Introduction
Tracking multiple targets in unconstrained environments is extremely challenging. Even after several decades of research, it is still far from reaching the accuracy of human labelling. (cf. MOTChallenge [LealTaixé et al.2015]). The task itself constitutes locating all targets of interest in a video sequence and maintaining their identity over time. One of the obvious questions that arises immediately is how to model the vast variety of data present in arbitrary videos that may include different view points or camera motion, various lighting conditions or levels of occlusion, a varying number of targets, etc. Trackingbydetection has emerged as one of the most successful strategies to tackle this challenge. Here, all “unused” data that is available in a video sequence is discarded and reduced to just a few single measurements per frame, typically by running an object detector. The task is then to associate each measurement to a corresponding target, i.e. to address the problem of data association. Moreover, due to clutter and an unknown number of targets, the option to discard a measurement as a false alarm and a strategy to initiate new targets as well as terminate exiting ones must be addressed.
With the recent rise of deep learning, there has been surprisingly little work related to multitarget tracking. We presume that this is due to several reasons. First, when dealing with a large number of parameters, deep models require huge amounts of training data, which is not yet available in the case of multitarget tracking. Second, both the data and the desired solution can be quite variable. One is faced with both discrete and continuous variables, unknown cardinality for input and output, and variable lengths of video sequences. One interesting exception in this direction is the recent work of Ondrúška and Posner Ondruska:2016:AAAI that introduces deep recurrent neural networks to the task of state estimation. Although this work shows promising results, it only demonstrates its efficacy on simulated data with nearperfect sensor measurements, a known number of targets, and smooth, linear motion. Their followup work introduces realworld measurements and multiclass scenarios [Ondruska et al.2016], however, in both cases, tracking is formulated as estimating the world occupancy, without explicit data association.
With this paper, we make an important step towards endtoend model learning for online tracking of multiple targets in realistic scenarios. Our main contributions are as follows:

Inspired by the wellstudied Bayesian filtering idea, we present a recurrent neural network capable of performing all multitarget tracking tasks including prediction, data association, state update as well as initiation and termination of targets within a unified network structure (Fig. 1). One of the main advantages of this approach is that it is completely modelfree, i.e. it does not require any prior knowledge about target dynamics, clutter distributions, etc. It can therefore capture linear (cf
. Kalman filter), nonlinear (
cf. particle filter), and higherorder dependencies. 
We further show, that a model for the challenging combinatorial problem of data association including birth and death of targets can be learned entirely from data. This timevarying cardinality component demonstrates that it is possible to utilise RNNs not only to predict sequences with fixedsized input and output vectors, but in fact to infer unordered sets with unknown cardinality.

We present a way to generate arbitrary amounts of training data by sampling from a generative model.

Qualitative and quantitative results on simulated and real data show encouraging results, confirming the potential of this approach. We firmly believe that it will inspire other researchers to extend the presented ideas and to further advance the performance.
Related Work
Multiobject tracking.
A multitude of sophisticated models have been developed in the past to capture the complexity of the problem at hand. Early works include the multiple hypothesis tracker (MHT) [Reid1979] and joint probabilistic data association (JPDA) [Fortmann, BarShalom, and Scheffe1980]
. Both were developed in the realm of radar and sonar tracking but were considered too slow for computer vision applications for a long time. With the advances in computational power, they have found their way back and have recently been reintroduced in conjunction with novel appearance models
[Kim et al.2015], or suitable approximation methods [Rezatofighi et al.2015]. Recently, a large amount of work focused on simplified models that could be solved to (near) global optimality [Jiang, Fels, and Little2007, Zhang, Li, and Nevatia2008, Berclaz et al.2011, Butt and Collins2013]. Here, the problem is cast as a linear program and solved via relaxation, shortestpath, or mincost algorithms. Conversely, more complex cost functions have been considered in
[Leibe, Schindler, and Van Gool2007, Milan, Roth, and Schindler2014], but without any theoretical bounds on optimality. The optimization techniques range from quadratic boolean programming, over customised alphaexpansion to greedy constraint propagation. More recently, graph multicut formulations [Tang et al.2016] have also been employed.Deep learning.
