1,041 research outputs found

    Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

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    In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria including location heading speed velocity curvature sinuosity curviness and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria or any combination of these criteria. In this framework a segmentation can generally be computed in O(n log n) time where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach

    Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

    Get PDF
    In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria, including location, heading, speed, velocity, curvature, sinuosity, curviness, and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria, or any combination of these criteria. In this framework, a segmentation can generally be computed in O(n log n) time, where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach.Peer ReviewedPostprint (published version

    A Semi-Supervised Approach for the Semantic Segmentation of Trajectories

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    A first fundamental step in the process of analyzing movement data is trajectory segmentation, i.e., splitting trajecto- ries into homogeneous segments based on some criteria. Although trajectory segmentation has been the object of several approaches in the last decade, a proposal based on a semi-supervised approach remains inexistent. A semi-supervised approach means that a user labels manually a small set of trajectories with meaningful segments and, from this set, the method infers in an unsupervised way the segments of the remaining trajecto- ries. The main advantage of this method compared to pure supervised ones is that it reduces the human effort to label the number of trajectories. In this work, we propose the use of the Minimum Description Length (MDL) principle to measure homogeneity inside segments. We also introduce the Reactive Greedy Randomized Adaptive Search Procedure for semantic Semi- supervised Trajectory Segmentation (RGRASP-SemTS) algorithm that segments trajectories by combining a limited user labeling phase with a low number of input parameters and no predefined segmenting criteria. The approach and the algorithm are pre- sented in detail throughout the paper, and the experiments are carried out on two real-world datasets. The evaluation tests prove how our approach outperforms state-of-the-art competitors when compared to ground truth. This is a preprint version of the full article published by IEEE at https://ieeexplore.ieee.org/document/841127

    Model-based segmentation and classification of trajectories (Extended abstract)

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    We present efficient algorithms for segmenting and classifying a trajectory based on a parameterized movement model like the Brownian bridge movement model. Segmentation is the problem of subdividing a trajectory into parts such that each art is homogeneous in its movement characteristics. We formalize this using the likelihood of the model parameter. We consider the case where a discrete set of m parameter values is given and present an algorithm to compute an optimal segmentation with respect to an information criterion in O(nm) time for a trajectory with n sampling points. Classification is the problem of assigning trajectories to classes. We present an algorithm for discrete classification given a set of trajectories. Our algorithm computes the optimal classification with respect to an information criterion in O(m^2 + mk(log m + log k)) time for m parameter values and k trajectories, assuming bitonic likelihood functions

    Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences

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    We give the first subquadratic-time approximation schemes for dynamic time warping (DTW) and edit distance (ED) of several natural families of point sequences in Rd\mathbb{R}^d, for any fixed d≥1d \ge 1. In particular, our algorithms compute (1+ε)(1+\varepsilon)-approximations of DTW and ED in time near-linear for point sequences drawn from k-packed or k-bounded curves, and subquadratic for backbone sequences. Roughly speaking, a curve is κ\kappa-packed if the length of its intersection with any ball of radius rr is at most κ⋅r\kappa \cdot r, and a curve is κ\kappa-bounded if the sub-curve between two curve points does not go too far from the two points compared to the distance between the two points. In backbone sequences, consecutive points are spaced at approximately equal distances apart, and no two points lie very close together. Recent results suggest that a subquadratic algorithm for DTW or ED is unlikely for an arbitrary pair of point sequences even for d=1d=1. Our algorithms work by constructing a small set of rectangular regions that cover the entries of the dynamic programming table commonly used for these distance measures. The weights of entries inside each rectangle are roughly the same, so we are able to use efficient procedures to approximately compute the cheapest paths through these rectangles

    Asymptotic behavior of coupled dynamical systems with multiscale aspects

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    We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic control of coupled sytems.Comment: 20 page

    Algorithms for the Analysis of Spatio-Temporal Data from Team Sports

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    Modern object tracking systems are able to simultaneously record trajectories—sequences of time-stamped location points—for large numbers of objects with high frequency and accuracy. The availability of trajectory datasets has resulted in a consequent demand for algorithms and tools to extract information from these data. In this thesis, we present several contributions intended to do this, and in particular, to extract information from trajectories tracking football (soccer) players during matches. Football player trajectories have particular properties that both facilitate and present challenges for the algorithmic approaches to information extraction. The key property that we look to exploit is that the movement of the players reveals information about their objectives through cooperative and adversarial coordinated behaviour, and this, in turn, reveals the tactics and strategies employed to achieve the objectives. While the approaches presented here naturally deal with the application-specific properties of football player trajectories, they also apply to other domains where objects are tracked, for example behavioural ecology, traffic and urban planning
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