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Title
The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Author
Chen, Jun

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
263
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representations. Anyway, either moving object types or spatio-
temporal constraints explicitly reveal only one spatio-temporal
semantic, i.e., location change semantic. In a sense of geometry
or point-set theory, location as a coordinate point is an atomic
unit to describe spatial objects, and location change certainly is
the most basic spatial change. However, it is known that point
set or point-string or coordinate-sequence data structures not
only increase difficulties of data storage and access, but also
bring overburden to spatial analysis. This means that much
useful semantic information has to be extracted by algorithms or
user’s understanding. To overcome these shortcomings,
semantically rich data structures like node-arc-polygon and
point-edge-triangle with connectivity and neighborhood
relationships, are preferred in practice. Again, in a knowledge
sense, location change is only one of four spatial primitives
(Reginald G. Golledge, 1995), and spatio-temporal semantics
should be modeled at multi-levels, not only at the level of
coordinate point. Amazingly, direction is being identified as an
independent spatial object recently (Shashi Shekhar and Xuan
Liu, 1998). Taking the forest management as example, enlarging
planting area of a tree species intuitively is a change of area of a
tree stand, rather than its location change, and changing tree
planting stand from square to strip intuitively is a shape change
of a tree stand. The lack of semantics in current data models
and presentation of direction object motivate us to study spatio-
temporal semantics.
In general, time has two kinds of semantic, i.e., time-scale
semantic and event-sequence semantic. By these two kinds of
time semantic, accordingly M.F. Worboys (1994) developed a
spatio-temporal complex model, where time and space are two
semantically independent dimensions unified in a mathematical
form of complex, and D. J. Peuquet et ai. (1995) designed an
event-based spatio-temporal data model TRIAD. To a large
extent, event-sequence time semantics or spatial change
modeling seems more important than time-scale time semantics
or spatio-temporal position modeling. To enrich time semantics
of spatial event, we examine existing taxonomies of spatial
change in section 2. In section 3, three levels of spatial change
(scene change, object change and property change) are
identified. In section 4, relevant cognitive understandings are
given. In the concluding section, we made a further discussion.
Note that terms of event and change are interchangeably used
in this paper.
2 PREVIOUS WORK ON CHANGE CLASSIFICATIONS BY
DIFFERENT CRITERIA
As stated above, event sequence presents human an image of
time. In other words, events reveal an inherent time semantic.
The structure and types of event imply time semantics. In
databases, an event is generally represented with a function of
state change. A spatial event is a function of spatial state
change. That is, spatial changes indicate spatio-temporal
semantics. In the following, we investigate previous work on
change classifications based on different criteria.
2.1 The Criterion of Time-varying Patterns
Patterns are distribution laws of elements in a set. Time-varying
patterns refer to distribution laws of time sequence data spatial
or thematic. Basic time-varying patterns have discrete, stepwise
and continuous changes. These time-varying patterns are firstly
examined by Segev A. and Shoshani A.(1987), who called them
time-series types. Afterwards, Yeh, T.S. and B. De Cambray
(1993) introduced them into Temporal GIS, and called them
behavior functions of data. Formally, given a time sequence of
data, {(a1, t1), (a2, t2), .... (an, tn)}, t1 three time-varying patterns:
• Discrete change. The data value sequence (a1, a2, ..., an)
completely depends on observation or measurement, and no
computational laws are available. For example, wood product
volumes of a tree stand are recorded at different times.
• Stepwise change. In the time sequence {(a1, t1) (ai, ti),
.... (an, tn)), the data value ai remains constant from an time
instant ti through next instant ti+1. For example, tree stand
changes (splitting, merging, enlargement or reshaping) are
stepwise changes.
• Continuous change. The data value ai can be computed by
mathematical functions such as a spline function, a linear
functions, etc. For example, temperature change in forestry is a
kind of continuous changes.
In fact, three kinds of change can be viewed as three forms of a
time-varying function at different discretization degrees, that is,
continuous function for continuous change, segmented function
for stepwise change and approximated function with a set of
discrete values for discrete change. Meanwhile, discrete change
at a small scale can be generalized into continuous change at a
larger scale. Anyway, in a semantic modeling sense, three time-
varying patterns reveal three time-varying laws or three time
semantics, which facilitate human time information
comprehension.
2.2 The Joint Criterion of Geometrical Dimensionality and
Time-varying Patterns
In Nancy J. Yattaw’s thesis, geographic movements are
categorized by characteristics of change in space and time.
Spatially, geographic phenomena are abstracted with
geometrical point, line, area and volume, and spatial changes
are categorized into point change, line change, area change and
volume change. For simplicity, volume phenomenon is omitted in
this paper. Temporally, dynamic phenomena are characterized
by continuous, cyclical and intermittent changes. Continuous
change indicates that a phenomenon moves uninterruptedly
throughout a period of examination. Movement, which is
discontinuous during examination and stops periodically, is said
to be fluctuating. For cyclical change (periodical fluctuation), the
frequency of every movement is predictable and regular.
Intermittent change is a fluctuation, which is sporadic or
irregular. By combining three kinds of spatial change with three
kinds of temporal change, geographic movements are
categorized into nine groups, in the mathematical form, {point
change, line change, area change) X {continuous change,
cyclical change, intermittent change)= {continuous point change,
continuous line change, continuous area change, cyclical point
change, cyclical line change, cyclical area change, intermittent
point change, intermittent line change, intermittent area change),
where “X” is Cartesian Product (Nancy J. Yattaw, 1997).
It is evident that point, line and area are classified by criterion of
geometrical dimensionality. Point, denoted by geometric
coordinate (x, y), is a zero-dimensional geometric object without
extent. Line, with a certain length and zero width, is a one
dimensional geometric object. Area is two-dimensional extended
geometric object. In general, we coarsely group time-varying
patterns into continuous change and discontinuous change first,
then finely group discontinuous changes into cyclical change
and intermittent change in terms of whether the frequency of
change is predictable. Change with an unpredictable frequency
is intermittent, whereas change with a predictable frequency is
cyclical. Intermittent change and cyclical change are similar to
discrete change and stepwise change respectively in section
2.1. Nancy J. Yattaw's change classification is based on the joint
criterion of geometrical dimensionality and time-varying patterns.
2.3 The Joint Criterion of Geometrical Dimensionality and
Location Movement
It is realized that spatial data is varying over time discretely or
continuously. In the course of mobile computation, Sistla, A.P.,
O. Wolfson et al. (1997) put forward the concept of moving
object, whose location is varying over time. In their moving
object spatio-temporal data model (MOST), dynamic spatial
property (changing location) is represented with a motion vector.