Early ideas of biologically inspired learning systems date back many decades [Ivakhnenko and Lapa1966]
. Later, convolutional neural networks (also known as CNNs) and the back propagation algorithm were developed and mainly applied to handwritten digit recognition
[LeCun et al.1998]. However, despite their effectiveness on certain tasks, they could hardly compete with other wellestablished approaches. This was mainly due to their major limitation of requiring huge amounts of training data in order not to overfit the high number of parameters. With faster multiprocessor hardware and with a sudden increase in labelled data, CNNs have become increasingly popular, initiated by a recent breakthrough on the task of image classification [Krizhevsky, Sutskever, and Hinton2012]. CNNs achieve stateoftheart results in many applications [Wang et al.2012, Eigen and Fergus2015] but are restrictive in their output format. Conversely, recurrent neural networks (RNNs) [Goller and Küchler1996] include a loop between the input and the output. This not only enables to simulate a memory effect, but also allows for mapping input sequences to arbitrary output sequences, as long as the sequence alignment and the input and output dimensions are known in advance.Our work is inspired by the recent success of recurrent neural nets (RNNs) and their application to language modeling [Vinyals et al.2015]. However, it is not straightforward to apply the same strategies to the problem of multitarget tracking for numerous reasons. First, the state space is multidimensional. Instead of predicting one character or one word, at each time step the state of all targets should be considered at once. Second, the state consists of both continuous and discrete variables. The former represents the actual location (and possibly further properties such as velocities) of targets, while a discrete representation is required to resolve data association. Further indicator variables may also be used to infer certain target states like the track state, the occlusion level, etc. Third, the desired number of outputs (e.g. targets) varies over time. In this paper, we introduce a method for addressing all these issues and demonstrate how RNNs can be used for endtoend learning of multitarget tracking systems.
Background
Recurrent Neural Networks
Broadly speaking, RNNs work in a sequential manner, where a prediction is made at each time step, given the previous state and possibly an additional input. The core of an RNN is its hidden state of size that acts as the main control mechanism for predicting the output, one step at a time. In general, RNNs may have layers. We will denote as the hidden state at time on layer . can be thought of as the input layer, holding the input vector, while holds the final embedded representation used to produce the desired output . The hidden state for a particular layer and time is computed as where is a matrix of learnable parameters.
The RNN as described above performs well on the task of motion prediction and state update. However, we found that it cannot properly handle the combinatorial task of data association. To that end, we consider the long shortterm memory (LSTM) recurrence
[Hochreiter and Schmidhuber1997]. Next to the hidden state, the LSTM unit also keeps an embedded representation of the state that acts as a memory. A gated mechanism controls how much of the previous state should be “forgotten” or replaced by the new input (see Fig. 2, right, for an illustration). More formally, the hidden representations are computed as
and where represents elementwise multiplication. The input, output and forget gates are all vectors of sizeand model the memory update in a binary fashion using a sigmoid function:
(1) 
with a separate weight matrix for each gate.
Bayesian Filtering
In Bayseian filtering, the goal is to estimate the true state from noisy measurements . Under the Markov assumption, the state distribution at time given all past measurements is estimated recursively as
(2) 
where is the last observation likelihood and
the state transition probability. Typically, Eq. (
2) is evaluated in two steps: a prediction step that evaluates the state dynamics, and an update step that corrects the belief about the state based on the current measurements. Two of the most widely used techniques for solving the above equation are Kalman filter [Kalman1960] and particle filter [Doucet, Godsill, and Andrieu2000]. The former performs exact state estimation under linear and Gaussian assumptions for the state and measurements models, while the latter approximates arbitrary distributions using sequential importance sampling.When dealing with multiple targets, one is faced with two additional challenges. 1) Before the state update can be performed, it is crucial to determine which measurements are associated with which targets. A number of algorithms have been proposed to address this problem of data association including simple greedy techniques, and sophisticated probabilistic approaches like JPDA (see [BarShalom and Fortmann1988]
for an overview). 2) To allow for a timevarying number of targets, it is necessary to provide a mechanism to spawn new targets that enter the scene, and remove existing ones that disappear indefinitely. Like data association, this task is nontrivial, since each unassigned measurement can potentially be either the start of a new trajectory or a false alarm. Conversely, a missing measurement for a certain target could mean that the target has disappeared, or that the detector has failed. To address this challenge, online tracking approaches typically base their decisions about births and deaths of tracks on heuristics that consider the number of consecutive measurement errors.
