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TRAJECTORY GROUPING STRUCTURE
 JOURNAL OF COMPUTATIONAL GEOMETRY
, 2015
"... The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept fro ..."
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The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity interdistance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial, algorithmic, and experimental results.
Space transformation for understanding group movement
 IEEE Trans. Vis. Comput. Graph
"... Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/ ..."
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Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/
Visualization of urban concepts of . . .
, 2009
"... This study pursues questions about the topdown and the bottomup directions of geographical thinking. A question about the topdown direction: 1) how geographical concepts could influence spatial data, is asked in the first half of the study, and another question for the bottomup direction: 2) how ..."
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This study pursues questions about the topdown and the bottomup directions of geographical thinking. A question about the topdown direction: 1) how geographical concepts could influence spatial data, is asked in the first half of the study, and another question for the bottomup direction: 2) how existing data could inform geographical concepts, is asked in another half of the study. To answer the first question, Part 1 deals with the uncertainty of an exurban concept as a primary example, since there are many different definitions of exurbanization and the spatial boundaries based on them are not identical. Several definitions of exurbanization are investigated to determine how they represent exurban areas, and formal representations of the fuzzyset approach are developed to analyze and visualize the uncertainty of the exurban definitions. The study develops a software interface that would allow interactive exploration, analysis, negotiation, and visualization of uncertain geographical concepts. Selected exurban definitions and empirical spatial data demonstrate concept comparison and concept creation activities using the interface. A case study of five different definitions of
A Reeb Graph Approach to Tractography∗
"... We propose an efficient algorithm for discovering the highlevel topological structure of a collection of 3dimensional 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 ..."
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We propose an efficient algorithm for discovering the highlevel topological structure of a collection of 3dimensional 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 generalpurpose 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 timeindependent 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).
DEVELOPING A WILDLIFE TRACKING EXTENSION FOR ArcGIS
, 2009
"... Wildlife tracking is an essential task to gain better understanding of the migration pattern and use of space of the wildlife. Advances in computer technology and global positioning systems (GPS) have lowered costs, reduced processing time, and improved accuracy for tracking wild animals. In this th ..."
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Wildlife tracking is an essential task to gain better understanding of the migration pattern and use of space of the wildlife. Advances in computer technology and global positioning systems (GPS) have lowered costs, reduced processing time, and improved accuracy for tracking wild animals. In this thesis, a wildlife tracking extension is developed for ArcGIS 9.x, which allows biologists and ecologists to effectively track, visualize and analyze the movement patterns of wild animals. The extension has four major components: (1) data import; (2) tracking; (3) spatial and temporal analysis; and (4) data export. Compared with existing software tools for wildlife tracking, the major features of the extension include: (1) wildlife tracking capabilities using a dynamic data layer supported by a file geodatabase with 1 TB storage limit; (2) spatial clustering of wildlife locations; (3) lacunarity analysis of onedimensional individual animal trajectories and twodimensional animal locations for better understanding of animal movement patterns; and (4) herds evolvement modeling and graphic representation. The application of the extension is demonstrated using simulated data, test data collected by a GPS collar, and a real dataset collected by ARGOS satellite telemetry for albatrosses in the Pacific Ocean. ii