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Towards an Analytical Framework for Enriching Movement Trajectories with Spatio-Temporal Context Data

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Although there are numerous studies in which movement trajectories were analysed based on their geometry alone, a more holistic interpretation requires their contextual setting to be incorporated into the analytical process as well. Among other influences, for instance, several attributes of the underlying physical space can have an effect on movement. Thus, a critical task is to semantically enrich movement trajectories with attribute values derived from one or more underlying layers with spatio-temporal data. This process, however, is not always trivial due to the fact that currently, there exists no comprehensive framework or toolset for such purposes. Further, communicating the exact procedure which was used in a study is impeded by a lack of formal terminology required to unambiguously define the involved methods and operators. In this paper, we address these issues and conceptualize an analytical framework for the process of enriching movement trajectories with spatio-temporal context data from underlying data layers, as well as propose a terminology to explicitly define the spatio-temporal scope of the analysis. We demonstrate the validity of our concept on a practical example.
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1 Introduction
Numerous studies have analysed movement data in order to
examine characteristics, patterns and dynamics of movement
and the moving entity. Frequently, such work has focused on
analyzing the geometry of the trajectory, while ignoring its
contextual setting (Laube 2014, Demsar et al. 2015). In fact,
however, movement is always set in context, which can
involve the underlying physical space, the time, static or
dynamic objects, or events (Andrienko et al. 2011). For this
reason, the prevalent context-independent view on trajectories
has been identified as one of the major pitfalls of movement
analysis (Buchin et al. 2012). As a reaction, there has been
work on enriching raw trajectories with context information in
order to create semantic trajectories, which allow for detecting
relations between movement and its contextual setting
(Spaccapietra and Parent 2011, Andrienko et al. 2011).
In this research, we focus on the semantic enrichment of
trajectories, and explicitly on annotating raw movement data
with attributes of the physical environment, as derived from
external data sources. In practice, the most common approach
for this is to overlay a trajectory with context data, often in the
form of separate raster layers, and annotate each point of the
trajectory with the underlying cell value (cf. Buchin et al.
In many cases, however, this procedure is not sufficient.
Rather than treating each position fix separately, it can make
sense to view them as parts of larger meaningful units, such as
all positions recorded while walking to work, or within a
certain time interval, and in some way combine their
underlying cell values for the analysis (e.g. to identify the
maximum temperature a person was exposed to during a
walking trip). Further, allocating a cell (and its value) to a
position fix based on their locational equivalence is highly
sensitive with regards to possible positional inaccuracies of
the movement data and the spatial resolution of the context
data. Therefore, for some scenarios, it can be more
appropriate to choose an approach which takes not just one,
but a combination of several neighboring cells into account
(e.g. calculate the average of all temperature values of cells
within 50 meters of a position fix). Furthermore, a context
dataset typically represents a static snapshot of a dynamic
environmental attribute, e.g. the temperature recorded at a
certain point in time. Often, though, this particular instant will
not completely correspond to the time at which the movement
took place. In such cases, it can be worthwhile to extend the
temporal scope of the analysis to combine several datasets
with different time stamps (e.g. combine the temperature
values recorded in a certain time window around a position
Currently, despite the fact that conceptual frameworks for
general semantic trajectory annotation have been proposed
(e.g. Andrienko et al. 2011), the specific process of annotating
movement trajectories with underlying spatio-temporal
context data is still a challenging task. There exists no
comprehensive framework or even a toolset to be used for
these purposes, especially with regards to more complex
application scenarios, as briefly outlined before. Further,
communicating the exact procedure used in a study is
impeded by the lack of a formal terminology to
unambiguously define the involved methods and operators.
In this paper, we address these issues and conceptualize an
analytical framework for the process of enriching movement
trajectories with spatio-temporal context data from underlying
raster data layers. Drawing heavily from Tomlin’s (1990) map
algebra and follow-up work (e.g. Laube et al. 2007), we
Towards an Analytical Framework for Enriching Movement Trajectories
with Spatio-Temporal Context Data
David Jonietz
ETH Zürich
Inst. of Cartography
and Geoinformation
Stefano-Franscini-Platz 5
8092 Zurich, Switzerland
Dominik Bucher
ETH Zürich
Inst. of Cartography
and Geoinformation
Stefano-Franscini Platz 5
8092 Zurich, Switzerland
Although there are numerous studies in which movement trajectories were analysed based on their geometry alone, a more holistic
interpretation requires their contextual setting to be incorporated into the analytical process as well. Among other influences, for instance,
several attributes of the underlying physical space can have an effect on movement. Thus, a critical task is to semantically enrich movement
trajectories with attribute values derived from one or more underlying raster layers with spatio-temporal data. This process, however, is not
always trivial due to the fact that currently, there exists no comprehensive framework or toolset for such purposes. Further, communicating
the exact procedure which was used in a study is impeded by a lack of formal terminology required to unambiguously define the involved
methods and operators. In this paper, we address these issues and conceptualize an analytical framework for the process of enriching
movement trajectories with spatio-temporal context data from underlying raster layers, as well as propose a terminology to explicitly define
the spatio-temporal scope of the analysis. We demonstrate the validity of our concept on a practical example.