Our Approach
We will now describe our approach to cast the classical Bayesian state estimation, data association as well as track initiation and termination tasks as a recurrent neural net, allowing for full endtoend learning of the model.
Preliminaries and Notation
We begin by defining as the vector containing the states for all targets at one time instance. In our setting, the targets are represented by their bounding box coordinates , such that . Note that it is conceptually straightforward to extend the state to an arbitrary dimension, e.g. to incorporate velocity, acceleration or appearance model. is the number of interacting targets that are represented (or tracked) simultaneously in one particular frame and refers to the state of the target. is what we call the network’s order and captures the spatial dependencies between targets. Here, we consider a special case with where all targets are assumed to move independently. In other words, the same RNN is used for each target. Similar to the state vector above, is the vector of all measurements in one frame, where is maximum number of detections per frame.
The assignment probability matrix represents for each target (row) the distribution of assigning individual measurements to that target, i.e. and . Note that an extra column in is needed to incorporate the case that a measurement is missing. Finally, is an indicator vector that represents the existence probability of a target and is necessary to deal with an unknown and timevarying number of targets. We will use () to explicitly denote the ground truth variables.
MultiTarget Tracking with RNNs
As motivated above, we decompose the problem at hand into two major blocks: state prediction and update as well as track management on one side, and data association on the other. This strategy has several advantages. First, one can isolate and debug individual components effectively. Second, the framework becomes modular, making it easy to replace each module or to add new ones. Third, it enables one to (pre)train every block separately, which not only significantly speeds up the learning process but turns out to be necessary in practice to enable convergence. We will now describe both building blocks in detail.
Target Motion
Let us first turn to state prediction and update. We rely on a temporal RNN depicted in Fig. 2 (left) to learn the temporal dynamic model of targets as well as an indicator to determine births and deaths of targets (see next section). At time , the RNN outputs four values^{1}^{1}1We omit the RNN’s hidden state at this point in order to reduce notation clutter. for the next time step: A vector of predicted states for all targets, a vector of all updated states, a vector of probabilities indicating for each target how likely it is a real trajectory, and , which is the absolute difference to . This decision is computed based on the current state and existence probabilities as well as the measurements and data association in the following frame. This building block has three primary objectives:

Prediction: Learn a complex dynamic model for predicting target motion in the absence of measurements.

Update: Learn to correct the state distribution, given targettomeasurement assignments.

Birth / death: Learn to identify track initiation and termination based on the state, the measurements and the data association.
The prediction for the next frame depends solely on the current state and the network’s hidden state . Once the data association for the following frame is available, the state is updated according to assignment probabilities. To that end, all measurements and the predicted state are concatenated to form weighted by the assignment probabilities . This is performed for all state dimensions. At the same time, the track existence probability for the following frame is computed.
Loss.
