In real-world applications, GPS trajectories often suffer from low sampling rates, with large and irregular intervals between consecutive GPS points. This sparse characteristic presents challenges for their direct use in GPS-based systems. This paper addresses the task of map-constrained trajectory recovery, aiming to enhance trajectory sampling rates of GPS trajectories. Previous studies commonly adopt a sequence-to-sequence framework, where an encoder captures the trajectory patterns and a decoder reconstructs the target trajectory. Within this framework, effectively representing the road network and extracting relevant trajectory features are crucial for overall performance. Despite advancements in these models, they fail to fully leverage the complex spatio-temporal dynamics present in both the trajectory and the road network. To overcome these limitations, we categorize the spatio-temporal dynamics of trajectory data into two distinct aspects: spatial-temporal traffic dynamics and trajectory dynamics. Furthermore, We propose TedTrajRec, a novel method for trajectory recovery. To capture spatio-temporal traffic dynamics, we introduce PD-GNN, which models periodic patterns and learns topologically aware dynamics concurrently for each road segment. For spatio-temporal trajectory dynamics, we present TedFormer, a time-aware Transformer that incorporates temporal dynamics for each GPS location by integrating closed-form neural ordinary differential equations into the attention mechanism. This allows TedFormer to effectively handle irregularly sampled data. Extensive experiments on three real-world datasets demonstrate the superior performance of TedTrajRec. The code is publicly available at https://github.com/ysygMhdxw/TEDTrajRec/.
Discovering co-movement patterns from urban-scale video data sources has emerged as an attractive topic. This task aims to identify groups of objects that travel together along a common route, which offers effective support for government agencies in enhancing smart city management. However, the previous work has made a strong assumption on the accuracy of recovered trajectories from videos and their co-movement pattern definition requires the group of objects to appear across consecutive cameras along the common route. In practice, this often leads to missing patterns if a vehicle is not correctly identified from a certain camera due to object occlusion or vehicle mis-matching. To address this challenge, we propose a relaxed definition of co-movement patterns from video data, which removes the consecutiveness requirement in the common route and accommodates a certain number of missing captured cameras for objects within the group. Moreover, a novel enumeration framework called MaxGrowth is developed to efficiently retrieve the relaxed patterns. Unlike previous filter-and-refine frameworks comprising both candidate enumeration and subsequent candidate verification procedures, MaxGrowth incurs no verification cost for the candidate patterns. It treats the co-movement pattern as an equivalent sequence of clusters, enumerating candidates with increasing sequence length while avoiding the generation of any false positives. Additionally, we also propose two effective pruning rules to efficiently filter the non-maximal patterns. Extensive experiments are conducted to validate the efficiency of MaxGrowth and the quality of its generated co-movement patterns. Our MaxGrowth runs up to two orders of magnitude faster than the baseline algorithm. It also demonstrates high accuracy in real video dataset when the trajectory recovery algorithm is not perfect.
Once analysed, location trajectories can provide valuable insights beneficial to various applications. However, such data is also highly sensitive, rendering them susceptible to privacy risks in the event of mismanagement, for example, revealing an individual's identity, home address, or political affiliations. Hence, ensuring that privacy is preserved for this data is a priority. One commonly taken measure to mitigate this concern is aggregation. Previous work by Xu et al. shows that trajectories are still recoverable from anonymised and aggregated datasets. However, the study lacks implementation details, obfuscating the mechanisms of the attack. Additionally, the attack was evaluated on commercial non-public datasets, rendering the results and subsequent claims unverifiable. This study reimplements the trajectory recovery attack from scratch and evaluates it on two open-source datasets, detailing the preprocessing steps and implementation. Results confirm that privacy leakage still exists despite common anonymisation and aggregation methods but also indicate that the initial accuracy claims may have been overly ambitious. We release all code as open-source to ensure the results are entirely reproducible and, therefore, verifiable. Moreover, we propose a stronger attack by designing a series of enhancements to the baseline attack. These enhancements yield higher accuracies by up to 16%, providing an improved benchmark for future research in trajectory recovery methods. Our improvements also enable online execution of the attack, allowing partial attacks on larger datasets previously considered unprocessable, thereby furthering the extent of privacy leakage. The findings emphasise the importance of using strong privacy-preserving mechanisms when releasing aggregated mobility data and not solely relying on aggregation as a means of anonymisation.
