We present a new compressed representation of free trajectories of moving objects. It combines a partial-sums-based structure that retrieves in constant time the position of the object at any instant, with a hierarchical minimum-bounding-boxes representation that allows determining if the object is seen in a certain rectangular area during a time period. Combined with spatial snapshots at regular intervals, the representation is shown to outperform classical ones by orders of magnitude in space, and also to outperform previous compressed representations in time performance, when using the same amount of space.
The closest predecessor of our work, GraCT @cite_9 , assumes regular timestamps and stores trajectories using two components. At regular time instants, it represents the position of all the objects in a structure called . The positions of objects between snapshots are represented in a structure called .
@cite_9
2144475703 2160388022 2810912957 2964019074
In this paper, we propose a citywide and real-time model for estimating the travel time of any path (represented as a sequence of connected road segments) in real time in a city, based on the GPS trajectories of vehicles received in current time slots and over a period of history as well as map data sources. Though this is a strategically important task in many traffic monitoring and routing systems, the problem has not been well solved yet given the following three challenges. The first is the data sparsity problem, i.e., many road segments may not be traveled by any GPS-equipped vehicles in present time slot. In most cases, we cannot find a trajectory exactly traversing a query path either. Second, for the fragment of a path with trajectories, they are multiple ways of using (or combining) the trajectories to estimate the corresponding travel time. Finding an optimal combination is a challenging problem, subject to a tradeoff between the length of a path and the number of trajectories traversing the path (i.e., support). Third, we need to instantly answer users' queries which may occur in any part of a given city. This calls for an efficient, scalable and effective solution that can enable a citywide and real-time travel time estimation. To address these challenges, we model different drivers' travel times on different road segments in different time slots with a three dimension tensor. Combined with geospatial, temporal and historical contexts learned from trajectories and map data, we fill in the tensor's missing values through a context-aware tensor decomposition approach. We then devise and prove an object function to model the aforementioned tradeoff, with which we find the most optimal concatenation of trajectories for an estimate through a dynamic programming solution. In addition, we propose using frequent trajectory patterns (mined from historical trajectories) to scale down the candidates of concatenation and a suffix-tree-based index to manage the trajectories received in the present time slot. We evaluate our method based on extensive experiments, using GPS trajectories generated by more than 32,000 taxis over a period of two months. The results demonstrate the effectiveness, efficiency and scalability of our method beyond baseline approaches. The objective of this paper is to parse object trajectories in surveillance video against occlusion, interruption, and background clutter. We present a spatio-temporal graph (ST-Graph) representation and a cluster sampling algorithm via deferred inference. An object trajectory in the ST-Graph is represented by a bundle of “motion primitives”, each of which consists of a small number of matched features (interesting patches) generated by adaptive feature pursuit and a tracking process. Each motion primitive is a graph vertex and has six bonds connecting to neighboring vertices. Based on the ST-Graph, we jointly solve three tasks: 1) spatial segmentation; 2) temporal correspondence and 3) object recognition, by flipping the labels of the motion primitives. We also adapt the scene geometric and statistical information as strong prior. Then the inference computation is formulated in a Markov chain and solved by an efficient cluster sampling. We apply the proposed approach to various challenging videos from a number of public datasets and show it outperform other state of the art methods. In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes — the spatial covariance — in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skelet al data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks. The main challenge of online multi-object tracking is to reliably associate object trajectories with detections in each video frame based on their tracking history. In this work, we propose the Recurrent Autoregressive Network (RAN), a temporal generative modeling framework to characterize the appearance and motion dynamics of multiple objects over time. The RAN couples an external memory and an internal memory. The external memory explicitly stores previous inputs of each trajectory in a time window, while the internal memory learns to summarize long-term tracking history and associate detections by processing the external memory. We conduct experiments on the MOT 2015 and 2016 datasets to demonstrate the robustness of our tracking method in highly crowded and occluded scenes. Our method achieves top-ranked results on the two benchmarks.