ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
263 
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storage structures, but the latter is at the low level of logical 
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<t2<...<tn, we can define 
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.