ContextBased Path Prediction for Targets with Switching Dynamics
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Abstract
Anticipating future situations from streaming sensor data is a key perception challenge for mobile robotics and automated vehicles. We address the problem of predicting the path of objects with multiple dynamic modes. The dynamics of such targets can be described by a Switching Linear Dynamical System (SLDS). However, predictions from this probabilistic model cannot anticipate when a change in dynamic mode will occur. We propose to extract various types of cues with computer vision to provide context on the target’s behavior, and incorporate these in a Dynamic Bayesian Network (DBN). The DBN extends the SLDS by conditioning the mode transition probabilities on additional context states. We describe efficient online inference in this DBN for probabilistic path prediction, accounting for uncertainty in both measurements and target behavior. Our approach is illustrated on two scenarios in the Intelligent Vehicles domain concerning pedestrians and cyclists, socalled Vulnerable Road Users (VRUs). Here, context cues include the static environment of the VRU, its dynamic environment, and its observed actions. Experiments using stereo vision data from a moving vehicle demonstrate that the proposed approach results in more accurate path prediction than SLDS at the relevant short time horizon (1 s). It slightly outperforms a computationally more demanding stateoftheart method.
Keywords
Intelligent vehicles Path prediction Situational awareness Vulnerable road users Intention estimation Dynamic Bayesian Network Probabilistic inference1 Introduction
To improve path prediction of objects with switching dynamics, we propose to exploit context cues that can be extracted from sensor data. Especially vision can provide measurements for a diverse set of relevant cues. But incorporating more observations in the prediction process also increases sensitivity to measurement uncertainty. In fact, uncertainty is an inherent property of any prediction on future events. To deal with uncertainties, we leverage existing probabilistic filters for switching dynamics, which are common for tracking maneuvering targets (BarShalom et al. 2001). Our proposed method therefore extends a Switching Linear Dynamical System (SLDS) with dynamic latent states that represent context. The resulting model is a Dynamic Bayesian Network (DBN) (Murphy 2002), where the latent states control the switching probabilities between the dynamic modes. We can utilize existing theory for approximate posterior inference in DBNs to efficiently compute predictive distributions on the future state of the target.
In this paper, we focus on applications in the Intelligent Vehicle (IV) domain. More specifically, we demonstrate our method on path prediction of pedestrians and cyclists, i.e. the socalled Vulnerable Road Users (VRUs). For automated vehicles, forecasting the future locations of traffic participants is a crucial input to plan safe, comfortable and efficient paths though traffic (Althoff et al. 2009; Paden et al. 2016). However, the current active pedestrian systems are designed conservatively in their warning and control strategy, emphasizing the current pedestrian state (i.e. position) rather than prediction, in order to avoid false system activations. Small deviations in the prediction of, say, 30 cm in the estimated lateral position of VRUs can make all the difference, as this might place them just inside or outside the driving corridor. Better predictions can therefore warn the driver further ahead of time at the same false alarm rate, and more reliably initiate automatic braking and evasive steering (Keller et al. 2011; Köhler et al. 2013).
We evaluate our approach on two scenarios. The first scenario that we target considers a pedestrian intending to laterally cross the street, as observed by a stereo camera onboard an approaching vehicle, see Fig. 1a. Accident analysis shows that this scenario accounts for a majority of all pedestrian fatalities in traffic (Meinecke et al. 2003). We argue that the pedestrian’s decision to stop can be predicted to a large degree from three cues: the existence of an approaching vehicle on collision course, the pedestrian’s awareness thereof, and the spatial layout of the static environment. Likewise, the second scenario considers a cyclist driving on the same lane as the egovehicle, who may turn left at an upcoming crossing in front of the vehicle, see Fig. 1b. This scenario also has three predictive cues, namely the cyclist raising an arm to indicate intent to turn at the crossing, the cyclist’s proximity to the crossing, and the existence of an approaching vehicle.
Our approach is general though, and can be extended with additional motion types (e.g. pedestrian crossing the road in a curved path), or to other application domains, such as robot navigation in humaninhabited environments. Our method also does not prohibit the use of other sensors or computer vision methods than the ones considered here.
2 Related Work
In this section we discuss existing work on state estimation and path prediction, especially for pedestrians and cyclists. We also present different context cues from vision that have been explored to improve behavior prediction.
2.1 Detection and Tracking
Object Detection The classical object detection pipeline first applies a sliding window on the input image to extract image features at candidate regions, and classify each region as containing the target object. In recent years, stateoftheart detection and classification performance is instead achieved by deep ConvNets trained on large datasets. For online applications, ConvNet architectures are now also achieving realtime performance by combining detection and classification in a single forward pass, e.g. Single Shot Multibox Detector (Liu et al. 2016) or YOLO (Redmon et al. 2016).
There are many datasets for pedestrian detection, e.g. those presented in Enzweiler and Gavrila (2009), and Dollár et al. (2012). For an overview on visionbased pedestrian detection, see surveys from Enzweiler and Gavrila (2009), Dollár et al. (2012) and OhnBar and Trivedi (2016). For cyclists, there is the TsinghuaDaimler Cyclist Benchmark from Li et al. (2016). These datasets make it possible to create sophisticated models that require large amounts of training data, for instance for unified pedestrian and cyclist detection (Li et al. 2017), or recovering the 3D pose of vehicles and VRUs (Braun et al. 2016). Indeed, the IV domain is used in many challenging Computer Vision benchmarks, e.g. KITTI (Geiger et al. 2012; Menze and Geiger 2015) and ADE20K (Zhou et al. 2017), hence we expect VRU detection to improve even further in the near future.
State Estimation In the IV domain, state estimation is typically done in a 3D world coordinate system, where also information from other sensors (e.g. lidar, radar) is fused. Image detections can be projected to this world coordinates through depth estimation from monocular or stereocamera setup (Hirschmüller 2008).
The perframe spatial position of detections can then be incorporated in a tracking framework where the measurements are assigned to tracks, and temporally filtered. Filtering provides estimates and uncertainty bounds on the objects’ true position and dynamical states. State estimation often models the state and measurements as a Linear Dynamical System (LDS), which assumes that the model is linear and that noise is Gaussian. In this case, the Kalman filter (KF) (Blackman and Popoli 1999) is an optimal filtering algorithm. In the intelligent vehicle domain, the KF is the most popular choice for pedestrian tracking (see Schneider and Gavrila 2013 for an overview). The Extended and Unscented KF (Meuter et al. 2008) can, to a certain degree, account for nonlinear dynamical or measurement models, but multiple motion models are needed for maneuvering targets that alternate various dynamics.
The SLDS is a type of DBN which can model multiple possible dynamics. It extends the LDS with a toplevel discrete Markov chain. At each time step, the state of this chain determines which of the various possible motion dynamics is applied to the underlying LDS, allowing to ‘switch’ the dynamics through discrete state transitions. Unfortunately, exact inference and learning in an SLDS becomes intractable, as the number of modes in the posterior distribution grows exponential over time in the number of the switching states (Pavlovic et al. 2000). There is however a large body of literature on approximate inference in such DBNs. One solution is to approximate the posterior by samples using some Markov Chain Monte Carlo method (Oh et al. 2008; Rosti and Gales 2004; Kooij et al. 2016). However, sampling is impractical for online realtime inference as convergence can be slow. Instead, Assumed Density Filtering (ADF) (Bishop 2006; Minka 2001) approximates the posterior at every time step with a simpler distribution. It has generally been applied to mixed discretecontinuous state spaces with conditional Gaussian posterior (Lauritzen 1992), and to discrete state DBNs, where it is also known as BoyenKoller inference (Boyen and Koller 1998). ADF will be further discussed in Sect. 3.2.
The Interacting Multiple Model (IMM) KF (Blackman and Popoli 1999) is another popular algorithm to track a maneuvering target, mixes the states of several KF filters running in parallel. It has been applied for path prediction in the intelligent vehicle domain for pedestrian (Keller and Gavrila 2014; Schneider and Gavrila 2013), and cyclists (Cho et al. 2011) tracking. IMM can be seen as doing an alternative form of approximate inference in a SLDS (Murphy 2002).
2.2 Context Cues for VRU Behaviors
Even though SLDSs can account for changes in dynamics, a switch in dynamics will only be acknowledged after sufficient observations contradict the currently active dynamic model. If we wish to anticipate instead of reacting to changes in dynamics, a model should include possible causes for change.
Various papers provide naturalistic studies on pedestrians behavior, e.g. during encounters at unsignalized crossing (Chen et al. 2017), to predict when a pedestrian will cross (Völz et al. 2016), or to categorizing danger in vehiclepedestrian encounters (Otsuka et al. 2017). Similar studies are also being performed for cyclists. Zernetsch et al. (2016) collected data at a single intersection for path prediction of a starting cyclists, and Hubert et al. (2017) used the same data to find indicators of cyclist starting behavior. Some studies have used naturalistic data to detect and classify critical vehiclecyclist interactions at intersections (Sayed et al. 2013; Vanparijs et al. 2015; Cara and de Gelder 2015), while others use simulations to study bicycle motion at intersections (Huang et al. 2017; Zhang et al. 2017).
