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local
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Fig. 2.3 Lifeline context operators in analogy to Tomlin's map algebra. Intervals can be delimited
through a temporal window of fixed time ( δ t )orfixednumberoffixes ( ± 3 ) , adapted from Laube
et al. ( P3 . 2007 ) (Reprinted from Computers, Environment and Urban Systems , 31(5), Laube, P.,
Dennis, T., Forer, P., and Walker, M., Movement Beyond the Snapshot—Dynamic Analysis of
Geospatial Lifelines, page 486, Copyright (2007), with permission from Elsevier)
of instantaneous (relating to Tomlin's “local” operators), interval (“focal”), episodal
(“zonal”) and global (“global”) operators were suggested for computing descriptive
movement parameters (see Fig. 2.3 ). Interval operators, just as the focal operations in
the two-dimensional case, compute movement descriptors at any fix along a trajectory
as a function of the temporal fix neighborhood. This fix neighborhood can be defined
through a defined number of neighboring fixes, or, allowing for irregular sampling
or missing values, through a defined temporal interval. Also similar to the 2D case,
weighted neighborhood functions were discussed, assigning temporally close fixes
higher weights.
That study not only featured the above listed commonly used movement descrip-
tors but also exemplified the development of additional measures tailored towards a
specific application field, here avian navigation research. Navigational displacement
measures at any given point along the trajectory the deviation angle of a homing bird
from the direct path to its loft. Approaching rate measures whether or not and to what
degree a bird moves towards loft. These two measures were developed in a close and
 
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