2,740 research outputs found
Progressive Simplification of Polygonal Curves
Simplifying polygonal curves at different levels of detail is an important
problem with many applications. Existing geometric optimization algorithms are
only capable of minimizing the complexity of a simplified curve for a single
level of detail. We present an -time algorithm that takes a polygonal
curve of n vertices and produces a set of consistent simplifications for m
scales while minimizing the cumulative simplification complexity. This
algorithm is compatible with distance measures such as the Hausdorff, the
Fr\'echet and area-based distances, and enables simplification for continuous
scaling in time. To speed up this algorithm in practice, we present
new techniques for constructing and representing so-called shortcut graphs.
Experimental evaluation of these techniques on trajectory data reveals a
significant improvement of using shortcut graphs for progressive and
non-progressive curve simplification, both in terms of running time and memory
usage.Comment: 20 pages, 20 figure
Algorithms for the Analysis of Spatio-Temporal Data from Team Sports
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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