For online prediction of VRU behavior, cues must be extracted from sensor data. Especially computer vision provides many types of context cues, as the following subsections will discuss. From the extract features, behavior predicting can then be treated as a classification problem (Bonnin et al. 2014; Köhler et al. 2013). However, probabilistic methods integrate the inherent detection uncertainty directly into path prediction (Schulz and Stiefelhagen 2015a, b; Keller and Gavrila 2014; Kooij et al. 2014a).
Static Environment Cues The relation between spatial regions of an environment and typical behavior has been extensively researched in visual surveillance, where the viewpoint is static. For instance, different motion dynamics may frequently occur at specific space coordinates (Morris and Trivedi 2011; Kooij et al. 2016; Robicquet et al. 2016; Yi et al. 2016; Jacobs et al. 2017). Another approach is to interpret the environment, e.g. detect semantic regions and learn how these affect agent behavior (Kitani et al. 2012; Rehder and Kloeden 2015). Such semantics enable knowledge transfer to new scenes too (Ballan et al. 2016). In surveillance, agent models are also used to reason about intent (Bandyopadhyay et al. 2013), i.e. where the pedestrian intends to go.
In the IV domain, behavior is typically tied to road infrastructure (Oniga et al. 2008; Geiger et al. 2014; Kooij et al. 2014b; Sattarov et al. 2014; Pool et al. 2017). Road layout can be obtained from localization using GPS and INS sensors (Schreiber et al. 2013) to retrieve information map data on the surrounding infrastructure. SLAM techniques provide another means for accurate selflocalization in a world coordinate frame, and are also used in automotive research (Geiger et al. 2012; MurArtal and Tardós 2017). Another approach is to infer local road layout directly from sensor data (Geiger et al. 2014; Yi et al. 2017). Here, too, semantic scene segmentation with ConvNets can be used to identify static and dynamic objects, and drivable road [c.f. Cityscapes benchmark (Cordts et al. 2016)].
Dynamic Environment Cues VRU behavior may also be influenced by other dynamic objects in their surrounding. For instance, social force models (Antonini et al. 2006; Helbing and Molnár 1995; Huang et al. 2017) expect agents to avoid collisions with other agents. Tamura et al. (2012) extended social force towards group behavior by introducing subgoals such as “following a person”. The related Linear Trajectory Avoidance model (Pellegrini et al. 2009) for shortterm path prediction uses the expected point of closest approach to foreshadow and avoid possible collisions.
Neural nets can also learn how multiple agents move in each others presence (Alahi et al. 2016; Yi et al. 2016), even from a vehicle perspective (Karasev et al. 2016; Lee et al. 2017). In the IV domain, interaction of road users with the egovehicle is especially important. An often used indicator is the TimeToCollision (TTC) which is the time that remains until a collision between two objects occurs if their course and speeds are maintained (Sayed et al. 2013). A related indicator is the minimum future distance between two agents, which like TTC assumes both travel with fixed velocity (Pellegrini et al. 2009; Cara and de Gelder 2015).
Beyond accounting for the presence of other road users, traffic participants also negotiate right of way to coordinate their actions. Rasouli et al. (2017) presents a study of such interactions between drivers and pedestrians.
Object Cues People may not always be fully aware of their surroundings, and inattentive pedestrians are an important safety case in the IV context. A study on pedestrian behavior prediction by Schmidt and Färber (2009) found that human drivers look for body cues, such as head movement and motion dynamics, though exactly determining the pedestrian’s gaze is not necessary. Hamaoka et al. (2013) presents a study on head turning behaviors at pedestrian crosswalks regarding the best point of warning for inattentive pedestrians. They use gyro sensors to record head turning and let pedestrians press a button when they recognize an approaching vehicle. Continuous head estimation can be obtained by interpolating the results of multiple discrete orientation classifiers, adding physical constraints and temporal filtering to improve robustness (Enzweiler and Gavrila 2010; Flohr et al. 2015). Benfold and Reid (2009) uses a Histogram of Oriented Gradients (HOG) based head detector to determine pedestrian attention for automated surveillance. Ba and Odobez (2011) combines context cues in a DBN to model the influence of group interaction on focus of attention. Recent work uses ConvNets for realtime 2D estimation of the full body skeleton (Cao et al. 2017).
The full body appearance can also be informative for path prediction, e.g. to classify the object and predict a classspecific path (Klostermann et al. 2016), or to identify predictive poses. Köhler et al. (2013) rely on infrastructurebased sensors to classify whether a pedestrian standing at the curbside will start to walk. Keller and Gavrila (2014) estimates whether a crossing pedestrian will stop at the curbside using dense optical flow features in the pedestrian bounding box. They propose two nonlinear, higher order Markov models, one using Gaussian Process Dynamical Models (GPDM), and one using Probabilistic Hierarchical Trajectory Matching (PHTM). Both approaches are shown to perform similar, and outperform the firstorder Markov LDS and SLDS models, albeit at a large computational cost.
3 Proposed Approach
We are interested in predicting the path of an object with switching motion dynamics. We consider that nonmaneuvering movement (i.e. where the type of motion is not changing) is well captured by a LDS with a basic motion model [e.g. constant position, constant velocity, constant turn rate (Blackman and Popoli 1999)]. An SLDS combines multiple of such motion models into a single model, using an additional switching state to indicate which of the basic motion model is in use at any moment. These probabilistic models can express the state probability given all past position measurements (i.e. online filtering), or given all past and future measurements (i.e. offline smoothing). Similarly, it is also possible to infer future state probability given only the current past measurements (i.e. prediction). Details on inference will be presented in Sect. 3.2.
While the SLDS can provide good predictions overall, we shall demonstrate that this unfortunately comes at the cost of bad predictions when a switch in dynamics occurs between the current time step and the predicted time step. To tackle the shortcomings of the SLDS, we propose an online filtering and prediction method that exploits context information on factors that may influence the target’s motion dynamics. More specifically, for VRU path prediction we consider three types of context, namely interaction with the dynamic environment, the relation of the VRU to the static environment, and the VRU’s observed behavior.
 1.
We present a generic approach to exploit context cues to improve predictions with a SLDS. The cues are represented as discrete latent nodes in a DBN that extends the SLDS. These nodes influence the switching probabilities between dynamic modes of the SLDS. An algorithm for approximate online inference and path prediction is provided.
 2.
We apply our approach to VRU path prediction. Various context cues are extracted with computer vision. The context includes the dynamic environment, the static environment, and the target’s behavior. The proposed approach goes beyond existing work in this domain that has considered no or limited context. We show the influence of different types of context cues on path prediction, and the importance of combining them.
 3.
Our work targets online applications in realworld environments. We use stereo vision data collected from a moving vehicle, and compare computational performance to a stateoftheart method in the IV domain.
3.1 Contextual Extension of SLDS
Given noisy positional measurements \(Y_t\) of a moving target, the target’s true dynamics can be modeled as a Linear Dynamical System (LDS) with a latent continuous state \(X_t\). The process defines the next state as a linear transformation A of the previous state, with process noise \(\epsilon _t \sim {\mathcal {N}}(0,Q)\) added through linear transformation \(B\). Observation \(Y_t\) results from a linear transformation C of the true state \(X_t\) with also Gaussian noise \(\eta _t \sim {\mathcal {N}}(0,R)\) added, referred to as the measurement noise.
As an example, consider predicting the future position of a moving target which exhibits two types of motion, namely, moving in positive x direction (type A), and moving in positive x and y direction (type B). The target performs motion type A for 10 time steps, and then type B for another 10 time steps. The target’s motion dynamics are known, and a LDS is selected to filter and predict its future position for three steps ahead. An LDS with a \(1\text {st}\)order state space only includes position in its state, \(X_t = [x_t]\). The target velocity is assumed to be fixed. Each time step, this LDS adds the fixed velocity and random Gaussian noise to the position. For the considered target, the optimal fixed velocity of the LDS is an average of the two possible motion directions. Figure 2 illustrates this example, and shows predictions made using this LDS in blue. The LDS provides poor predictive distribution which do not adapt to the target motion.
An LDS with a \(2\text {nd}\)order state space also includes the velocity in the state, \(X_t = [x_t, \dot{x}_t]^\top \). Through process noise on the velocity, this LDS can account for changes in the target direction. However, its spatial uncertainty grows rapidly when predicting ahead as the velocity uncertainty increases without bounds. The figure shows its predictions in purple.
We make a simple observation to tackle the poor SLDS performance during a switch. Consider having information that the target approaches a region with higher probability of switching than usual, i.e. spatial context. Outside this region the SLDS behaves as before. But inside, the switching probability is set to 1 / 2, which makes every dynamic mode equally likely in the future such. The SLDS then behaves as the original \(1\text {st}\)order LDS. By selectively adapting the transition probabilities based on the spatial context, this model can ideally take best of both worlds, as the yellow loglikelihood plot in Fig. 2 confirms.
