Trajectory Grouping Structure

Buchin, Kevin; Buchin, Maike; Kreveld, Marc van; Speckmann, Bettina; Staals, Frank

doi:10.1007/978-3-642-40104-6_19

Cited by 28 publications

(20 citation statements)

References 18 publications

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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%

“…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. Our approach extends their technique to time-independent trajectories, which is a strictly harder case, and refines the grouping definition so that the resulting Reeb graph also partitions the set of input points, so that the groups can be labeled with domain-specific information such as anatomical features.…”

Section: Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Previous Workmentioning

confidence: 99%

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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“…Clustering on complete trajectories will not represent information about interesting parts of trajectories; for this clustering on subtrajectories is needed [5,12]. A set of trajectories that forms different groups over time may be captured by a grouping structure [6]. These approaches also focus on location over time.…”

Section: Introductionmentioning

confidence: 99%

Compact Flow Diagrams for State Sequences

Buchin

Gudmundsson

et al. 2016

Experimental Algorithms

Self Cite

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Abstract. We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified, our aim is to generate a small flow diagram that models the flow of states of all the state sequences given as input. For a small number of state sequences we present efficient algorithms to compute a minimal flow diagram. For a large number of state sequences we show that it is unlikely that efficient algorithms exist. More specifically, the problem is W [1]-hard if the number of state sequences is taken as a parameter. We thus introduce several heuristics for this problem. We argue about the usefulness of the flow diagram by applying the algorithms to two problems in sports analysis. We evaluate the performance of our algorithms on a football data set and generated data.

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“…This has led to a large amount of trajectory data capturing the movement of animals, vehicles, and people [1]. Radio Frequency Identification (RFID) is a technology of automatic object identification that uses radio waves to transfer data from an electronic tag, called RFID tag or label, attached to an object through a reader for the purpose of identifying and tracking the object [2].…”

Section: Introductionmentioning

confidence: 99%