Pedestrian trajectory prediction is an important component in a range of applications such as social robots and self-driving vehicles, and plays a key role in understanding human movement behaviors. This task is not easy due to three key properties in pedestrian trajectory prediction: (i) social interaction: People are not always walking alone in a public space. Pedestrians often socially interact with others to avoid collisions, walk with friends or keep a certain distance from strangers; (ii) environmental scene constraints: Besides social interaction, pedestrians’ routes also need to obey scene constraints such as obstacles and building layouts; and (iii) multimodal nature of future prediction: People can follow different routes as long as these routes are both socially and environmentally acceptable. For example, a person can choose to turn right or turn left to bypass an obstacle.
Recently, researchers have made progress in incorporating these properties into the trajectory prediction process. For example, the Social LSTM model [Alahi et al.2016] is one of the methods that can capture social influence information in a local neighborhood around each pedestrian. Based on the generative model GAN [Goodfellow et al.2014], the SGAN model proposed by Gupta et al. [Gupta et al.2018]
can handle multimodality in the prediction process while also capturing the social influence from other pedestrians in the scene. To deal with the scene constraints, Convolutional Neural Networks (CNNs) are often used to extract scene information in the trajectory prediction network, such as SS-LSTM[Xue et al.2018], SoPhie [Sadeghian et al.2019], and Social-BiGAT [Kosaraju et al.2019] .
While other methods like [Su et al.2017, Vemula et al.2018, Hasan et al.2018, Zou et al.2018, Xue et al.2019, Li2019, Zhang et al.2019] miss one or two aforementioned key properties, SoPhie [Sadeghian et al.2019], Liang et al. [Liang et al.2019], and Social-BiGAT [Kosaraju et al.2019] are three typical papers that have taken all three properties into consideration. However, these methods predict the future locations recurrently. There are two main limitations in using autoregression to generate trajectory prediction: (i) the autoregressive prediction process works in a recursive manner and so the prediction errors accumulated from previous time steps are passed to the prediction for the next time step; (ii) the process cannot be parallelized, i.e., predictions must be generated sequentially, even though one might be interested in generating only the final destination of the pedestrian rather than the entire trajectory.
To overcome the above limitations and inspired by the application of non-autoregressive decoder in other areas such as machine translation [Gu et al.2018, Guo et al.2019] and time series forecasting [Wen et al.2017], we propose a novel trajectory prediction method that can predict future trajectories non-autoregressively. We name our method NAP (short for Non-Autoregressive Prediction). Our research contributions are threefold: (i)
To the best of our knowledge, we are the first to explore non-autoregressive trajectory prediction. The network architecture of NAP includes trainable context generators to ensure that context vectors are available for the non-autoregressive decoder to forecast good quality predictions. The state-of-the-art performance of NAP is demonstrated through the extensive experiments and ablation study conducted.(ii) Both the social and scene influences are handled by NAP through specially designed feature encoders. The social influence is captured by social graph features propagated through an LSTM; the scene influence is modeled by a CNN. The effectiveness of these encoders is confirmed from the performance of NAP. (iii) Unlike previous work in the literature, NAP tackles multimodal predictions by training a latent variable generator to learn the latent variables of the sampling distribution for each pedestrian’s trajectory. The generator is shown to give NAP top performance in multimodal predictions.
2.1 Problem Definition
Pedestrian trajectory prediction is defined as forecasting the future trajectory of the person given his/her observed trajectory. We assume that trajectories have already been obtained in the format of time sequences of coordinates (i.e., ). The length of the observed trajectory and predicted trajectory are represented by and . Thus, considering the observed trajectory , our target is to generate the prediction .
2.2 Autoregressive and Non-Autoregressive Predictions
Mathematically, to generate the predicted trajectory from a given observed trajectory
, the conditional probabilitywith parameter for an autoregressive predictor is defined as:
where generating the prediction of time step requires the prediction of all previous time steps in the prediction phase. This recursive prediction process can not be parallelized.
