Spatiotemporal (ST) Module: Main Concepts

This module contains a set of classes to deal with continuous changes. Continuous changes occur when what we study changes its state constantly. Such changes refer to phenomena that vary continuously over time and space. Examples include cars in a highway, animals, temperature and precipitation in a city. All cases of continuous change have a common feature: we watch their state at given times and infer their change between observations. From sequences of locations we deduce animal tracks. We look at a sequence of images from the same area at different times and infer land cover change. Thus, observations are our means for capturing continuous change.

This module is mainly based on five concepts: observation, time series, moving object, coverage and interpolator.

An observation is the measured value of a phenomenon in a particular position in space and time. Observations are our base building blocks to build spatiotemporal data types. We allow a user to define different abstractions on the same observation set, meeting application needs. For example, consider a set of cars equipped with GPS and air pollution sensors. The figure below shows the tracks of three cars as green points in a city map. These cars generate an observation set, where each one contains a car location, an instant and a pollution value at that location and instant. From this set, we can extract two kinds of information: car trajectories and air pollution. On car trajectories, we use queries such as “How long did car c01 stay in the south region of the city?” and “How close did cars c01 and c02 come during the day?” to inform us how the cars move over time and space. On air pollution, we use queries such as “What city district had the worst pollution during this week?” and “How did pollution vary over time at place l01?” to inform us how pollution varies over time in the city.

We define three data types as abstractions on observations: time series, moving object, and coverage.

A time series is a continuous variation of a property value over time. The figure below shows examples of time series used in disease surveillance of dengue in the city of Recife.

A moving object is a continuous variation of the spatial location or extent of an entity or object over time. The figure below shows examples of moving objects: animal tracking and deforested region evolution.

Animal Tracking	Deforested region evolution

Given a spatial extent, a coverage represents how an attribute value varies over time inside it. For every point within such extent, it is possible to compute the value of this attribute. Two examples of coverage: the variation of temperature and of precipitation in a city.

Temperature	Precipitation

Observations are discrete by nature. We cannot sample every location at every instant. To represent continuous change, the data types (time series, moving object and coverage) combine discrete observations with interpolation functions. These functions allow us to estimate values at locations in space and moments in time for which there is no data. The main idea is to allow a user to choose the most suitable interpolation function for each type instance. For example, consider two observations of a moving car, one at instant 4 and the other at 8, shown in the figure below. There are different methods to estimate the car location at the non-observed time 6. Choices include a linear interpolator or a method that uses a street map as a spatial constraint.