Keywords: semantic trajectory, annotation, map algebra
AGILE 2017 Wageningen, May 9-12, 2017
propose a terminology to explicitly define the spatio-temporal
scope of the analysis at the trajectory as well as the context
data level. We implement our framework and demonstrate its
validity on a practical example.
This paper is structured as follows: first, background
information is provided on movement data and its semantic
annotation, as well as the concept of map algebra. Then, our
framework is presented and tested in an exemplary
application. Finally, the results are discussed and the paper is
2 Background
2.1 Movement Data
Intuitively, the movement of an entity, e.g. a person, involves
a change in its physical position based on a reference system
such as geographical space (Andrienko et al. 2008). Various
types of sensors, including Global Navigation Satellite
Systems-based positioning (GNSS), can be used to record this
movement in the form of series of chronologically ordered x,
y-coordinate position fixes with a distinct id and enriched with
a time stamp t:
Since these position fixes are chronologically ordered, it is
possible to determine for each individual fix its immediate
neighbours as a sub-sequence of position fixes P recorded
within a certain time interval (ts, te), using a sliding window
Apart from sliding time windows, one can also create
meaningful sub-sets of position fixes, which Spaccapietra and
Parent (2011) refer to as a trajectory, e.g. all movements
recorded on a certain day:
The entirety of recorded movements for a moving entity,
finally, is called a movement track by Spaccapietra and Parent
(2011), and includes all recorded trajectories:
2.2 Setting Movement Data in its Environmental
When analyzing the movement behavior of humans or
animals, various information can be extracted from a
geometrical analysis of the raw movement data, such as the
speed, direction, sinuosity, stationary locations and many
more (cf. Laube 2014). For a more holistic interpretation of
movement behavior, however, the contextual setting should be
incorporated into the analytical process (Demsar et al. 2015).
From the various types of context, this study puts its focus on
attributes of physical space, which includes for instance the
underlying topography (e.g. Cagnacci et al. 2011), the wind
speed and direction (e.g. Shamoun-Baranes et al. 2012), the
temperature (Andrienko et al. 2008), or ocean currents (Block
et al. 2011), all of which can have an influence on the
observed movement behavior.
Such information on the environmental context can either be
derived from external datasets, e.g. temperature or slope raster
layers, or simultaneously collected from various mobile
sensors (Demsar et al. 2015). With regards to the former
option, which is in the focus of this study, the raw movement
data is typically annotated based on a spatio-temporal
correspondence of the recorded position fixes and the
underlying raster cells. For instance, Buchin et al. (2012)
identify as a trajectory’s context the sub-set of cells from one
or more raster layers which directly underlie its position fixes,
Block et al. (2011) calculate marine species hotspots from
trajectories and relate them to oceanographic variables in the
underlying grid cell, and Andrienko et al. (2011) link
movement events to context elements based on their spatio-
temporal position. To the best of our knowledge, however,
there is currently no comprehensive framework or toolset,
which would be applicable to more complex spatio-temporal
analyses, as outlined in the introduction.
2.3 Map Algebra
Map algebra, proposed by Tomlin (1990), describes a formal
system of arithmetic operations in a grid-based cartographic
model, and aims to generalize and standardize the related
analytic functionalities of GIS. A map algebra statement is
typically in the form of:
The function takes as input one, two or more layers, but
always produces one distinct output layer. The value
processing functions can be arithmetic, statistical or logical,
always depending on the spatial scope of the analysis
(Albrecht 2007, Tomlin 1990). These include e.g. a local
operation, which focuses on values from the same cell or
single location at a time, whereas a neighbourhood operation
combines a value from a location with a sub-set of locations
within its direct vicinity. In contrast, zonal operations divide
their input into zones based on homogeneous cell values, and
finally, global operations take all cells of a layer into
consideration (Tomlin 1990).