Different from the autoregressive prediction process, by treating and , for all , as independent, the above conditional probability in non-autoregressive predictors becomes:
Compared to the autoregression based prediction where the prediction at time step depends on the information at time step , non-autoregression based predictors do not need to generate predictions sequentially. However, the removal of this sequential dependency in non-autoregression based methods means that the time awareness ability is compromised in the prediction model, leading to poorer prediction performance. To compensate for the loss of time awareness ability, we design context generators (detailed in Section 3.2) that are trained on the training trajectories. This allows context vectors to be generated from the observed trajectories in the testing stage for the prediction process. As these context vectors can be computed before the start of the prediction phase, predictions at different time steps can be forecast in parallel.
3 Proposed Method
Our proposed NAP comprises four major parts (Fig. 1): (i) feature encoders which are used to encode the input information such as observed trajectories and scene images (Section 3.1); (ii) context generators to yield context vectors for prediction (Section 3.2); (iii) a latent variable generator for multimodality (Section 3.3); and (iv) a non-autoregressive decoder for predicting future trajectories (Section 3.4). Details of these parts are described in the following subsections.
3.1 Feature Encoders
In NAP, there are three feature encoders: a trajectory encoder, to learn the representation of the observed history movement of each pedestrian; a social encoder, to learn the representation of the influence from other pedestrians; and a scene encoder, to learn the representation of the scene features.
The coordinates of the pedestrian in the observation phase () are firstly embedded into a higher dimensional space through an embedding layer . Then, across different time steps, the embedded features are used as inputs of an LSTM layer (denoted by ) to get the encoded hidden state which captures the observed path information. This trajectory encoding is given by:
where and are trainable weights of the corresponding layers.
At each time step , NAP captures the social influence on the pedestrian through a graph . The pedestrian and all other pedestrians at the same time step are considered as nodes in the set . Edges linking the pedestrian and pedestrians in form the edge set .
We then use a graph convolutional network (GCN) to process these graphs. In the graph convolutional layer, the node feature of pedestrian is aggregated as follows:
where and are the weight matrix and bias term. At the first layer, we initialize the node feature as the location coordinates of the pedestrian, i.e., .
The social graph feature (Eq. (6)) is designed to model the surrounding (or social) information of pedestrian at each time step . To compute this feature, the node features, denoted by , from the final GCN layer across all the time steps in the observation phase are passed through an LSTM layer with trainable weights , i.e.,
Different from other methods (such as [Xue et al.2018, Sadeghian et al.2019]) that process each image frame in the observation phase, the scene encoder of NAP takes only image as input, since the scene encoder focuses on the static information like scene layouts and obstacles. Not only does this save the computation time, but it also supplies the most up-to-date and sufficient scene context before prediction kicks in at . We use a CNN to model the scene feature as follows:
We take the merit of DeepLabv3+ [Chen et al.2018], a state-of-the-art semantic segmentation architecture, and set the initial value of to the weight matrix from DeepLabv3+ that is pre-trained on the Cityscapes dataset [Cordts et al.2016].
3.2 Context Generators
The role of the context generators is to aggregate the outputs of the feature encoders for the downstream decoder for trajectory forecasting. We use two context generators in NAP: (i) a personal context generator that is time-agnostic, as its input is the hidden state computed from the pedestrian’s own trajectory only; (ii) an interaction context generator that is time-specific as its input includes both social graph and scene interaction features also.
Personal Context Generator (PCG).
We use a Multi-Layer Perceptron (MLP) to model this context generator. The output context vectoris computed as
where is the corresponding weight matrix. The context captures the “personal” cues such as the pedestrian’s preferable walking speed and direction in the observation phase, oblivious of his/her surrounding. This context is time-agnostic because, without considering the social and scene influences, such personal cues can remain the same for the entire trajectory, e.g., the pedestrian can continue to walk in a straight line or at a fast pace with no penalty when bumping into obstacles or other pedestrians since both the social graph and scene features are not present in the equation.