We also introduce a set of measurements \(E_t\), which provide evidence for the latent context variables through conditional probability \(P(E_t  Z_t)\). The bottom plot in Fig. 2 demonstrates this likelihood for the example. Even though the context \(Z_t\) is discrete, during inference the uncertainty propagates from the observables to these variables, resulting in posterior distributions that assign realvalued probabilities to the possible contextual configurations.
Like the SLDS, this extended model is also a DBN. Figure 3 shows all variables as nodes in a graphical representation of the DBN. The arrows indicate that child nodes are conditionally dependent on their parents. The dashed arrows show conditional dependency on the nodes in the previous time step.
3.2 Online Inference
The DBN is used in a forward filtering procedure to incorporate all available observations of new time instances directly when they are received. We have a mixed discretecontinuous DBN where the exact posterior includes a mixture of \(M^T\) Gaussian modes after T time steps, hence exact online inference is intractable (Pavlovic et al. 2000). We therefore resort to Assumed Density Filtering (ADF) (Bishop 2006; Minka 2001) as an approximate inference technique. The filtering procedure consists of executing the three steps for each time instance: predict, update, and collapse. These steps will also be used for predicting the target’s future path for a given prediction horizon, as described later in Sect. 3.4.
3.2.1 Predict
To predict time t we use the posterior distribution of \(t1\), which is factorized into the joint distribution over the latent discrete nodes \(\widetilde{P}_{t1} (M_{t1}, Z_{t1})\), and into the conditional distribution and the dynamical state, \(\widetilde{P}_{t1}(X_{t1}  M_{t1}) = {\mathcal {N}}(X_{t1}  \widetilde{\mu }_{t1}^{(M_{t1})}, \widetilde{\varSigma }_{t1}^{(M_{t1})})\).
3.2.2 Update
In case there is no observation for a given time step, there is no difference between the predicted and updated probabilities, which means both Eqs. 11 and 12 simplify to \(\widehat{P}_{t}(\cdot ) = \overline{P}_{t}(\cdot )\).
3.2.3 Collapse
3.3 Context for VRU Motion

Dynamic environment context: the presence of other traffic participants can deter the VRU to move too closely. In our experiments we only consider the presence of the egovehicle. Context indicator \(Z^\text {DYN}_t\) thus refers to a possible collision course, and therefore if the situation is potentially critical.

Static environment context: the location of the VRU in the scene relative to the main infrastructure. \(Z^\text {STAT}_t\) is true iff the VRU is at the location where change typically occurs.

Object context: \(Z^\text {ACT}_t\) indicates if the VRU’s current actions provide insight in the VRU’s intention (e.g. signaling direction), or awareness (e.g. line of gaze). The related context \(Z^\text {ACTED}_t\) captures whether the VRU performed the relevant actions in the past.
3.4 VRU Path Prediction
However, the static environment context \(Z^\text {STAT}\) exploits the relation between VRU’s position and the static environment. Since the expected position is readily available during path prediction, we can estimate the future influence of the static environment on the predicted continuous state of the VRU. For instance, while predicting a walking pedestrian’s path, we can also predict the decreasing distance of the pedestrian to the static curbside.
4 VRU Scenarios
The previous section explained the general approach of using a DBN to incorporate context cues, infer current and future use of dynamics, and ultimately perform future path prediction. This section now specifies the dynamics and context used for the two VRU scenarios of interest.
4.1 Crossing Pedestrian
The first scenario concerns the pedestrian wanting to cross the road, and approaching the curb from the right, as illustrated in Fig. 1a.
Since the latent \(\dot{x}^{m_{w}}\) is constant over the duration of a single track, \(\dot{x}^{m_{w}}_t = \dot{x}^{m_{w}}_{t1}\). Still, it varies between pedestrians. We include the velocity \(\dot{x}^{m_{w}}\) in the state of an SLDS together with the position \(x_t\) such that we can filter both. The prior on \(\dot{x}^{m_{w}}_0\) represent walking speed variations between pedestrians. By filtering, the posterior on \(\dot{x}^{m_{w}}_t\) converges to the preferred walking speed of the current track.
Context Following the study on driver perception (Schmidt and Färber 2009), the context cues in the pedestrian scenario are collision risk, pedestrian head orientation, and where the pedestrian is relative to the curb. The context observations \(E_t\) for this scenario are illustrated in Fig. 6. The related Fig. 7 shows the empirical distributions of the context observations estimated on annotated training data from a pedestrian dataset. The dataset will be discussed in more detail in Sect. 5.1.
4.2 Cyclist Approaching Intersection
The second scenario concerns the egovehicle driving behind a cyclist, and approaching an intersection. As illustrated in Fig. 1b, the cyclist may or may not turn left at the intersection, but can indicate intent to turn by raising an arm in advance. In our training data, the cyclist always does this when turning in a critical situation where the egovehicle is quickly approaching. But in noncritical situations, cyclists may turn even without raising an arm. The context observables of this scenario are illustrated in Figs. 8, and 9 shows the empirical distributions of the observables on the cyclist dataset that will be presented later in Sect. 5.2.
5 Datasets and Feature Extraction
The experiments in this paper used two stereocamera datasets of VRU encounters recorded from a moving vehicle, one for the crossing pedestrian and one for the cyclist at intersection scenario. Due to the focus on potentially critical situations, both driver and pedestrian/cyclist were instructed during recording sessions. A sufficient safety distance between vehicle and VRU was applied in all scenarios recorded. In the following sections, ‘critical situation’ thus refers to a theoretic outcome where both the approaching vehicle and pedestrian would not stop.
5.1 Pedestrian Dataset
For pedestrian path prediction, we use a dataset (c.f. Kooij et al. 2014a) consisting of 58 sequences recorded using a stereo camera mounted behind the windshield of a vehicle (baseline 22 cm, 16 fps, \(1176 \times 640\) 12bit color images). All sequences involve single pedestrians with the intention to cross the street, but feature different interactions (Critical vs. Noncritical), pedestrian situational awareness (Vehicle seen vs. Vehicle not seen) and pedestrian behavior (Stopping at the curbside vs. Crossing). The dataset contains four different male pedestrians and eight different locations. Each sequence lasts several seconds (min / max / mean: 2.5 s / 13.3 s / 7.2 s), and pedestrians are generally unoccluded, though brief occlusions by poles or trees occur in three sequences.
Positional ground truth (GT) is obtained by manual labeling of the pedestrian bounding boxes and computing the median disparity over the upper pedestrian body area using dense stereo (Hirschmüller 2008). These positions are then corrected for vehicle egomotion provided by GPS and IMU, and projected to world coordinates. From this correction we obtain the pedestrian’s GT lateral position, and use the temporal difference as the GT lateral speed.
The GT for context observations is obtained by labeling the head orientation of each pedestrian. The 16 labeled discrete orientation classes were reduced to 8 GT orientation bins by merging three neighbored orientation classes (c.f. Flohr et al. 2015) together.
Breakdown of the number of tracks in the pedestrian dataset (c.f. Kooij et al. 2014a) for the four normal subscenarios (above the line), and in the anomalous one (below the line)
Pedestrian scenario (58 tracks)  

Subscenario  Occurences  
Noncritical  Vehicle not seen  Crossing  9 
Noncritical  Vehicle seen  Crossing  14 
Critical  Vehicle not seen  Crossing  11 
Critical  Vehicle seen  Stopping  14 
Critical  Vehicle seen  Crossing  10 
Breakdown of the number of tracks in the cyclist dataset for the normal (above the line) and anomalous (below the line) subscenarios
Cyclist scenario (42 tracks)  

Subscenario  Occurrences  
Noncritical  Arm not raised  Straight/Turn  6/6 
Noncritical  Arm raised  Turn  6 
Critical  Arm not raised  Straight  10 
Critical  Arm raised  Turn  7 
Critical  Arm not raised  Turn  7 
5.2 Cyclist Dataset
A new dataset was collected for the cyclist scenario, in a similar fashion to the pedestrian dataset. This new dataset contains 42 sequences with another stereo camera setup in the vehicle (baseline 21 cm, 16 fps, \(2048\times 1024\) 12bit color images). The cyclist and vehicle are driving on the same road, such that the cyclist is observed from the back, and they approach an intersection with an opportunity for the cyclist to turn left.
The cyclist GT positions are obtained similarly to the pedestrian scenario from stereo vision. To obtain information about the road layout further ahead, intelligent vehicles can rely on map information and selflocalization. Since the cyclist scenario was collected in a confined road area, we use Stereo ORBSLAM2 (MurArtal and Tardós 2017) on all collected stereo video to build a 3D map of the environment for our experiments. This results in a fixed world coordinate system shared by all tracks. The spatial layout of the crossing (road width and intersection point) is expressed in these world coordinates, and the detected cyclist positions can be projected to this global coordinate system too. In a preprocessing step GT cyclist tracks are smoothed to compensate for the estimation noise for stereo vision, which especially affects the longitudinal position. The aligned road layout and cyclist tracks are shown in Fig. 8c.