A loss or objective is required by any machine learning algorithm to compute the goodnessoffit of the model,
i.e. how close the prediction corresponds to the true solution. It is typically a continuous function, chosen such that minimising the loss maximises the performance of the given task. In our case, we are therefore interested in a loss that correlates with the tracking performance. This poses at least two challenges. First, measuring the performance of multitarget tracking is far from trivial [Milan, Schindler, and Roth2013]and moreover highly dependent on the particular application. For example, in vehicle assistance systems it is absolutely crucial to maintain the highest precision and recall to avoid accidents and to maintain robustness to false positives. On the other hand, in sports analysis it becomes more important to avoid ID switches between different players. One of the most widely accepted metrics is the multiobject tracking accuracy (MOTA)
[Bernardin and Stiefelhagen2008]that combines the three error types mentioned above and gives a reasonable assessment of the overall performance. Ideally, one would train an algorithm directly on the desired performance measure. This, however, poses a second challenge. The MOTA computation involves a complex algorithm with nondifferentiable zerogradient components, that cannot easily be incorporated into an analytical loss function. Hence, we propose the following loss that satisfies our needs:
(3) 
where , and are the predicted values, and and are the true values, respectively. Note that we omit the time index here for better readability. In practice the loss for one training sample is averaged over all frames in the sequence.
The loss consists of four components. Let us first concentrate on the first two, assuming for now that the number of targets is fixed. Intuitively, we aim to learn a network that predicts trajectories that are close to the ground truth tracks. This should hold for both, predicting the target’s motion in the absence of any measurements, as well as correcting the track in light of new measurements. To that end, we minimise the mean squared error (MSE) between state predictions and state update and the ground truth.
Initiation and Termination
Tracking multiple targets in realworld situations is complicated by the fact that targets can appear and disappear in the area of interest. This aspect must not be ignored but is difficult to model within the fixedsized vector paradigm in traditional neural network architectures. We propose to capture the timevarying number of targets by an additional variable that mimics the probability that a target exists () or not () at one particular time instance. At test time, we then simply discard all targets for which is below a threshold ( in our experiments).
Loss.
The last two terms of the loss in Eq. (3) guide the learning to predict the existence of each target at any given time. This is necessary to allow for target initiation and termination. Here, we employ the widely used binary cross entropy (BCE) loss
(4) 
that approximates the probability of the existence for each target. Note that the true values here correspond to a box function over time (cf. Fig. 3, left). When using the BCE loss alone, the RNN learns to make rather hard decisions, which results in track termination at each frame when a measurement is missing. To remedy this, we propose to add a smoothness prior that essentially minimises the absolute difference between two consecutive values for .
Data Association with LSTMs
Arguably, the data association, i.e
. the task to uniquely classify the corresponding measurement for each target, is the most challenging component of tracking multiple targets. Greedy solutions are efficient, but do not yield good results in general, especially in crowded scenes with clutter and occlusions. Approaches like JPDA are on the other side of the spectrum. They consider
all possible assignment hypotheses jointly, which results in an NPhard combinatorial problem. Hence, in practice, efficient approximations must be used.In this section, we describe an LSTMbased architecture that is able to learn to solve this task entirely from training data. This is somewhat surprising for multiple reasons. First, joint data association is in general a highly complex, discrete combinatorial problem. Second, most solutions in the output space are merely permutations of each other w.r.t. the input features. Finally, any possible assignment should meet the onetoone constraint to prevent the same measurement to be assigned to multiple targets. We believe that the LSTM’s nonlinear transformations and its strong memory component are the main driving force that allows for all these challenges to be learned effectively.
Method  Rcll  Prcn  MT  ML  FP  FN  IDs  FM  MOTA  MOTP 

KalmanHA  28.5  79.0  32  334  3,031  28,520  685  837  19.2  69.9 
KalmanHA2*  28.3  83.4  39  354  2,245  28,626  105  342  22.4  69.4 
JPDA*  30.6  81.7  38  348  2,728  27,707  109  380  23.5  69.0 
RNN_HA  37.8  75.2  50  267  4,984  24,832  518  963  24.0  68.7 
RNN_LSTM  37.1  73.5  50  260  5,327  25,094  572  983  22.3  69.0 
To support this claim, we demonstrate the capability of LSTMbased data association on the example of replicating the linear assignment problem. Our model is illustrated in Figures 1 and 2 (right). The main idea is to exploit the LSTM’s temporal stepbystep functionality to predict the assignment for each target one target at a time. The input at each step , next to the hidden state and the cell state , is the entire feature vector. For our purpose, we use the pairwisedistance matrix , where is the Euclidean distance between the predicted state of target and measurement . Note that it is straightforward to extend the feature vector to incorporate appearance or any other similarity information. The output that we are interested in is then a vector of probabilities
for one target and all available measurements, obtained by applying a softmax layer with normalisation to the predicted values. Here,
denotes the row of .Loss.