With the proliferation of GPS-equipped edge devices, huge trajectory data is generated and accumulated in various domains, motivating a variety of urban applications. Due to the limited acquisition capabilities of edge devices, a lot of trajectories are recorded at a low sampling rate, which may lead to the effectiveness drop of urban applications. We aim to recover a high-sampled trajectory based on the low-sampled trajectory in free space, i.e., without road network information, to enhance the usability of trajectory data and support urban applications more effectively. Recent proposals targeting trajectory recovery often assume that trajectories are available at a central location, which fail to handle the decentralized trajectories and hurt privacy. To bridge the gap between decentralized training and trajectory recovery, we propose a lightweight framework, LightTR, for federated trajectory recovery based on a client-server architecture, while keeping the data decentralized and private in each client/platform center (e.g., each data center of a company). Specifically, considering the limited processing capabilities of edge devices, LightTR encompasses a light local trajectory embedding module that offers improved computational efficiency without compromising its feature extraction capabilities. LightTR also features a meta-knowledge enhanced local-global training scheme to reduce communication costs between the server and clients and thus further offer efficiency improvement. Extensive experiments demonstrate the effectiveness and efficiency of the proposed framework.
Vehicle movement is frequently captured in the form of GPS trajectories, i.e., sequences of timestamped GPS locations. Such data is widely used for various tasks such as travel-time estimation, trajectory recovery, and trajectory prediction. A universal vehicle trajectory model could be applied to different tasks, removing the need to maintain multiple specialized models, thereby reducing computational and storage costs. However, creating such a model is challenging when the integrity of trajectory features is compromised, i.e., in scenarios where only partial features are available or the trajectories are sparse. To address these challenges, we propose the Universal Vehicle Trajectory Model (UVTM), which can effectively adapt to different tasks without excessive retraining. UVTM incorporates two specialized designs. First, it divides trajectory features into three distinct domains. Each domain can be masked and generated independently to accommodate tasks with only partially available features. Second, UVTM is pre-trained by reconstructing dense, feature-complete trajectories from sparse, feature-incomplete counterparts, enabling strong performance even when the integrity of trajectory features is compromised. Experiments involving four representative trajectory-related tasks on three real-world vehicle trajectory datasets provide insight into the performance of UVTM and offer evidence that it is capable of meeting its objectives.
Trajectory recovery based on the snapshots from the city-wide multi-camera network facilitates urban mobility sensing and driveway optimization. The state-of-the-art solutions devoted to such a vision-based scheme typically incorporate predefined rules or unsupervised iterative feedback, struggling with multi-fold challenges such as lack of open-source datasets for training the whole pipeline, and the vulnerability to the noises from visual inputs. In response to the dilemma, this paper proposes VisionTraj, the first learning-based model that reconstructs vehicle trajectories from snapshots recorded by road network cameras. Coupled with it, we elaborate on two rational vision-trajectory datasets, which produce extensive trajectory data along with corresponding visual snapshots, enabling supervised vision-trajectory interplay extraction. Following the data creation, based on the results from the off-the-shelf multi-modal vehicle clustering, we first re-formulate the trajectory recovery problem as a generative task and introduce the canonical Transformer as the autoregressive backbone. Then, to identify clustering noises (e.g., false positives) with the bound on the snapshots' spatiotemporal dependencies, a GCN-based soft-denoising module is conducted based on the fine- and coarse-grained Re-ID clusters. Additionally, we harness strong semantic information extracted from the tracklet to provide detailed insights into the vehicle's entry and exit actions during trajectory recovery. The denoising and tracklet components can also act as plug-and-play modules to boost baselines. Experimental results on the two hand-crafted datasets show that the proposed VisionTraj achieves a maximum +11.5% improvement against the sub-best model.