Interaction Context Generator (ICG).
This context generator incorporates both the social graph and scene features. These two types of influences allow the context generator to be time-specific, e.g., while a pedestrian can walk at a fast pace in the initial part of his/her trajectory, he/she would need to slow down or detour at a later part of the trajectory in order to avoid other pedestrians or scene obstacles. Similar to PCG, we use an MLP to model ICG but its input, being the concatenation of , , and , contains richer information. The output of ICG comprises different context vectors for different time steps in the prediction phase, as given below:
where is the corresponding weight matrix.
3.3 Latent Variable Generator
For multimodal prediction, NAP is designed to generate multiple trajectories through the latent variables and (see Fig. 1). Although several existing trajectory prediction methods such as [Lee et al.2017, Gupta et al.2018, Li2019, Huang et al.2019]
also use latent variables to handle multimodality, the latent variables in these methods are either directly sampled from the normal distribution or a multivariate normal distribution conditioned on the observed trajectories. To make our latent variables more aware of the social and scene cues, we design NAP to learn the parameters (and ) of the sampling distribution from the observed trajectories, the social influence, and the scene influence features. To this end, the concatenated feature is passed to two different MLPs (Eqs. (10)-(11)) to yield the mean vector
and varianceand finally for the downstream non-autoregressive decoder:
where and are trainable weights of and . The reparameterization trick [Kingma and Welling2013] is applied to sample the latent variable .
3.4 Non-Autoregressive Decoder (NAD)
In the work of [Gu et al.2018], the authors introduce in their model a component that enhances the inputs passed to the decoder for their machine translation problem. The idea is to help the model learn the internal dependencies (which are absent in their non-autoregressive translator) within a sentence. In the work of [Guo et al.2019], the authors use a positional module to improve the decoder’s ability to perform local reordering. The context generators in NAP play a similar role as these two approaches. In the testing stage, the trained PCG and ICG are able to generate context vectors for new (unseen) observed trajectories to help the decoder improve its time awareness for trajectory prediction. While the ICG, which generates time-specific contexts , is obviously more important than the PCG, the time-agnostic PCG is also needed so as to help the NAD tie with the specific trajectory being considered.
To make multimodal predictions at time step , the NAD therefore takes the concatenation of the two contexts and and the latent variable as inputs, modeled by the MLP below (see Fig. 2):
where is the MLP used for predicting the location coordinates. Its parameter is shared across all the time steps in the prediction phase. Note that the input passed to the NAD in Fig. 2 is different for each time step in the prediction phase as depends on . We can consider that the contexts function like the hidden states in the decoder of an LSTM except that they are not recursively defined.
3.5 Implementation Details
The embedding layer in Eq. (3) is modeled as a single-layer perceptron that outputs 32-dimensional embedded vectors for the input location coordinates. The dimensions of the hidden states of the LSTM layers for both the Trajectory and Social Encoders are 32. The GCN in the Social Encoder is a single graph convolutional layer (i.e., in Eq. (5)). For the ICG, is a three-layer MLP with ReLU activations. All the other MLPs used in Eqs. (8), (10), (11), and (13) are single-layer MLPs. Except for in Section 4.4 where we explore the prediction performance for different prediction lengths, the observed length of input trajectories is 8 time steps () and the prediction length is 12 time steps () for all other experiments.
4.1 Datasets and Metrics
We use the popular ETH [Pellegrini et al.2009] and UCY [Lerner et al.2007] datasets, which, altogether, include 5 scenes: ETH, HOTEL, UNIV, ZARA1, and ZARA2. Similar to [Sadeghian et al.2019, Zhang et al.2019], we normalize each pedestrian’s coordinates and augment the training data by rotating trajectories. As raw scene images are used as inputs for extracting scene features, we also rotate the input images when input trajectories are rotated. Same as previous work in the literature [Alahi et al.2016, Gupta et al.2018, Sadeghian et al.2019, Huang et al.2019], the leave-one-out strategy is adopted for training and testing. All methods are evaluated based on two standard metrics: the Average Displacement Error (ADE) and the Final Displacement Error (FDE). Smaller errors indicate better prediction performance.