To measure the misassignment cost, we employ the common negative loglikelihood loss
(5) 
where is the correct assignment and is the target to measurement assignment probability, as described earlier.
Training Data
It is well known that deep architectures require vast amounts of training data to avoid overfitting the model. Huge labelled datasets like ImageNET
[Russakovsky et al.2014] or Microsoft COCO [Lin et al.2014]have enabled deep learning methods to unfold their potential on tasks like image classification or pixel labelling. Unfortunately, mainly due to the very tedious and timeconsuming task of video annotation, only very limited amount of labelled data for pedestrian tracking is publicly available today. We therefore resort to synthetic generation by sampling from a simple generative trajectory model learned from real data. To that end, we first learn a trajectory model from each training sequence. For simplicity, we only estimate the mean and the variance of two features: the start location
and the average velocity from all annotated trajectories in that sequence. For each training sample we then generate up totracks by sampling from a normal distribution with the learned parameters. Note that this simplistic approach enables easy generation of realistic data, but does not accomodate any observations.
Implementation Details
We implemented our framework in Lua and Torch7. Both our entire code base as well as pretrained models are publicly available.^{2}^{2}2https://bitbucket.org/amilan/rnntracking Finding correct hyperparameters for deep architectures still remains a nontrivial task [Greff et al.2015]. In this section we will point out some of the most important parameters and implementation details. We follow some of the best practices found in the literature [Greff et al.2015, Karpathy, Johnson, and Li2015], such as setting the initial weights for the forget gates higher ( in our case), and also employ a standard grid search to find the best setting for the present task.
Network size.
The RNN for state estimation and track management is trained with one layer and 300 hidden units. The data association is a more complex task, requiring more representation power. To that end, the LSTM module employed to learn the data association consists of two layers and 500 hidden units.
Optimisation.
We use the RMSprop
[Tieleman and Hinton2012] to minimise the loss. The learning rate is set initially to and is decreased by every iterations. We set the maximum number of iterations to , which is enough to reach convergence. The training of both modules takes approximately 30 hours on a CPU. With a more accurate implementation and the use of GPUs we believe that training can be sped up significantly.Data.
The RNN is trained with approximately K frame long sequences. The data is divided into minibatches of samples per batch and normalised to the range , w.r.t. the image dimensions. We experimented with the more popular zeromean and unitvariance data normalisation but found that the fixed one based on the image size yields superior performance.
Experiments
Method  MOTA  MOTP  MT%  ML%  FP  FN  IDs  FM  FPS 

MDP (Xiang et al. 2015)  30.3%  71.3%  13.0  38.4  9,717  32,422  680  1,500  1.1 
SCEA [Hong Yoon et al.2016]  29.1%  71.7%  8.9  47.3  6,060  36,912  604  1,182  6.8 
JPDA* [Rezatofighi et al.2015]  23.8%  68.2%  5.0  58.1  6,373  40,084  365  869  32.6 
TC_ODAL [Bae and Yoon2014]  15.1%  70.5%  3.2  55.8  12,970  38,538  637  1,716  1.7 
RNN_LSTM (ours)  19.0%  71.0%  5.5  45.6  11,578  36,706  1,490  2,081  165.2 
To demonstrate the functionality of our approach, we first perform experiments on simulated data. Fig. 4 shows an example of the tracking results on synthetic data. Here, five targets with random birth and death times are generated in a rather cluttered environment. The initiation / termination indicators are illustrated in the bottom row.