This dataset is also divided into several subscenarios, with the number of recordings for each subscenario listed in Table 2. We consider that initially the cyclist intent is unknown, i.e. whether he will turn or go straight at the intersection. By raising an arm, he can give a visual indication of the intent to turn left. However, the cyclist might not always properly raise an arm in noncritical situations. Therefore, in noncritical situations without raising an arm, our data contains an equal number of tracks with turning and going straight. In summary, the normal subscenarios reflect situations where the cyclist must indicate intent in critical situations with the approaching egovehicle, but could neglect to do this in noncritical cases. The additional anomalous subscenario contains a turning cyclist in a critical situation, without having raised an arm.
5.3 Feature Extraction
Both cyclist and pedestrian are detected by using neural networks with local receptive fields (Wöhler and Anlauf 1999), given regionofinterests supplied by an obstacle detection component using dense stereo data. The resulting bounding boxes are used to calculate a median disparity over the upper pedestrian body area. The vehicle egomotion compensated position in world coordinates is then used as positional observation \(Y_t\).
For an estimation of the pedestrian head orientation \(\textit{HO}_t\), the method described in Flohr et al. (2015) is used. The angular domain of \([0^\circ , 360^\circ )\) is split into eight discrete orientation classes of \(0^\circ , 45^\circ , \cdots , 315^\circ \). We trained a detector for each class, i.e. \(f_{0}, \cdots , f_{315}\), using again neural networks with local receptive fields. The detector response \(f_{o}(I_t)\) is the strength for the evidence that the observed image region \(I_t\) contains the head in orientation class o. We used a separate training set with 9300 manually contour labeled head samples from 6389 grayvalue images with a min./max./mean pedestrian height of 69/344/122 pixels (c.f. Flohr et al. 2015). For additional training data, head samples were mirrored and shifted, and 22109 nonhead samples were generated in areas around heads and from false positive pedestrian detections. For detection, we generate candidate head regions in the upper pedestrian detection bounding box from disparity based image segmentation. The most likely head image region \(I^\star \) is selected from all candidates based on disparity information and detector responses. Before classification, head image patches are rescaled to \(16\times 16\,px\). The head observation \(\textit{HO}_t = [f_{0}(I^\star _t), \cdots , f_{315}(I^\star _t)]\) contains the orientation confidences of the selected region.
The expected minimum distance \(D^{min}\) between pedestrian and vehicle is calculated as in Pellegrini et al. (2009) for each time step based on current position and velocity. Vehicle speed is provided by onboard sensors, for pedestrians the first order derivative is used and averaged over the last 10 frames. For \(\textit{DTC}\), the curbside is detected with a basic Hough transform (Duda and Hart 1972). Though other approaches are available, e.g. stereo (Oniga et al. 2008) or scene segmentation (Cordts et al. 2016), this simple approach was already sufficient for our experiments. The image region of interest is determined by the specified accuracy of the vehicle localization using typical onboard sensors (GPS+INS) and map data (Schreiber et al. 2013). \(Y^{\text {curb}}_t\) is then the mean lateral position of the detected line backprojected to world coordinates.
To determine whether the cyclist raises an arm (\(\textit{AD}_{t}=1\)), or not (\(\textit{AD}_{t}=0\)), we apply the chamfer matching approach from Gavrila and Giebel (2002). First, a binary foreground segmentation of the cyclist is generated from the disparity values in the tracked cyclist bounding box r. The foreground consists of all pixels with a disparity in the range of \([{\tilde{d}}_r\epsilon , {\tilde{d}}_r+\epsilon ]\). Here \(\tilde{d_r}\) is the median disparity value in region r. We set \(\epsilon _D=1.5\) to account for disparity errors. The binary segmentation is then matched against multiple rectangular contour templates near the expected shoulder location in the bounding box. These arm templates vary in length, width and angle. The arm detector \(\textit{AD}_t\) is the output of a Naive Bayesian Classifier which integrates several likelihood terms over all templates: a Gamma distribution for the chamfer matching score, and a Gaussian mixture for both the intensity and disparity values in the segmented foreground. This classifier uses a uniform prior.
5.4 Parameter Estimation
Estimating the parameters of the conditional distributions is straightforward, if the values of the latent variables are known. We have therefore annotated the dataset with ground truth (GT) labels for all latent variables in the sequences. During training, the distributions are then fitted on the training data using maximum likelihood estimation. The ExpectationMaximization (Dempster et al. 1977) algorithm is used to fit the Gaussian mixtures. We now explain for both scenarios how the GT labels were obtained.
5.4.1 Pedestrian Scenario
Sequences where potentially critical situations occur, i.e. when either pedestrian or vehicle should stop to avoid a collision, have been labeled as critical. Sequences are further labeled with event tags and timetoevent (TTE, in frames) values. For stopping pedestrians, \(\text {TTE}=0\) is when the last foot is placed on the ground at the curbside, and for crossing pedestrians at the closest point to the curbside (before entering the roadway). Frames before/after an event have negative/positive TTE values. For stopping sequences, the GT switching state is defined as \(M_t = m_{s}\) at moments with TTE \(\ge 0\), and as \(M_t = m_{w}\) at all other moments, crossing sequences always have \(M_t = m_{w}\).
Considering head observation \(\textit{HO}\), we assume pedestrians recognize an approaching vehicle (GT label \(Z^\text {ACT}_t=\text {true}\)) when the GT head direction is in a range of \(\pm 45^\circ \) around angle \(0^\circ \) (head is pointing towards the camera), and do not see the vehicle (\(Z^\text {ACT}_t=\text {false}\)) for angles outside this range (future human studies could allow a more precise threshold, or provide an angle distribution, the study in Hamaoka et al. (2013) only reported the frequency of head turning). For each ground truth label sv, we estimate the orientation class distributions \(p_{sv}\) by averaging the class weights in the corresponding head measurements.
For the observation \(D^{min}\), we define per trajectory one value for all \(Z^\text {DYN}_t\) labels (\(\forall _t \; Z^\text {DYN}_t = \text {true}\) for trajectories with critical situations, \(\forall _t \; Z^\text {DYN}_t = \text {false}\) otherwise), and fit the distributions \(\varGamma (D^{min} a_{sc}, b_{sc})\).
The distributions \({\mathcal {N}}(\textit{DTC}_t  \mu _{ac}, \sigma _{ac})\) are estimated from GT curb positions and the spacial \(Z^\text {STAT}_t\) labels, where \(Z^\text {STAT}_t = \text {true}\) only at time instances where \(1 \le \text {TTE} \le 1\) when crossing, and \(\text {TTE} \ge 1\) when stopping.
The histogram of the GT distributions and the estimated fits can be seen in Fig. 7.
5.4.2 Cyclist Scenario
The turning cyclists have \(\text {TTE}=0\) defined at the frame where it is first visible that they are turning. For the cyclists going straight, \(\text {TTE}=0\) is defined as the first frame where they pass the point at which \(25\%\) of all turning cyclists have passed their \(\text {TTE}=0\). For all turning cases, the GT switching state is defined as \(M_t = m_{tu}\) at moments with \(\text {TTE} \ge 0\). All other moments, and all straight cases have their GT state defined as \(M_t = m_{st}\) These average turning velocity of a track is estimated on its frames where \(M_t = m_{tu}\). The prior for the speed of the turning cyclist is estimated on these average turning velocities.
The GT for \(Z^\text {ACT}_t\) is taken from annotated GT arm angles. When the arm is raised further than \(30^\circ \), \(Z^\text {ACT}_t = \text {true}\). Below \(30^\circ \), the arm is considered down, or \(Z^\text {ACT}_t = \text {false}\).
We define one value for all \(Z^\text {DYN}_t\) labels of a specific track. It is set as true if the egovehicle would overtake the cyclist in two seconds at \(\text {TTE}=0\), assuming the cyclist has no more longitudinal speed. This can be interpreted as the worstcase scenario, where a cyclist would make an instant 90degree turn.
Finally, the spatial extent of the turning region is determined from smallest and largest longitudinal position of all turning cyclists at \(\text {TTE}=0\). The GT label for \(Z^\text {STAT}\) is set to true whenever the cyclist is in this region.
5.4.3 Both Scenarios
In both scenarios, we compute maximum likelihood estimates of the parameters for the priors and noise distributions using the GT position and speed profiles. For each pedestrian track, we take the average speed during the walking motion type as GT preferred walking speed \(\dot{x}^{m_{w}}\). Similarly, for each cyclist track we take averages of their GT speeds during each motion type as GT of the preferred speeds \(\dot{x}_{t}^{m_{tu}}\), \(\dot{y}_{t}^{m_{tu}}\), \(\dot{x}_{t}^{m_{st}}\) and \(\dot{y}_{t}^{m_{st}}\).
