Median Trajectories

Buchin, Kevin; Buchin, Maike; Kreveld, Marc van; Löffler, Maarten; Silveira, Rodrigo I.; Wenk, Carola; Wiratma, Lionov

doi:10.1007/s00453-012-9654-2

Cited by 52 publications

(41 citation statements)

References 32 publications

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“…It is less suited when curved trajectories, or, more precisely, trajectories not following one major directions, are involved. In such situations, computing a median trajectory [6] is advantageous: This approach constructs the arrangement, i.e., the embedded graph, induced by the set of segments of all subtrajectories in question. It then assembles the median trajectory via traversing this graph, moving along all segments for which the same number of other segments lie on either side.…”

Section: Computation Of Representative Trajectoriesmentioning

confidence: 99%

“…Hence, positioning in or around buildings often has static local biases, distorting the positioning estimate in a specific direction. By aggregating all subtrajectories that correspond to a particular segment of the (approximate or known) route network into an average [18] or median trajectory [6] we compute a representative of the estimated movement pattern along this segment; see the blue trajectory in Figure 1 (left). Using a route network (given or reconstructed) and these representative trajectories, we can determine the static biases in the positioning system at specific locations and along paths typically used; see the red areas in Figure 1 (left).…”

Section: Introductionmentioning

confidence: 99%

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Making Sense of Trajectory Data in Indoor Spaces

Prentow

Thom

Blunck

et al. 2015

2015 16th IEEE International Conference on Mobile Data Management

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The increasing prevalence of positioning and tracking systems has helped simplify tracking large amounts of, e.g., people moving through buildings or cars traveling on roads, over long periods of time. However, technical limitations of positioning algorithms and traditional sensing infrastructures are likely, especially indoors, to induce errors and biases in the resulting data. In particular, the resulting motion trajectories often do not conform perfectly to the underlying route network. As a consequence, analyses of trajectory sets are impeded by these phenomena, as it becomes hard to identify which route was taken in a particular travel instance or whether two travel instances followed the same route. In this paper, we present a bootstrapping approach and several algorithms to mitigate error biases and related phenomena, focusing on indoor scenarios. In particular, we are able to estimate and iteratively refine an underlying route network from a set of motion trajectories. Secondly, we represent subtrajectories, i.e., movements on individual elements of the route network, by their median subtrajectory. The resulting aggregated and cleaned-up data set facilitates using further, domain-specific analysis tools. Additionally, it allows to predict the locally occurring expected positioning error biases. This in turn allows improved positioning, e.g., for real-time navigation assistance scenarios. We evaluate the proposed methods using trajectory data from employees at a large hospital complex. In particular, we show that we can reconstruct the hospital's route network accurately, and that we can furthermore extract median subtrajectories for almost all individual corridors. Finally, we illustrate that median trajectories deliver useful deviation maps to learn, and correct for, the expected local biases in positioning.

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Section: Computation Of Representative Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Making Sense of Trajectory Data in Indoor Spaces

Prentow

Thom

Blunck

et al. 2015

2015 16th IEEE International Conference on Mobile Data Management

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“…To mitigate the effects of positioning inaccuracies, we smooth the position sequence by computing the median trajectory of the given positions [4]. We then use these smoothed positions to compute the speed between each consecutive position estimates, from which we for each window compute the mean, maximum, minimum and end-to-end speed in the window, which are used as features.…”

Section: Movement Speedmentioning

confidence: 99%

Towards Indoor Transportation Mode Detection Using Mobile Sensing

Prentow

Blunck

Kjærgaard

et al. 2015

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. Transportation mode detection is a growing field of research, in which a variety of methods have been developed for detecting transportation modes foremost for outdoor travels. It has been employed in application areas such as public transportation, environmental footprint profiling, and context-aware mobile assistants. For indoor travels the problem of transportation mode detection has received comparatively little attention, even though diverse transportation modes, such as biking, electric vehicles, and scooters, are used indoors, especially in large building complexes. The potential applications are diverse, and may also extend beyond indoor variants of the above outdoor applications, and include, e.g., scheduling and progress tracking for mobile workers, management of vehicular resources, and navigation support. However, for indoor transportation mode detection, the physical environment as well as the availability and reliability of sensing resources differ drastically from outdoor scenarios. Owing to these differences, many of the methods developed for outdoor transportation mode detection cannot be easily and reliably applied indoors. In this paper, we explore indoor transportation scenarios to arrive at a conceptual model of indoor transportation modes, and then compare challenges for outdoor and indoor transportation mode detection. In addition, we explore methods for transportation mode detection we deem suitable in indoor settings, and we perform an extensive real-world evaluation of (combinations of) such methods at a large hospital complex. The evaluation presented here utilizes Wi-Fi and accelerometer data collected through smartphones carried by several hospital workers throughout four days of work routines. The results show that the methods can distinguish between six common modes of transportation used by the hospital workers with an F-score of 84.2%.

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“…Trajectory grouping algorithms that allow segmentation in order to discover common substructure are desecribed in [14,17,2,19]. Methods for summarizing the grouping structure are explord in [17,5,6,22]. Notably, [6] introduces the application of the Reeb graph as a way to succinctly represent trajectory data in a way that encodes the merging and splitting structure.…”

Section: Previous Workmentioning

confidence: 99%

A reeb graph approach to tractography

Sun

Cieslak

Grafton

et al. 2015

Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems

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We propose an efficient algorithm for discovering the highlevel topological structure of a collection of 3-dimensional trajectories. Our algorithm computes a sparse graph representing the latent "bundling" and "unbundling" structure of the trajectory data. This graph can serve both as a compact signature of the trajectory data set as well as a tool for efficient comparison among different data sets. Our problem formulation and the algorithms are broadly applicable and general-purpose but we focus on a particular neuroscience application to highlight the key features. In particular, our motivation stems from the emerging area of brain tractography, which aims to construct the connectome of human brain white matter fibers. These fibers can be inferred noninvasively using magnetic resonance imaging (MRI) diffusion scans of the brain interior and modeled abstractly as a set of time-independent geometric trajectories in a threedimensional brain space. Real neuronal fiber pathways exhibit complex but natural bundling structures, which elude existing MRI reconstruction techniques, but are easily captured by our algorithm. We validate our algorithms both theoretically (uniqueness of the graph representation and provably efficient algorithms) and empirically (using both synthetic and real scanned brain data sets).

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Median Trajectories

Cited by 52 publications

References 32 publications

Making Sense of Trajectory Data in Indoor Spaces

Making Sense of Trajectory Data in Indoor Spaces

Towards Indoor Transportation Mode Detection Using Mobile Sensing

A reeb graph approach to tractography

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