment approaches penalize displacements of objects in terms of squared distance between objects of adjacent time frames. [sent-246, score-0.237]
64 The transition prior φtr can then be computed based on the detection centers corrected by those offsets to find the displacement relative to the motion of the object’s neighborhood. [sent-255, score-0.229]
65 Table 1: Cell tracking results on dataset A: precision (= TPT +P FP), recall (= TPT +P FN), andf-measure (= 2·pprerecc. [sent-272, score-0.166]
66 ) for the overall pairwise eve)n,t asn (dmf-omvee,a appearance, disappearance, divisions) and divisions in particular. [sent-276, score-0.254]
67 Experiments and Results Cell tracking is a natural application for the tracking of dividing objects, particularly challenging due to their almost texture-less appearances, which makes them nearly indistinguishable from each other. [sent-284, score-0.481]
68 Especially in dense cell populations, undersegmentation is a common cause for errors. [sent-286, score-0.413]
69 Furthermore, the density of cell populations due to their diverging stages in the developmental process of the embryo are highly diverging. [sent-289, score-0.353]
70 In all experiments, we use random forests [3] each comprising 100 trees grown to purity as classifiers for cell number φdet and cell mitosis, φdiv. [sent-290, score-0.449]
71 ≤ For 3 a fair comparison, we used the same cell number classifier in our method and the competitive model. [sent-292, score-0.207]
72 2 W,3e6 t2a×ke9 9t4he× published segmentation of this dataset and its gold standard to compare with the recently published cell tracking model by Kausler et al. [sent-297, score-0.467]
73 Their segmentation contains no merged objects and thus, we set in our model the maximal number of objects per detection to one, i. [sent-299, score-0.431]
74 In this experiment, we use the cell detection classifier of [5] and set our parameters to α = 25, wapp = 50, wvan = 50, wtr = 13, wdiv = 28, where the latter two parameters weight the transition and division priors versus the detection prior. [sent-302, score-0.972]
75 The f-measure for divisions in [5] is slightly better than ours, namely 0. [sent-310, score-0.254]
76 90, which is due to their model making assumptions about minimal durations between division events (cf. [sent-312, score-0.191]
77 Due to the embryonic development, the cell population is now much denser than in dataset B, resulting in a high number of undersegmented objects (cf. [sent-316, score-0.396]
78 The design parameters in our factor graph for the case of allowing maximally 4 cells in one detection (i. [sent-323, score-0.315]
79 m = 4) are set to α = 5, wapp = 100, wvan = 100, wtr = 24, wdiv = 36. [sent-325, score-0.356]
80 2) show that our method outperforms the cell tracking model in [5]. [sent-330, score-0.373]
81 06 ofthe competitive model, the explicit modeling and distinction of demerging and dividing together with the probabilistic division prior φdiv brings a boost in the detection of mitotic events. [sent-333, score-0.54]
82 Besides, due to the consideration of all detections of all frames in one holistic model and due to the conservation laws posed, our factor graph can accurately (precision of 0. [sent-334, score-0.691]
83 68, our framework can resolve the original – – – – 2933 Table 2: Cell tracking results on datasets B and C: Our model with a different number of objects in one detection allowed (m = 1to m = 4) can best handle the under-/oversegmentation errors occurring in these datasets. [sent-338, score-0.391]
84 Here, merged objects are only counted as true positives if the true number (≥ 2) of objects in the connected component is found. [sent-339, score-0.362]
85 Finally, resolved mergers inntdeidc aastes t,r uheo wpo many so if th thee merged objects ≥ha 2v)e o bfe eonb erecstosl ivned th teo cthoneinre original midpeonntietnites i saf ftoeur demerging. [sent-340, score-0.4]
86 (re*)s oNlvoetde that in Classifiers only, it is only evaluated whether the particular cell is dividing whereas in the tracking models, we go beyond that and additionally require the correct links to the daughter cells. [sent-341, score-0.538]
87 The ground truth of dataset B (dataset C) contains 56,029 (34,985) moves, 216 (440) divisions, 1,878 (1,189) mergers, and 1,466 (533) resolved mergers events. [sent-342, score-0.187]
88 In particular, the associations between the distinct objects after demerging are evaluated as true positives only if they link to the true respective objects before merging – possibly over long sequences of being merged. [sent-348, score-0.333]
89 In our model, we again treat each connected component as one detection and set the parameters (for m = 4) to α = 5, wapp = 100, wvan = 100, wtr = 10, wdiv = 16. [sent-350, score-0.504]
90 76 for divisions and mergers) improves significantly over the results of the rather weak local division and merger classifiers (0. [sent-353, score-0.466]
91 The results of mergers and divisions seem to depend more on the parameter setting, however, the standard deviation is only 0. [sent-361, score-0.381]
92 The results of our model can be further improved by designing even more features for object classification and division detection. [sent-364, score-0.161]
93 This additional local evidence can then be put into global context within the factor graph. [sent-365, score-0.158]
94 It should be noted that the object classification and division detection modules can be fully adopted to the particular application domain. [sent-366, score-0.247]
95 Conclusion We have proposed a probabilistic graphical model which due to the explicit modeling of global conservation laws can robustly correct errors from a previous detection step. [sent-368, score-0.711]
96 We have shown that the proposed factor graph can outperform a recently published cell tracking method on sequences of proliferating cells in a dense populations thanks – – to the consideration of over- and undersegmentation errors. [sent-369, score-0.867]
97 In addition, our model can partition and track previously merged objects while preserving their original identities. [sent-370, score-0.213]
98 Multi-class object tracking algorithm that handles fragmentation and grouping. [sent-389, score-0.244]
99 Coupled minimum-cost flow cell tracking for high-throughput quantitative analysis. [sent-460, score-0.407]
100 Global data association for multi-object tracking using network flows. [sent-507, score-0.264]
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