With all continuous states \(X_{t}\) fully defined for all tracks, we can compute the \(\epsilon _t\) using Eq. (1), i.e. \(B\epsilon _t = X_t  A^{(M_t)} X_{t1}\). From these \(\epsilon _t\) the process noise covariance \(Q\) is estimated. Likewise, observation noise covariance R is estimated from the differences between GT and measured positions, since \(\eta _t = Y_t  C X_{t}\) from Equation(2). Finally, the mean and covariance parameters of the state priors can be estimated from the \(X_0\) of all training tracks.
The prior and transition probability tables for the discrete context states \(Z^\text {ACT}\), \(Z^\text {STAT}\) are obtained by counting and normalizing the occurrences in the GT labels. The same applies to the dynamic switching state \(M\), conditioned on \(Z^\text {ACTED}\), \(Z^\text {DYN}\) and \(Z^\text {STAT}\). The transition probability for \(Z^\text {ACTED}\) is a logical OR, as described in Sect. 3.3. Since we only got one \(Z^\text {DYN}\) label per track, we fix the \(Z^\text {DYN}\) transition probability to 1 / 100 for changing state.
6 Experiments
In the experiments, we compare the proposed DBNs using all context cues to variants using less cues, and to baseline approaches. We also compare the use of visual detections to using GT annotations as measurements, and we investigate computational performance.
6.1 Pedestrian Scenario
6.1.1 Comparison of Model Variations
Prediction log likelihood of the GT pedestrian position for \(t_{p}=16\) frames (\(\sim 1\) s) ahead, for different subscenarios (rows) and models (columns), for TTE \(\in \) [\(\,15, 0\)]
Subscenario  Full model  \(E^\text {DYN}\text {+}E^\text {ACT}\)  \(E^\text {ACT}\)  \(E^\text {DYN}\)  SLDS  LDS  

Normal  Noncritical  Vehicle not seen  Crossing  \(\) 0.61  \(\) 0.53  \(\) 0.52  \(\) 0.59  \(\) 0.59  \(\) 1.90 
Noncritical  Vehicle seen  Crossing  \(\) 0.53  \(\) 0.45  \(\) 0.46  \(\) 0.47  \(\) 0.49  \(\) 1.93  
Critical  Vehicle not seen  Crossing  \(\) 0.48  \(\) 0.34  \(\) 0.17  \(\) 0.59  \(\) 0.33  \(\) 1.88  
Critical  Vehicle seen  Stopping  \(\) 0.33  \(\) 0.70  \(\) 1.13  \(\) 0.80  \(\) 1.26  \(\) 1.88  
Over all normal subscenarios  \(\) 0.51  \(\) 0.52  \(\) 0.58  \(\) 0.61  \(\) 0.66  \(\) 1.90  
Anomalous  Critical  Vehicle seen  Crossing  \(\) 0.90  \(\) 0.27  \(\) 0.15  \(\) 0.25  \(\) 0.13  \(\) 1.88 
For the anomalous subscenario, only the proposed model results in lower likelihood than for normal behavior, which is a useful property for anomaly detection as mentioned in Sect. 3.1. A future driver warning strategy could benefit from the more accurate path prediction of our full model in high likelihood situations, whereas falling back to simpler models/strategies when anomalies are detected.
6.1.2 Detailed Analysis on a Single Track
Fig. 10 illustrates a sequence from the stopping subscenario (fourth row in Table 3), with a snapshot just before (\(\text {TTE}=\,20\)) and after (\(\text {TTE}=\,9\)) the pedestrian becomes aware of the critical situation. At \(\text {TTE}=\,20\), the predicted distributions of all models are close together and indicate that the pedestrian continues walking (the LDS does so with high uncertainty). At \(\text {TTE}=9\), the mean position predictions of the LDS are furthest away from the GT (still within one std. dev. because of high uncertainty). The SLDSonly prediction shows a comparatively low uncertainty, but the predicted means have a high distance to the GT (not within one std. dev.). Predictions of the \(E^\text {DYN}\text {+}E^\text {ACT}\) model are closer to the true positions, since it captures the situational awareness of the pedestrian and therefore assigns a higher probability, compared to SLDS, to switch to the standing model \(m_{s}\). The full model makes the best predictions as it also anticipates where the pedestrian will stop, namely at the curbside.
For instance, at \(t = 23\), \(Z^\text {ACTED}_{t}\) starts to change as it becomes more probable that the pedestrian has seen the vehicle, and indeed around \(t = 29\) the pedestrian stops at the curb.
6.1.3 Comparison Over Time
In the context of action classification, Fig. 11 shows for various model variations, the standing probability \({\tilde{P}}_t(M_t = m_{s})\), and the \(error(t_p  t)\) for predictions made \(t_p = 16\) frames ahead, plotted against the TTE. In the first subscenario (top row), the pedestrian crosses in a critical situation without seeing the approaching vehicle. All models have a very low stopping probability (Fig. 11a), but since a few sequences have ambiguous head observations, our proposed model does not exclude the possibility that the vehicle has been seen. This translates to a higher stopping probability near the curb, and to a higher error of the average prediction (Fig. 11b) for a short while. Still, the model recuperates as the pedestrian approaches the curb and shows no sign of slowing down, which informs the model that the pedestrian did not see the vehicle (i.e. joint inference also means that observed motion dynamics can disambiguate lowlevel head orientation estimation). In the second subscenario (bottom row), the pedestrian is aware of the critical situation and stops at the curb. Now, all models show an increasing stopping probability (Fig. 11c) towards the event point. In a few scenarios, the SLDS switches too early to the standing state, reacting to perceived deacceleration (noise) of the pedestrian walking, hence the high std. dev. of the SLDS over all sequences early on. However, on average the SLDS assigns a higher probability to standing (\(> 0.5\)) than walking after the pedestrian has already reached the curb (\(\text {TTE} > 0\)). It can only react to changing dynamics, but not anticipate it. Our proposed model, on the other hand, gives the best action classification (highest stopping probability at \(\text {TTE}=0\)). It anticipates the change in motion dynamics a few frames earlier as the SLDS, benefiting from the combined knowledge about pedestrian awareness, interaction, and spatial layout. Further, the knowledge about the spatial layout helps to keep the standing probability low while the pedestrian is still far away from the curb. The model with limited context information ends up in between proposed model and SLDS. Accordingly, our proposed model has the lowest prediction error (Fig. 11d). Averaged over the sequences, it outperforms the baseline SLDS model by up to 0.39 m (at \(\text {TTE}=1\)) and the \(E^\text {DYN}\text {+}E^\text {ACT}\) model by up to 0.16 m (at \(\text {TTE}=10\)).
6.1.4 Idealized Vision Measurements
To investigate how the vision components affect performance, we train and test using GT as idealized measurements for pedestrian location, curb location, and head orientation. We find that the lateral pedestrian and curb measurements are sufficiently accurate: the use of GT as measurements does not notably improve the results. Ideal head measurements alter the five subscenario scores of the full model w.r.t. Table 3 to \(\,0.57\), \(\,1.08\), \(\,0.32\), \(\,0.12\) (“normal” cases), and to \(\,3.67\) (anomalous case). Predictions became more accurate for critical subscenarios. However the second subscenario (Noncritical, Vehicle seen, Crossing) became less accurate, as some moments were deemed critical, and seeing the vehicle implied stopping, Still, the likelihood of the anomalous fifth subscenario is much lower than all other subscenarios.
6.1.5 Comparison with PHTM and Computational Cost
Pedestrian scenario. Computational costs for the different models per frame (avg. per frame, in ms)
Approach  Observables  State est. & pred.  Total 

Full model  160  40  200 
SLDS  60  10  70 
LDS  60  0.4  60 
PHTM  70  600  670 
The computational costs of the various approaches were assessed on standard PC hardware (Intel Core i7 X990 CPU at \(3.47\,\)GHz), see Table 4. We differentiate between the computational cost for obtaining the observables and that for performing state estimation and prediction. In terms of observables, all approaches used positional information derived from a dense stereobased pedestrian detector (about 60 ms). The additional observables used in our proposed full model (e.g. head orientation and curb detection) cost an extra 100 ms to compute. PHTM on the other hand requires computing dense optical flow within the pedestrian bounding box (about 10 ms). But, as seen in Table 4, the proposed model is one order of magnitude more efficient than PHTM when considering only the state estimation and prediction component [this even though PHTM implements its trajectory matching by an efficient hierarchical technique (Keller and Gavrila 2014)], and it is three times more efficient in total.
6.2 Cyclist Scenario
To demonstrate that our approach is not specific for the crossing pedestrian scenario, we compare the full model to SLDS and LDS baselines on the cyclist scenario. Like the pedestrian scenario, we use an LDS baseline with the dynamic model from Eq. (35), except that the state is extended to \([x_t, \dot{x}_{t}, y_t, \dot{y}_{t} ]\).