|Method||#||ETH & UCY scenes|
|Social-LSTM [Alahi et al.2016]||1.09 / 2.35||0.79 / 1.76||0.67 / 1.40||0.47 / 1.00||0.56 / 1.17||0.72 / 1.54|
|SGAN 1V-1 [Gupta et al.2018]||1.13 / 2.21||1.01 / 2.18||0.60 / 1.28||0.42 / 0.91||0.52 / 1.11||0.74 / 1.54|
|MX-LSTM [Hasan et al.2018]||–||–||0.49 / 1.12||0.59 / 1.31||0.35 / 0.79||–|
|Nikhil & Morris [Nikhil and Morris2018]||1.04 / 2.07||0.59 / 1.17||0.57 / 1.21||0.43 / 0.90||0.34 / 0.75||0.59 / 1.22|
|Liang et al. [Liang et al.2019]||0.88 / 1.98||0.36 / 0.74||0.62 / 1.32||0.42 / 0.90||0.34 / 0.75||0.52 / 1.14|
|MATF [Zhao et al.2019]||1.33 / 2.49||0.51 / 0.95||0.56 / 1.19||0.44 / 0.93||0.34 / 0.73||0.64 / 1.26|
|SR-LSTM [Zhang et al.2019]||0.63 / 1.25||0.37 / 0.74||0.51 / 1.10||0.41 / 0.90||0.32 / 0.70||0.45 / 0.94|
|STGAT 1V-1 [Huang et al.2019]||0.88 / 1.66||0.56 / 1.15||0.52 / 1.13||0.41 / 0.91||0.31 / 0.68||0.54 / 1.11|
|NAP (ours)||0.59 / 1.13||0.30 / 0.51||0.59 / 1.23||0.41 / 0.86||0.36 / 0.72||0.45 / 0.89|
|SGAN 20V-20 [Gupta et al.2018]||✔||0.81 / 1.52||0.72 / 1.61||0.60 / 1.26||0.34 / 0.69||0.42 / 0.84||0.58 / 1.18|
|SoPhie [Sadeghian et al.2019]||✔||0.70 / 1.43||0.76 / 1.67||0.54 / 1.24||0.30 / 0.63||0.38 / 0.78||0.54 / 1.15|
|Liang et al. [Liang et al.2019]||✔||0.73 / 1.65||0.30 / 0.59||0.60 / 1.27||0.38 / 0.81||0.31 / 0.68||0.46 / 1.00|
|MATF GAN [Zhao et al.2019]||✔||1.01 / 1.75||0.43 / 0.80||0.44 / 0.91||0.26 / 0.45||0.26 / 0.57||0.48 / 0.90|
|IDL [Li2019]||✔||0.59 / 1.30||0.46 / 0.83||0.51 / 1.27||0.22 / 0.49||0.23 / 0.55||0.40 / 0.89|
|STGAT 20V-20 [Huang et al.2019]||✔||0.65 / 1.12||0.35 / 0.66||0.52 / 1.10||0.34 / 0.69||0.29 / 0.60||0.43 / 0.83|
|Social-BiGAT [Kosaraju et al.2019]||✔||0.69 / 1.29||0.49 / 1.01||0.55 / 1.32||0.30 / 0.62||0.36 / 0.75||0.48 / 1.00|
|NAP (ours)||✔||0.53 / 1.08||0.26 / 0.46||0.58 / 1.22||0.30 / 0.65||0.28 / 0.60||0.39 / 0.80|
4.2 Comparison with Other Methods
We compare NAP against the following state-of-the-art trajectory prediction methods: Social-LSTM [Alahi et al.2016], SGAN [Gupta et al.2018], MX-LSTM [Hasan et al.2018], Nikhil & Morris [Nikhil and Morris2018], Liang et al. [Liang et al.2019], MATF [Zhao et al.2019], SR-LSTM [Zhang et al.2019], SoPhie [Sadeghian et al.2019], IDL [Li2019], STGAT [Huang et al.2019], and Social-BiGAT [Kosaraju et al.2019].