Today, map algebra has been conceptually extended in
various ways. Especially relevant for our work is a study by
Laube et al. (2007), in which the authors describe local
(instant), focal (interval), zonal (episode), and global
operators for defining the scope of the computation of
context-independent movement parameters such as the speed
or the sinuosity.
3 Concept
The proposed framework transfers the fundamentals of map
algebra to the context of semantic trajectory annotation.
Initially, we have a track, as a collection of position fixes,
and one or more underlying context raster layers with values
to be annotated to the position fixes.
AGILE 2017 Wageningen, May 9-12, 2017
As a first step of the annotation process, its spatio-temporal
scope is defined, both with regards to the movement data and
the involved context data. For this, we refer to Tomlin’s
context operators, our interpretation of which is listed in table
1 and visualized in figure 1.
With regards to the analytical scope of the movement data,
based on Spaccapietra and Parent (2011) and Laube et al.
(2007), we denote an elementary, point-like position recording
as a position. An interval is a sub-set of positions based on a
moving window of fixed temporal duration (e.g. all temporal
neighbors recorded 15 minutes before or after a position), and
a trajectory a semantically defined segmentation of a track
(e.g. all positions recorded while walking). Finally, a track
refers to the entire movement dataset available for a particular
moving entity.
Concerning the spatial scope of the involved contextual
data, we follow Tomlin (1990), and refer to a location as the
atomic unit of space with a distinct value assigned (a raster
cell), a neighborhood as a sub-set of locations within a certain
distance from a pre-defined location, in our case a position of
a moving entity, a zone as a sub-set of locations located within
a geographical area which is defined based on a separate zone
layer (e.g. all temperature values within a certain land use),
and finally a layer which spans the entire area of interest.
Concerning the temporal dimension of the context data, we
distinguish between an instant, a set of values recorded at a
certain fixed point in time (e.g. a temperature layer with
values recorded at 2016-06-01 04:05:06), an interval, a time
duration-based selection of n layers with attribute values
around a certain point in time (e.g. the sub-set of temperature
layers recorded maximal 2 hours before or after 2016-06-01
04:05:06), an era, a semantically defined selection of n layers
with attribute values (e.g. the sub-set of temperature layers
where the maximum temperature exceeded 16°C), and finally
total time, which denotes the entirety of the available data for
the full time span of interest (e.g. all available temperature
Based on these definitions, any combination of context
operators on the three levels unambiguously defines the
spatio-temporal scope of the trajectory annotation process.
Thus, an analysis of type LocalFocalZonal we define the
default order as movement data followed by context data
(spatial dimension) followed by context data (temporal
dimension) treats each individual position fix of the
movement track separately (local), and annotates them a value
resulting from some combination of the underlying cell values
within a certain neighborhood around their location (focal),
Table 1: Local, focal, zonal, and global equivalents on the levels of movement and spatio-temporal context data
Context Data
Spatial Dimension
Context Data
Temporal Dimension
time interval
total time
Figure 1: Levels of analytical scope of movement and spatio-temporal context data
AGILE 2017 Wageningen, May 9-12, 2017
however not just using the cell values of one but a selection of
several layers recorded at different points in time (zonal).
As a second step, for each level, the value processing
function needs to be determined to describe how the input
values, if more than just a single one, should be
mathematically combined. In principle, in accordance with
Tomlin’s original concept, these can be any arithmetic,
statistical or logical functions such as mean, sum, average,
maximum or minimum, majority or minority. Only in case of a
local context operator, no such function is needed, since there
is only one value.
With reference to traditional map algebra statements, figure
2 shows a formalized trajectory annotation statement in
accordance with our concept. On the left side, the enriched
movement dataset is set as the function’s output. On the right
side, the annotation function is defined with three slots to
define the spatio-temporal scope of the movement data and
the context datasets (shown in black), each of which is
followed by a specific value processing function (shown in
grey). Finally, connected by map algebra-typical modifiers
such as and, at or within, the input datasets are set, and the
function-specific neighborhood or zone definitions are
determined, e.g. by defining a time interval for a sliding
window, a distance threshold for a neighborhood, a zone layer
for a zone, or a SQL query for an era.