6.2.1 Comparison with Baselines
Cyclist scenario
Subscenario  Full model  SLDS  LDS  

Normal  Critical  Arm not raised  Straight  0.05  \(\) 0.23  0.00 
Noncritical  Arm raised  Turn  \(\) 2.36  \(\) 3.19  \(\) 22.75  
Critical  Arm raised  Turn  \(\) 2.38  \(\) 2.77  \(\) 16.66  
Noncritical  Arm not raised  Straight/Turn  \(\) 2.28  \(\) 2.22  \(\) 14.88  
Over all normal subscenarios  \(\) 1.93  \(\) 2.22  \(\) 14.60  
Anomalous  Critical  Arm not raised  Turn  \(\) 14.33  \(\) 4.62  \(\) 31.91 
The log likelihoods of the onesecondahead prediction (16 time steps) are shown in Table 5, averaged over \(\text {TTE}\in [\,15,15]\), i.e. starting with prediction for the moment when the cyclist either starts to turn, or keeps moving straight.
Since the cyclist tracks are long, and mostly consist of moving straight, the LDS predictions reflect the common behavior of straight motion with little variance. As a result, its predictions are accurate when the cyclist indeed does not turn. As expected, this comes at the cost of inaccurate predictions in normal and anomalous subscenarios where the cyclist does turn.
Compared to the LDS, the switching models demonstrate the benefit of having separate dynamics for straight and turning motion, as the predictions for turning subscenarios are considerably more accurate. Furthermore, our model outperforms the SLDS in almost all but one normal subscenarios. On the noncritical subscenario where there is ambiguity on whether the cyclist will turn or go straight, the SLDS performs best. Still, the proposed method performs best overall on all normal subscenarios, demonstrating that context does improve prediction accuracy generally compared to the LDS and SLDS baselines.
We also note that all models obtain lower predictive likelihood for turning than for moving straight. We find that this is a result from the large variance in how cyclists execute the turn. The data shows the cyclists vary in when they initiate the turn, and in used turning speed and angle. This variance is also reflected in the predictive distributions, which show larger uncertainty for turning than for moving straight.
During the evaluation period of Table 5 around \(\textit{TTE} = 0\), the cyclist is always near to the intersection. We note that our model outperforms the baselines in all subscenarios when including all earlier predictions (\(\textit{TTE} < \,15\)). When the cyclists are still far from the intersection, our full model benefits from the static environment context which predicts that turning is not feasible yet.
The final row of the table illustrates the predictive likelihood for the anomalous subscenario where the cyclist turns in a critical situation without raising an arm. Here, our model performs more similar to the LDS, as both expect the cyclist to continue moving straight. The next session will show a more detailed analysis of all subscenarios.
6.2.2 Comparison Over Time
Figure 14 shows the prediction log likelihood for two subscenarios where the cyclist turns in critical situations, namely the normal subscenario where the turn happens after raising an arm (Fig. 14a), and the anomalous subscenario where the turn happens without raising an arm (Fig. 14b). In both cases, the LDS likelihood drops fast, as it predicts continuation of the past motion instead of turning. Our full model also expects moving straight in case the arm was not raised, therefore its predictive likelihood declines too for the anomaly. Interestingly, the model does adapt after \(\textit{TTE} = 0\) when the turning behavior becomes apparent. Later, at \(\textit{TTE} = 10\), the predictive log likelihood of all models drops due to the variation in turning behavior.
6.2.3 Detailed Analysis on a Single Track
Figure 15 shows two snapshots of the prediction over time for a cyclist who is turning at the intersection after holding his arm up while the situation is not critical. Before the cyclist arrives at the intersection, at \(t=67\), the prediction of the full model is very specific. Even though it was already detected that the cyclist raised his arm, he is expected to keep moving straight as he is not yet close enough to the intersection to turn. This prediction is done with less uncertainty than the baseline LDS because the process noise on the LDS must also account for the parts where the cyclist is turning left. At \(t=132\), when the cyclist is at the intersection, there is an increased probability that he could turn left. As a result, the expected future position also shifts left, and the uncertainty region of the prediction increases. The one standard deviation area of the prediction reflects the possibility that the cyclist may still move straight before turning.
7 Discussion
Our DBN provides predictive distributions of the future position of the tracked objects, reflecting uncertainty on possible trajectories. But as our results show, different scenarios give rise to different sources of uncertainty. For instance, if the system anticipates a change in dynamics, the future stopping position near the curb can be determined quite accurately for the pedestrian scenario. However, in the cyclist scenario there is more variance in turning behavior than in moving straight ahead, making accurate path predictions for the anticipated switch in dynamics more challenging. The available context may also be insufficient to unambiguously predict the behavior, as was seen in a cyclist subscenario. Here, our model’s performance approximated that of the SLDS baseline.
Another property of our model is that it is not a black box, but explicitly defines the relation between context observables, states, motion modes, and their dynamics. This ensures that a designer can inspect the system, investigate how it assesses the context, and determine causes for failure or success. The explicit formulation also facilitates adding additional cues, or improve individual parts (e.g. using different dynamical models) while keeping existing parts unchanged. The generic formulation also ensures that many forms of information can be included, from uptodate map data, to past image classification results. Accordingly, our method and the PHTM approach do not stand directly in competition, as they use different sources of information that could conceivably be combined.
Anomalous subscenarios contain situations not represented by the training data. In anomalous subscenarios, our method predicts position with lower likelihood than for the normal subscenarios. Therefore, lowlikelihood predictions can be used to detect anomalous behavior, for instance to switch to an emergency control strategy of the vehicle. Of course, anomalous situations are expected to be rare, since the training data is expected to be representative of ‘normal’ behavior. Larger realistic datasets should therefore provide better estimates of ‘normal’ behavior, though the principle demonstrated on our example scenarios should remain the same.
Future work involves the incorporation of additional scene context (e.g. traffic light, pedestrian crossing) and the extension of the basic motion types of the SLDS (e.g. turning in different directions). Indeed, initial work has already begun on extending our earlier conference (Kooij et al. 2014a) submission, which only considered the pedestrian crossing scenario. For instance, (Roth et al. 2016) incorporated driver attention in the same framework, and (Hashimoto et al. 2016) tackled additional pedestrian scenarios with similar DBNs.
8 Conclusions
This paper investigated the use of DBNs for path prediction of maneuvering objects. As a toy example illustrated, SLDSs can make good overall predictions, but prediction accuracy suffers when an actual change in dynamics occurs. We therefore proposed to condition the switching probability on dynamic context variables. Measurements of various visual cues inform the model if and when changes in dynamics are likely to occur. An efficient approximate inference method was presented for online path prediction. Parameters are estimated on annotated training data.
We validated our approach on two use cases of VRU path prediction in the IV domain, a pedestrian and a cyclist scenario. Combining several context cues proved to improve overall prediction accuracy, namely the VRU’s interaction with the egovehicle as dynamic environment context, the VRU’s location in the static environment, and the VRU behavior indicating awareness or intent. The experiments demonstrate that the expected benefits of the context also occur with realworld vehicle measurements, and when using features extracted from vision. Compared to the SLDS, when predicting up to \(\sim 1\) s ahead, our method improved up to 0.39 m for the pedestrian scenario, and up to 0.41 m for the cyclist scenario. It also slightly outperforms the PHTM approach at less than a third of computational cost.
We are encouraged that the presented contextbased models can play an important role in saving lives for the future intelligent vehicles.
Notes
Acknowledgements
The research leading to the results of this work has received funding from the European Communitys Eighth Framework Program (Horizon2020) under Grant Agreement No. 634149, the PROSPECT project.