GPS trajectories are the essential foundations for many trajectory-based applications, such as travel time estimation, traffic prediction and trajectory similarity measurement. Most applications require a large amount of high sample rate trajectories to achieve a good performance. However, many real-life trajectories are collected with low sample rate due to energy concern or other constraints.We study the task of trajectory recovery in this paper as a means for increasing the sample rate of low sample trajectories. Currently, most existing works on trajectory recovery follow a sequence-to-sequence diagram, with an encoder to encode a trajectory and a decoder to recover real GPS points in the trajectory. However, these works ignore the topology of road network and only use grid information or raw GPS points as input. Therefore, the encoder model is not able to capture rich spatial information of the GPS points along the trajectory, making the prediction less accurate and lack spatial consistency. In this paper, we propose a road network enhanced transformer-based framework, namely RNTrajRec, for trajectory recovery. RNTrajRec first uses a graph model, namely GridGNN, to learn the embedding features of each road segment. It next develops a spatial-temporal transformer model, namely GPSFormer, to learn rich spatial and temporal features along with a Sub-Graph Generation module to capture the spatial features for each GPS point in the trajectory. It finally forwards the outputs of encoder model into a multi-task decoder model to recover the missing GPS points. Extensive experiments based on three large-scale real-life trajectory datasets confirm the effectiveness of our approach.
Trajectory Representation Learning (TRL) is a powerful tool for spatial-temporal data analysis and management. TRL aims to convert complicated raw trajectories into low-dimensional representation vectors, which can be applied to various downstream tasks, such as trajectory classification, clustering, and similarity computation. Existing TRL works usually treat trajectories as ordinary sequence data, while some important spatial-temporal characteristics, such as temporal regularities and travel semantics, are not fully exploited. To fill this gap, we propose a novel Self-supervised trajectory representation learning framework with TemporAl Regularities and Travel semantics, namely START. The proposed method consists of two stages. The first stage is a Trajectory Pattern-Enhanced Graph Attention Network (TPE-GAT), which converts the road network features and travel semantics into representation vectors of road segments. The second stage is a Time-Aware Trajectory Encoder (TAT-Enc), which encodes representation vectors of road segments in the same trajectory as a trajectory representation vector, meanwhile incorporating temporal regularities with the trajectory representation. Moreover, we also design two self-supervised tasks, i.e., span-masked trajectory recovery and trajectory contrastive learning, to introduce spatial-temporal characteristics of trajectories into the training process of our START framework. The effectiveness of the proposed method is verified by extensive experiments on two large-scale real-world datasets for three downstream tasks. The experiments also demonstrate that our method can be transferred across different cities to adapt heterogeneous trajectory datasets.
Many important tasks such as forensic signature verification, calligraphy synthesis, etc, rely on handwriting trajectory recovery of which, however, even an appropriate evaluation metric is still missing. Indeed, existing metrics only focus on the writing orders but overlook the fidelity of glyphs. Taking both facets into account, we come up with two new metrics, the adaptive intersection on union (AIoU) which eliminates the influence of various stroke widths, and the length-independent dynamic time warping (LDTW) which solves the trajectory-point alignment problem. After that, we then propose a novel handwriting trajectory recovery model named Parsing-and-tracing ENcoder-decoder Network (PEN-Net), in particular for characters with both complex glyph and long trajectory, which was believed very challenging. In the PEN-Net, a carefully designed double-stream parsing encoder parses the glyph structure, and a global tracing decoder overcomes the memory difficulty of long trajectory prediction. Our experiments demonstrate that the two new metrics AIoU and LDTW together can truly assess the quality of handwriting trajectory recovery and the proposed PEN-Net exhibits satisfactory performance in various complex-glyph languages including Chinese, Japanese and Indic.
Motion blur in dynamic scenes is an important yet challenging research topic. Recently, deep learning methods have achieved impressive performance for dynamic scene deblurring. However, the motion information contained in a blurry image has yet to be fully explored and accurately formulated because: (i) the ground truth of dynamic motion is difficult to obtain; (ii) the temporal ordering is destroyed during the exposure; and (iii) the motion estimation from a blurry image is highly ill-posed. By revisiting the principle of camera exposure, motion blur can be described by the relative motions of sharp content with respect to each exposed position. In this paper, we define exposure trajectories, which represent the motion information contained in a blurry image and explain the causes of motion blur. A novel motion offset estimation framework is proposed to model pixel-wise displacements of the latent sharp image at multiple timepoints. Under mild constraints, our method can recover dense, (non-)linear exposure trajectories, which significantly reduce temporal disorder and ill-posed problems. Finally, experiments demonstrate that the recovered exposure trajectories not only capture accurate and interpretable motion information from a blurry image, but also benefit motion-aware image deblurring and warping-based video extraction tasks. Codes are available on https://github.com/yjzhang96/Motion-ETR.