In Table 1, all the compared methods are put into two groups depending on whether they generate only one prediction (top half of the table) or multiple predictions (bottom half and indicated by a tick under the # column) for each input observed trajectory. The multimodal predictions being considered is 20. The reported ADEs and FDEs are computed from the best predictions out of the 20. Five methods report both single and multimodal prediction results and so they appear in both halves of the table: SGAN, MATF, STGAT, Liang et al., and NAP.
Our proposed method is able to achieve results on par with the state-of-the-art methods for the single prediction setting. Specifically, NAP has the same smallest average ADE (0.45m) as SR-LSTM while outperforming all methods on the average FDE (0.89m). In addition to NAP, SR-LSTM, MX-LSTM, and STGAT 1V-1 also have the best performance on one or more scenes. In the lower half of Table 1, results of multimodal predictions are given and compared. On average, our NAP achieves the smallest ADE of 0.39m and the smallest FDE of 0.80m. For each scene, the best performers that achieve the smallest ADE/FDE in the lower half of the table include NAP, IDL, MATF, and GAN. Taken together, these results demonstrate the efficacy of our proposed method in both single and multimodal prediction settings.
4.3 Ablation Study
To explore the effectiveness of different contexts working together in our proposed method, we consider four variants of NAP listed below:
NAP-ISg: In order to further investigate the impact of removing the scene influence, we drop the scene feature from the Interaction Context Generator in Eq. (9) to form this variant. That is, the interaction context in NAP-ISS is computed using both the social graph and scene features, whereas the in NAP-ISg is computed using the social graph feature only.
NAP-ISc: Similar to NAP-ISg, this variant is designed to investigate the impact of removing the social influence. We drop the social graph feature but keep the scene feature in Eq. (9) so the context is computed from the scene feature only.
|ETH||0.87 / 1.63||0.66 / 1.22||0.69 / 1.31||0.74 / 1.52|
|HOTEL||0.43 / 0.77||0.34 / 0.61||0.37 / 0.70||0.38 / 0.73|
|UNIV||0.71 / 1.42||0.68 / 1.37||0.68 / 1.35||0.70 / 1.39|
|ZARA1||0.46 / 0.95||0.45 / 0.94||0.47 / 0.96||0.45 / 0.95|
|ZARA2||0.44 / 0.88||0.42 / 0.83||0.44 / 0.84||0.44 / 0.86|
|Average||0.58 / 1.13||0.51 / 0.99||0.53 / 1.03||0.54 / 1.09|
In our ablation study, we compare only the single prediction performance (see Table 2) of these four variants, i.e., the latent variable for multimodality is removed from Eq. (13) in the experiments. In general, NAP-P, which uses only the personal context (time-agnostic), has a poorer performance than the other three variants. This is not unexpected as, without the time-specific context, the NAD is not able to forecast good predictions for different time steps in the prediction phase. Comparing the three interaction context based variants against each other, it is not surprising to see that NAP-ISS outperforms the other two variants due to the presence of both the social graph and scene features. As for NAP-ISg against NAP-ISc, we observe that NAP-ISg slightly outperforms NAP-ISc. This demonstrates that the social influence is more important than the scene influence. However, it should be noted that the five scenes in the ETH/UCY datasets do not have many obstacles scattered in the pedestrian pathways. The slightly better performance of NAP-ISg confirms that there are more social (pedestrian) interactions than scene interactions in these datasets.