References
 Alahi, A., Goel, K., Ramanathan, V., Robicquet, A., FeiFei, L., & Savarese, S. (2016). Social LSTM: Human trajectory prediction in crowded spaces. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR) (pp. 961–971).Google Scholar
 Althoff, M., Stursberg, O., & Buss, M. (2009). Modelbased probabilistic collision detection in autonomous driving. IEEE Transactions on Intelligent Transportation Systems, 10(2), 299–310.CrossRefGoogle Scholar
 Antonini, G., Martinez, S. V., Bierlaire, M., & Thiran, J. P. (2006). Behavioral priors for detection and tracking of pedestrians in video sequences. International Journal of Computer Vision, 69(2), 159–180.CrossRefGoogle Scholar
 Ba, S., & Odobez, J. (2011). Multiperson visual focus of attention from head pose and meeting contextual cues. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(1), 101–116.CrossRefGoogle Scholar
 Ballan, L., Castaldo, F., Alahi, A., Palmieri, F., & Savarese, S. (2016). Knowledge transfer for scenespecific motion prediction. In Proceedings of the European conference on computer vision (ECCV) (pp. 697–713). Springer.Google Scholar
 Bandyopadhyay, T., Won, K., Frazzoli, E., Hsu, D., Lee, W., & Rus, D. (2013). Intentionaware motion planning. In E. Frazzoli, T. LozanoPerez, N. Roy, & D. Rus (Eds.), Algorithmic foundations of robotics X (pp. 475–491). Berlin: Springer.CrossRefGoogle Scholar
 BarShalom, Y., Li, X., & Kirubarajan, T. (2001). Estimation with applications to tracking and navigation. Hoboken: WileyInterscience.CrossRefGoogle Scholar
 Benfold, B., & Reid, I. (2009). Guiding visual surveillance by tracking human attention. In Proceedings of the British machine vision conference (BMVC) Google Scholar
 Bishop, C. M. (2006). Pattern recognition and machine learning (Vol. 1). Berlin: Springer.zbMATHGoogle Scholar
 Blackman, S., & Popoli, R. (1999). Design and analysis of modern tracking systems. Norwood: Artech House Norwood.zbMATHGoogle Scholar
 Bonnin, S., Weisswange, T. H., Kummert, F., & Schmuedderich, J. (2014). General behavior prediction by a combination of scenariospecific models. IEEE Transactions on Intelligent Transportation Systems, 15(4), 1478–1488.CrossRefGoogle Scholar
 Boyen, X., & Koller, D. (1998). Tractable inference for complex stochastic processes. In Proceedings of uncertainty in artificial intelligence (UAI) (pp. 33–42). Morgan Kaufmann Publishers Inc.Google Scholar
 Braun, M., Rao, Q., Wang, Y., & Flohr, F. (2016). PoseRCNN: Joint object detection and pose estimation using 3d object proposals. In Proceedings of the IEEE intelligent transportation systems conference (pp. 1546–1551).Google Scholar
 Cao, Z., Simon, T., Wei, S. E., & Sheikh, Y. (2017). Realtime multiperson 2D pose estimation using part affinity fields. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR).Google Scholar
 Cara, I., & de Gelder, E. (2015). Classification for safetycritical carcyclist scenarios using machine learning. In Proceedings of the IEEE intelligent transportation systems conference (pp. 1995–2000).Google Scholar
 Chen, B., Zhao, D., & Peng, H. (2017). Evaluation of automated vehicles encountering pedestrians at unsignalized crossings. In Proceedings of the IEEE intelligent vehicles symposium Google Scholar
 Cho, H., Rybski, P. E., & Zhang, W. (2011). Visionbased 3D bicycle tracking using deformable part model and interacting multiple model filter. In Proceedings of the international conference on robotics and automation (ICRA) (pp. 4391–4398). IEEE.Google Scholar
 Cordts, M., Omran, M., Ramos, S., Rehfeld, T., Enzweiler, M., Benenson, R., et al. (2016). The cityscapes dataset for semantic urban scene understanding. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR) (pp. 3213–3223).Google Scholar
 Dempster, A., Laird, N., & Rubin, D. B. (1977). Maximumlikelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39, 1–38.MathSciNetzbMATHGoogle Scholar
 Dollár, P., Wojek, C., Schiele, B., & Perona, P. (2012). Pedestrian detection: An evaluation of the state of the art. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(4), 743–761.CrossRefGoogle Scholar
 Duda, R. O., & Hart, P. E. (1972). Use of the Hough transformation to detect lines and curves in pictures. Communications of ACM, 15(1), 11–15.CrossRefzbMATHGoogle Scholar
 Enzweiler, M., & Gavrila, D. M. (2009). Monocular pedestrian detection: Survey and experiments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(12), 2179–2195.CrossRefGoogle Scholar
 Enzweiler, M., & Gavrila, D.M. (2010). Integrated pedestrian classification and orientation estimation. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR) (pp. 982–989). IEEE.Google Scholar
 Flohr, F., DumitruGuzu, M., Kooij, J. F. P., & Gavrila, D. M. (2015). A probabilistic framework for joint pedestrian head and body orientation estimation. IEEE Transactions on Intelligent Transportation Systems, 16(4), 1872–1882.CrossRefGoogle Scholar
 Gavrila, D. M., & Giebel, J. (2002). Shapebased pedestrian detection and tracking. In Proceedings of the IEEE intelligent vehicles symposium (Vol. 1, pp. 8–14).Google Scholar
 Geiger, A., Lenz, P., & Urtasun, R. (2012). Are we ready for autonomous driving? The KITTI vision benchmark suite. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR).Google Scholar
 Geiger, A., Lauer, M., Wojek, C., Stiller, C., & Urtasun, R. (2014). 3d traffic scene understanding from movable platforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(5), 1012–1025.CrossRefGoogle Scholar
 Hamaoka, H., Hagiwara, T., Tada, M., & Munehiro, K. (2013). A study on the behavior of pedestrians when confirming approach of right/leftturning vehicle while crossing a crosswalk. In Proceedings of the IEEE intelligent vehicles symposium (pp. 106–110).Google Scholar
 Hashimoto, Y., Gu, Y., Hsu, L. T., IryoAsano, M., & Kamijo, S. (2016). A probabilistic model of pedestrian crossing behavior at signalized intersections for connected vehicles. Transportation Research Part C, 71, 164–181.CrossRefGoogle Scholar
 Helbing, D., & Molnár, P. (1995). Social force model for pedestrian dynamics. Physical Review E, 51(5), 4282.CrossRefGoogle Scholar
 Hirschmüller, H. (2008). Stereo processing by semiglobal matching and mutual information. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(2), 328–341.CrossRefGoogle Scholar
 Huang, L., Wu, J., You, F., Lv, Z., & Song, H. (2017). Cyclist social force model at unsignalized intersections with heterogeneous traffic. IEEE Transactions on Industrial Informatics, 13(2), 782–792.CrossRefGoogle Scholar
 Hubert, A., Zernetsch, S., Doll, K., & Sick, B. (2017). Cyclists’ starting behavior at intersections. In IEEE intelligent vehicles symposium (IV) (pp. 1071–1077). IEEE.Google Scholar
 Jacobs, H., Hughes, O., JohnsonRoberson, M., & Vasudevan, R. (2017). Realtime certified probabilistic pedestrian forecasting. IEEE Robotics and Automation Letters, 2, 2064–2071.CrossRefGoogle Scholar
 Karasev, V., Ayvaci, A., Heisele, B., & Soatto, S. (2016). Intentaware longterm prediction of pedestrian motion. In Proceeding of the international conference on robotics and automation (ICRA) (pp 2543–2549). IEEE.Google Scholar
 Keller, C. G., & Gavrila, D. M. (2014). Will the pedestrian cross? A study on pedestrian path prediction. IEEE Transactions on Intelligent Transportation Systems, 15(2), 494–506.CrossRefGoogle Scholar
 Keller, C. G., Dang, T., Fritz, H., Joos, A., Rabe, C., & Gavrila, D. M. (2011). Active pedestrian safety by automatic braking and evasive steering. IEEE Transactions on Intelligent Transportation Systems, 12(4), 1292–1304.CrossRefGoogle Scholar
 Kitani, K. M., Ziebart, B. D., Bagnell, J. A., & Hebert, M. (2012). Activity forecasting. In Proceedings of the European conference on computer vision (ECCV) (pp. 201–214). Springer.Google Scholar
 Klostermann, D., Osep, A., Stückler, J., & Leibe, B. (2016). Unsupervised learning of shapemotion patterns for objects in urban street scenes. In Proceedings of the British machine vision conference (BMVC).Google Scholar
 Köhler, S., Schreiner, B., Ronalter, S., Doll, K., Brunsmann, U., & Zindler, K. (2013). Autonomous evasive maneuvers triggered by infrastructurebased detection of pedestrian intentions. In Proceedings of the IEEE intelligent vehicles symposium (pp. 519–526).Google Scholar
 Kooij, J. F. P., Schneider, N., Flohr, F., & Gavrila, D. M. (2014a). Contextbased pedestrian path prediction. In Proceedings of the European conference on computer vision (ECCV) (pp. 618–633). Springer International Publishing.Google Scholar
 Kooij, J. F. P., Schneider, N., & Gavrila, D. M. (2014b). Analysis of pedestrian dynamics from a vehicle perspective. In Proceedings of the IEEE intelligent vehicles symposium (pp. 1445–1450).Google Scholar
 Kooij, J. F. P., Englebienne, G., & Gavrila, D. M. (2016). Mixture of switching linear dynamics to discover behavior patterns in object tracks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(2), 322–334.CrossRefGoogle Scholar