We further test our approach on realworld data, using the MOTChallenge 2015 benchmark [LealTaixé et al.2015]. This pedestrian tracking dataset is a collection of 22 video sequences (11/11 for training and testing, respectively), with a relatively high variation in target motion, camera motion, viewing angle and person density. The evaluation is performed on a server using unpublished ground truth. Next to precision and recall, we show the number of mostly tracked ( recovered) and mostly lost ( recovered) trajectories [Li, Huang, and Nevatia2009], the number of false positive (FP), false negative (FN) targets, identity swaps (IDs) and track fragmentations (FM). MOTA and MOTP are the widely used CLEAR metrics [Bernardin and Stiefelhagen2008] and summarise the tracking accuracy and precision, respectively. Arrows next to each metric indicate weather higher () or lower () values are better.
Baseline comparison.
We first compare the proposed approach to three baselines. The results on the training set are reported in Tab. 1. The first baseline (KalmanHA) employs a combination of a Kalman filter with bipartite matching solved via the Hungarian algorithm. Tracks are initiated at each unassigned measurement and terminated as soon as a measurement is missed. This baseline is the only one that fully fulfils the online state estimation without any heuristics, time delay or postprocessing. The second baseline (KalmanHA2) uses the same tracking and data association approach, but employs a set of heuristics to remove false tracks in an additional postprocessing step. Finally, JPDA is the full joint probabilistic data association approach, recently proposed in [Rezatofighi et al.2015], including postprocessing. We show the results of two variants of our method. One with learned motion model and Hungarian data association, and one in which both components were learned from data using RNNs and LSTMs. Both networks were trained separately. Our learned model performs favourably compared to the purely online solution (KalmanHA) and is even able to keep up with similar approaches but without any heuristics or delayed output. We believe that the results can be improved further by learning a more sophisticated data association technique, such as JPDA, as proposed by Milan et al. Milan:2017:AAAI_NP, or by introducing a slight time delay to increase robustness.
Benchmark results.
Next, we show our results on the benchmark test set in Tab. 2 next to three online methods. The current leaderboard lists over 70 different trackers, with the top ones reaching over MOTA. Even though the evaluation is performed by the benchmark organisers, there are still considerable differences between various submissions, that are worth pointing out. First, all topranked trackers use their own set of detections. While a better detector typically improves the tracking result, the direct comparison of the tracking method becomes rather meaningless. Therefore, we prefer to use the provided detections to guarantee a fair setting. Second, most methods perform socalled offline tracking, i.e. the solution is inferred either using the entire video sequence, or by peeking a few frames into the future, thus returning the tracking solution with a certain time delay. This is in contrast to our method, which aims to strictly compute and fix the solution with each incoming frame, before moving to the next one. Finally, it is important to note that many current methods use target appearance or other image features like optic flow [Choi2015] to improve the data association. Our method does not utilise any visual features and solely relies on geometric locations provided by the detector. We acknowledge the usefulness of such features for pedestrian tracking, but these are often not available in other application, such as e.g. cell or animal tracking. We therefore refrain from including them at this point.
Overall, our approach does not quite reach the top accuracy in pedestrian online tracking [Xiang, Alahi, and Savarese2015], but is two orders of magnitude faster. Fig. 6 shows some example frames from the test set.
Discussion and Future Work
We presented an approach to address the challenging problem of data association and trajectory estimation within a neural network setting. To the best of our knowledge, this is the first approach that employs recurrent neural networks to address online multitarget tracking. We showed that an RNNbased approach can be utilised to learn complex motion models in realistic environments. The second, somewhat surprising finding is that an LSTM network is able to learn onetoone assignment, which is a nontrivial task for such an architecture. We firmly believe that, by incorporating appearance and by learning a more robust association strategy, the results can be improved significantly.
Acknowledgments.
This work was supported by ARC Linkage Project LP130100154, ARC Laureate Fellowship FL130100102 and the ARC Centre of Excellence for Robotic Vision CE140100016.
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