4 Application
In this application example, we aim to assess a person’s
exposure to radiation per hour, e.g. a member of a disaster
response team in the aftermath of a nuclear accident. For this,
we created hypothetical test data, both with regards to the
movement track and the underlying radiation data, which,
together with the results of an implementation in Python, are
shown in figure 3. As one can see, we tested two variants: in
the first, we chose a simple LocalLocalLocal method, which
is similar to the common approach of simple cell-to-point
annotation as discussed earlier, but neither produces the
intended radiation per hour, nor takes into account any
positional inaccuracy of the track or temporal variation of the
context data. Thus, by means of our proposed framework, we
can also compute a more complex FocalAvgFocalAvgLocal
method, which creates a sliding window on the level of
movement data in order to receive the intended average
radiation per hour. Due to potential positional inaccuracy, a
spatial neighborhood of 25 meters is defined around each
position fix and the average radiation value is calculated.
5 Discussion and Conclusion
This study proposed an analytical framework for semantically
enriching movement trajectories with context data as well as a
terminology for unambiguously defining the spatio-temporal
scope of the analysis and the value processing method on each
level. We expect our work to assist movement data analysts in
selecting or developing a suitable annotation method based on
the exact aim of the study as well as the characteristics of the
available movement data, for instance with regards to the
expected positional inaccuracy, and the context data, e.g. in
terms of the spatial and temporal resolution. Our framework
Figure 3: Exposure to Radiation per Hour
Figure 2: An exemplary trajectory annotation statement
AGILE 2017 Wageningen, May 9-12, 2017
can be of particular value for more complex tasks, as sketched
in the introduction, which require a more elaborated method
than a simple cell-to-point annotation. At the same time, the
proposed terminology can be useful to communicate the used
Mainly due to the early stage of our research, however,
there are still several limitations. Thus, we have not fully
explored the potential ways to define focal or global spatio-
temporal scope levels of the context data. Apart from a simple
distance-based one, for instance, more complex neighborhood
definitions involving e.g. a direction might be needed.
Further, in case of multiple involved layers with multiple
cells, different orders of calculation could be possible.
Potential effects on the results need to be explored. Further,
our framework is currently only applicable to cases where
context data exists in the form of raster layers, and not to
scenarios which require context to be modeled with discrete
vector features.
For future work, we aim to address these shortcomings, and,
on this basis, develop and implement a comprehensive toolset,
which can then be tested in various scenarios.
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Recent advances in tracking technologies result in geographic information representing the movement of individuals at previously unseen spatial and temporal granularities. This new, inherently spatiotemporal, kind of geographic information offers new insights into dynamic geographic processes but also challenges the traditionally rather static spatial analysis toolbox. This chapter presents an introductory overview to movement data in general (Sect. 22.2), the theory for modeling and analyzing movement (Sects. 22.2.1, 22.3), as well as a set of key application fields of movement analysis (Sect. 22.3). Finally, the chapter addresses privacy concerns relevant to the analysis of human movement.
Geographical Information Science is challenged by an unprecedented increase in the availability of tracking data related to human and animal movement, typically captured through location-aware portable devices such as GPS receivers. Capture of trajectory data at fine temporal and spatial granularities has allowed with the representation of detailed geospatial lifelines, opening new options for analysis. In this respect we propose a dynamic perspective to analysis which, in contrast to summary trajectory statistics on speed, motion azimuth or sinuosity, that refers to the variability of motion properties throughout the developing lifeline. Four specific lifeline context operators are identified in this paper: ‘instantaneous’, ‘interval’, ‘episodal’ and ‘total’. Using this framework, we discuss standardisations that integrate the extended set of motion descriptors within various temporal and spatial frames of reference and the proposed lifeline context operators and standardisations are illustrated using high resolution trajectory data obtained from homing pigeons carrying miniature global positioning devices.
Current tracking technologies enable collection of data, describing movements of various kinds of objects, including people, animals, icebergs, vehicles, containers with goods and so on. Analysis of movement data is now a hot research topic. However, most of the suggested analysis methods deal with movement data alone. Little has been done to support the analysis of movement in its spatio-temporal context, which includes various spatial and temporal objects as well as diverse properties associated with spatial locations and time moments. Comprehensive analysis of movement requires detection and analysis of relations that occur between moving objects and elements of the context in the process of the movement. We suggest a conceptual model in which movement is considered as a combination of spatial events of diverse types and extents in space and time. Spatial and temporal relations occur between movement events and elements of the spatial and temporal contexts. The model gives a ground to a generic approach based on extraction of interesting events from trajectories and treating the events as independent objects. By means of a prototype implementation, we tested the approach on complex real data about movement of wild animals. The testing showed the validity of the approach.