 Lauritzen, S. L. (1992). Propagation of probabilities, means, and variances in mixed graphical association models. Journal of the American Statistical Association, 87(420), 1098–1108.MathSciNetCrossRefzbMATHGoogle Scholar
 Lee, N., Choi, W., Vernaza, P., Choy, C. B., Torr, P. H., & Chandraker, M. (2017). DESIRE: Distant future prediction in dynamic scenes with interacting agents. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR).Google Scholar
 Li, X., Flohr, F., Yang, Y., Xiong, H., Braun, M., Pan, S., et al. (2016). A new benchmark for visionbased cyclist detection. In Proceedings of the IEEE intelligent vehicles symposium (pp. 1028–1033). IEEEGoogle Scholar
 Li, X., Li, L., Flohr, F., Wang, J., Xiong, H., Bernhard, M., et al. (2017). A unified framework for concurrent pedestrian and cyclist detection. IEEE Transactions on Intelligent Transportation Systems, 18(2), 269–281.CrossRefGoogle Scholar
 Liu, W., Anguelov, D., Erhan, D., Szegedy, C., Reed, S., Fu, C. Y. et al. (2016). SSD: Single shot multibox detector. In Proceedings of the European conference on computer vision (ECCV) (pp. 21–37). Springer.Google Scholar
 Meinecke, M. M., Obojski, M., Gavrila, D. M., Marc, E., Morris, R., Töns, M., et al. (2003). Strategies in terms of vulnerable road user protection. In EU project SAVEU, Deliverable D6.Google Scholar
 Menze, M., & Geiger, A. (2015). Object scene flow for autonomous vehicles. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR).Google Scholar
 Meuter, M., Iurgel, U., Park, S. B., & Kummert, A. (2008). Unscented Kalman filter for pedestrian tracking from a moving host. In Proceedings of the IEEE intelligent vehicles symposium (pp. 37–42).Google Scholar
 Minka, T. P. (2001). Expectation propagation for approximate Bayesian inference. In Proceedings uncertainty in artificial intelligence (UAI) (pp. 362–369). Morgan Kaufmann Publishers Inc.Google Scholar
 Morris, B. T., & Trivedi, M. M. (2011). Trajectory learning for activity understanding: Unsupervised, multilevel, and longterm adaptive approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(11), 2287–2301.CrossRefGoogle Scholar
 MurArtal, R., & Tardós, J. D. (2017). ORBSLAM2: An opensource SLAM system for monocular, stereo, and RGBD cameras. IEEE Transactions on Robotics, 33(5), 1255–1262.CrossRefGoogle Scholar
 Murphy, K. P. (2002). Dynamic bayesian networks: Representation, inference and learning. PhD thesis, University of California, Berkeley.Google Scholar
 Oh, S. M., Rehg, J. M., Balch, T., & Dellaert, F. (2008). Learning and inferring motion patterns using parametric segmental switching linear dynamic systems. International Journal of Computer Vision, 77(1–3), 103–124.CrossRefGoogle Scholar
 OhnBar, E., & Trivedi, M. M. (2016). Looking at humans in the age of selfdriving and highly automated vehicles. IEEE Transactions on Intelligent Vehicles, 1(1), 90–104.CrossRefGoogle Scholar
 Oniga, F., Nedevschi, S., & Meinecke, M. M. (2008). Curb detection based on a multiframe persistence map for urban driving scenarios. In Proceedings of the IEEE intelligent transportation systems conference (pp. 67–72).Google Scholar
 Otsuka, K., Hara, K., Suzuki, T., & Aoki, Y. (2017). Danger level modeling and analysis of vehiclepedestrian encounter using situation dependent topic model. In Proceedings of the IEEE intelligent vehicles symposium (pp. 251–256).Google Scholar
 Paden, B., Čáp, M., Yong, S. Z., Yershov, D., & Frazzoli, E. (2016). A survey of motion planning and control techniques for selfdriving urban vehicles. IEEE Transactions on Intelligent Vehicles, 1(1), 33–55.CrossRefGoogle Scholar
 Pavlovic, V., Rehg, J. M., & MacCormick, J. (2000). Learning switching linear models of human motion. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems (NIPS) (pp. 981–987). Massachusetts, US: MIT Press.Google Scholar
 Pellegrini, S., Ess, A., Schindler, K., & Van Gool, L. (2009). You’ll never walk alone: Modeling social behavior for multitarget tracking. In Proceedings of the international conference on computer vision (ICCV) (pp. 261–268).Google Scholar
 Pool, E. A. I., Kooij, J. F. P., & Gavrila, D. M. (2017). Using road topology to improve cyclist path prediction. In Proceedings of the IEEE intelligent vehicles symposium (pp. 289–296). IEEE.Google Scholar
 Rasouli, A., Kotseruba, I., & Tsotsos, J. K. (2017). Agreeing to cross: How drivers and pedestrians communicate. In Proceedings of the IEEE intelligent vehicles symposium.Google Scholar
 Redmon, J., Divvala, S., Girshick, R., & Farhadi, A. (2016). You only look once: Unified, realtime object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR) (pp. 779–788).Google Scholar
 Rehder, E., & Kloeden, H. (2015). Goaldirected pedestrian prediction. In Proceedings of IEEE international conference on computer vision workshops (pp. 50–58).Google Scholar
 Robicquet, A., Sadeghian, A., Alahi, A., & Savarese, S. (2016). Learning social etiquette: Human trajectory understanding in crowded scenes. In Proceedings of the European conference on computer vision (ECCV) (pp. 549–565). Springer.Google Scholar
 Rosti, A. V. I., & Gales, M. J. F. (2004). RaoBlackwellised Gibbs sampling for switching linear dynamical systems. In Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP) (Vol. 1, pp. 809–812).Google Scholar
 Roth, M., Flohr, F., & Gavrila, D. M. (2016). Driver and pedestrian awarenessbased collision risk analysis. In Proceedings of the IEEE intelligent vehicles symposium (pp. 454–459).Google Scholar
 Sattarov, E., Gepperth, A., & Reynaud, R., et al. (2014). Contextbased vector fields for multiobject tracking in application to road traffic. In Proceedings of the IEEE intelligent transportation systems conference (pp. 1179–1185).Google Scholar
 Sayed, T., Zaki, M. H., & Autey, J. (2013). Automated safety diagnosis of vehicle–bicycle interactions using computer vision analysis. Safety Science, 59, 163–172.CrossRefGoogle Scholar
 Schmidt, S., & Färber, B. (2009). Pedestrians at the kerb—Recognising the action intentions of humans. Transportation Research Part F: Traffic Psychology and Behaviour, 12(4), 300–310.CrossRefGoogle Scholar
 Schneider, N., & Gavrila, D. M. (2013). Pedestrian path prediction with recursive Bayesian filters: A comparative study. In J. Weickert, M. Hein, & B. Schiele (Eds.), Lecture notes in computer science (Vol. 8142, pp. 174–183). Berlin, Heidelberg: SpringerVerlag.Google Scholar
 Schreiber, M., Knöppel, C., & Franke, U. (2013). LaneLoc: Lane marking based localization using highly accurate maps. In Proceedings of the IEEE intelligent vehicles symposium (pp. 449–454).Google Scholar
 Schulz, A. T., & Stiefelhagen, R. (2015a). A controlled interactive multiple model filter for combined pedestrian intention recognition and path prediction. In Proceedings of the IEEE intelligent transportation systems conference (pp. 173–178).Google Scholar
 Schulz, A. T., & Stiefelhagen, R. (2015b) Pedestrian intention recognition using latentdynamic conditional random fields. In Proceedings of the IEEE intelligent vehicles symposium (pp. 622–627).Google Scholar
 Tamura, Y., Le, P. D., Hitomi, K., Chandrasiri, N., Bando, T., Yamashita, A., et al. (2012). Development of pedestrian behavior model taking account of intention. In Proceedings IEEE international conference on intelligent robots and systems (IROS) (pp. 382–387).Google Scholar
 Vanparijs, J., Panis, L. I., Meeusen, R., & de Geus, B. (2015). Exposure measurement in bicycle safety analysis: A review of the literature. Accident Analysis & Prevention, 84, 9–19.CrossRefGoogle Scholar
 Völz, B., Mielenz, H., Siegwart, R., & Nieto, J. (2016). Predicting pedestrian crossing using quantile regression forests. In Proceeding of the IEEE intelligent vehicles symposium, pp. 426–432.Google Scholar
 Wöhler, C., & Anlauf, J. K. (1999). A time delay neural network algorithm for estimating imagepattern shape and motion. Image and Vision Computing, 17(3–4), 281–294.CrossRefGoogle Scholar
 Yi, S., Li, H., & Wang, X. (2016). Pedestrian behavior understanding and prediction with deep neural networks. In Proceedings of the European conference on computer vision (ECCV) (pp. 263–279). Springer.Google Scholar
 Yi, Y., Hao, L., Hao, Z., Songtian, S., Ningyi, L., & Wenjie, S. (2017). Intersection scan model and probability inference for vision based smallscale urban intersection detection. In Proceedings of the IEEE intelligent vehicles symposium (pp. 1393–1398).Google Scholar
 Zernetsch, S., Kohnen, S., Goldhammer, M., Doll, K., & Sick, B. (2016). Trajectory prediction of cyclists using a physical model and an artificial neural network. In Proceedings of the IEEE intelligent vehicles symposium (pp. 833–838).Google Scholar
 Zhang, R., Wu, J., Huang, L., & You, F. (2017). Study of bicycle movements in conflicts at mixed traffic unsignalized intersections. IEEE Access, 5, 10108–10117.CrossRefGoogle Scholar
 Zhou, B., Zhao, H., Puig, X., Fidler, S., Barriuso, A., & Torralba, A. (2017). Scene parsing through ADE20K dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR).Google Scholar
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