4.4 Different Prediction Lengths
|Social-LSTM||0.45 / 0.91||0.72 / 1.54||60.00% / 69.23%|
|SGAN 1V-1||0.49 / 1.00||0.74 / 1.54||51.02% / 54.00%|
|STGAT 1V-1||0.39 / 0.81||0.54 / 1.11||38.46% / 37.03%|
|NAP (ours)||0.35 / 0.67||0.45 / 0.89||28.57% / 32.84%|
|SGAN 20V-20||0.39 / 0.78||0.58 / 1.18||48.72% / 51.28%|
|STGAT 20V-20||0.31 / 0.62||0.43 / 0.83||38.71% / 33.87%|
|NAP (ours)||0.31 / 0.61||0.39 / 0.80||25.81% / 31.15%|
In addition to the prediction length setting ( frames, corresponding to 4.8 seconds) used in Tables 1 & 2 and similar to previous work such as SGAN [Gupta et al.2018] and STGAT [Huang et al.2019], we conduct experiments for the prediction length frames (or 3.2 seconds) to further evaluate the performance of NAP. Table 3 shows the average ADE/FDE results for this prediction length setting. The figures under the ‘’ column are copied from the Average column of Table 1. Each error increment (last column) due to the increase of is calculated as: , where and are errors (ADEs or FDEs) for and of the same method.
As expected, all methods shown in Table 3 have better performance for the shorter prediction length. In the top half of the table, when generating a predicted trajectory for each input, the error increments of Social-LSTM and SGAN 1V-1 are over 50%. Compared to these two methods, STGAT 1V-1 has smaller error increments for both ADE and FDE. For the multimodal predictions (bottom half of the table), STGAT 20V-20 again outperforms SGAN 20V-20.
We observe from Table 3 that NAP consistently outperforms all other methods for both prediction length settings and for both single and multimodal predictions. Furthermore, NAP also has the smallest error increments for both ADE and FDE when increases. This demonstrates that NAP is more robust in generating long trajectories. The reason is due to the non-autoregressive nature of the decoder, which not only allows the location coordinates at different time steps to be independently forecast but also helps minimize the accumulation of prediction errors when the prediction length increases.
4.5 Qualitative Results
Figure 3 illustrates some prediction examples generated by NAP. The observed and ground truth trajectories are shown in yellow and green; the best trajectory of the 20 predictions of each pedestrian is shown in pink. For better visualization, the video frames have been darkened and blurred. These examples cover different movement behaviors of pedestrians. For example, Fig. 3(a) shows two simple straight path scenarios, Fig. 3(b) and (c) show a gentle turning scenario, and Fig. 3(d) shows a more difficult scenario in which an abrupt turning occurs near the end of the observation phase. Although the predicted trajectory (in pink) in Fig. 3(d) does not perfectly overlap with the ground truth trajectory, NAP is still able to correctly predict the trajectory from the late turning cue.
Figure 4 shows two more difficult scenarios where all the 20 predicted trajectories are displayed as a heatmap around each pedestrian. For the pedestrian in Fig. 4(a) and the right pedestrian in Fig. 4(b), each made an abrupt turn at almost the last frame of the observation phase. However, NAP is still able to give good predicted trajectories, as all the plausible paths (including the ground truth trajectories (green)) are well covered by the heatmaps. The left pedestrian in Fig. 4(b) is a stopping scenario. After stopping, the pedestrian can remain still or resume walking in any direction. The generated heatmap shows a good coverage of possible paths; however, it has a small dent in the bottom left hand region due to the presence of a bench there, showing that the pedestrian must bypass the obstacle. This example shows the importance of including scene influence in the method.
We have presented a novel method called NAP which can handle both social influence and scene influence in the pedestrian trajectory prediction process. NAP captures these influences using the trainable feature encoders in the network. In addition, NAP handles multimodal predictions via a latent variable generator which models the sampling distribution that describes the multiple plausible paths of each pedestrian. Unlike existing trajectory prediction methods, the decoder of NAP is non-autoregressive. NAP is therefore able to forecast predictions for different time steps simultaneously or to forecast only for those time steps that are of interest. From our extensive experiments and ablation study, the context encoders used in NAP have been demonstrated to be effective. Not only does NAP achieve state-of-the-art performance, it also has smaller error increments when the prediction length increases.
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