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

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
The motion vector aims to support continuous change modeling,
to facilitate future queries, and simultaneously to reduce data
storage volume. MOST model makes possible real-time update
of spatial locations of object, but it doesn’t emphasize keeping
the whole history of spatial data. In contrast, Erwig, M., R.H.
Gueting et al. (1997) designed the abstract data type of moving
object into their geo-relational algebra. Extended geo-relational
algebra has formally defined two abstract data types of moving
object (moving point mpoint and moving region mregion) and
relevant operators. The types mpoint and mregion are defined
as mappings from time to space mathematically, that is,
Mpoint time ->point
Mregion: time ->region
The type mpoint indicates that the location of object is varying
over time. The type mregion indicates that extent of object is
varying over time, e.g., shrinking or expanding. The authors
insist that moving line is the trajectory of moving point, so it is
somewhat unnecessary to define moving line type.
In contrast to MOST model, extended geo-relational algebra put
special emphasis on history maintenance of time-varying spatial
data. Another difference is that MOST model pays more
attention to implementation with motion vector data structure, but
extended geo-relational algebra mainly focuses on conceptual
abstraction of time-varying property of geographical objects. It is
obvious that both MOST model and extended geo-relational
algebra classify spatial changes by the joint criterion of
geometrical dimensionality and location movement.
2.4 The Criterion of Spatial Variables
Pierre Gagnon, Yvan Bedard and Geoffrey Edwards (1992)
categorized spatial changes into three groups: one-entity
change, two-entity change and multi-entity change. One-entity
changes consist of existence, extinction, location (position)
change, direction (orientation) change, shape change and size
change of an entity. Two-entity changes consist of spatial
relationship (topological relationship) changes between two
entities. Multi-entity changes are population changes formed
with 3 entities or more, including location (position) change,
direction (orientation) change, shape change and size change
(cumulative size change or population size change) and change
of spatial distribution type of a population. The cumulative size is
the summation of all individual sizes of entities of a population.
When combined with the number of entities, it provides
“presence rate”. The spatial population size corresponds to the
size of distribution area, when combined with the number of
entities, it provides “occupation rate”, and when combined with
cumulative size, it provides “spatial density”. There are three
types of spatial distribution, regular, random and grouped
distributions. This change classification is referred to be based
on the criterion of spatial variables, spatial variables of a single
entity (location, direction, shape and size) and spatial variables
of multi-entity (cumulative size, population size and spatial
distribution type).
2.5 The Joint Criterion of Spatial Variables and
Geographical Functions
Christophe Claramunt and Marius Theriaut (1995, 1996) posed
three types of spatio-temporal process: (1) the evolution of a
single entity; (2) the processes involving functional relationships
between several entities; (3) the evolution of spatial structures
involving several entities.
For the evolution of a single entity, there exist three types of
• Basic processes including appearance, disappearance and
spatial stability to allow representation of attribute variation
without spatial effects;
• Transformation processes involving changes in shape or
size, including expansion, contraction and deformation (shape
modification without size change);
• Movement processes involving only position changes,
including displacement and rotation.
For the processes involving functional relationships, it can be
grouped into two categories:
• Replacement processes involving a sequence of entities of
comparable types that accomplish the same function or occupy
the same position in space (without necessarily having identical
locations), e.g., succession and permutation.
• Diffusion processes involving a transfer of characteristics
between two or more spatial entities. It seems useful to
distinguish between production (creation of new entities by
actions of one or more entities of different natures), reproduction
(creation of new entities by actions of essentially identical
entities called parents) and transmission (modification of
characteristics of a receiver due to influence of a transmitter).
Each process carries a precedence constraint. Contagion is a
specific form of diffusion.
For the evolution of spatial structures involving several entities,
three restructuring processes are introduced. They are splitting,
union and reallocation.
It is easy to know that the change classification of single entity is
mainly based on spatial variables (shape, size, location,
direction), and functional relationship evolutions on geographical
functions. Also, some basic processes of single entity and
spatial structure evolutions are associated with changes of
object identity
2.6 The Joint Criterion of Entity Identity and Geographical
Kathleen Hornsby and Max J.Egenhofer (1997, 1998) proposed
a change classification based on object identity and a set of
operations that preserve or change object identity. In conjunction
with geographical functions, they defined four kinds of change
(or operation): (1) transitions (concretely, transition between
object existence and object extinction, issue transition, and
separate transition); (2) identity operations on a single object
(creation, destruction, continuing existence, continuing non
existence, and equivalent reincarnation, same reincarnation);
issuing operations (spawning and metamorphosis); operations of
combining single objects (merge, generate and mix); splitting
operations (splinter and division); (3) Operations on a single
object and a composite object, i.e., operations of forming
composite object (aggregation, compound, union, amalgamation
and combination), operations of splitting composite objects
(secession and dissolution); (4) Operations of selecting an object
or a portion of an object.
From the above investigations, we can see that spatial changes
are usually described in four respects, i.e., spatial property
change, object identity change, spatial distribution change and
functional change. Among them, functional change is application
dependent, and is of various number, which can be explained at
different levels of abstraction. Thus, in a general form, we define
various changes at three levels, property change, object change
and scene change. Scene change is similar to spatial distribution
change, which is an overall change composed of property and
object changes. Meanwhile, we recognize time semantics with
three simple time-varying patterns, i.e., discrete change,
stepwise change and continuous change.
3.1 Three Levels of Spatial Change
In the bottom-up order, three levels of spatial change are spatial
property change, spatial object change and spatial scene
change (Figure 1). Spatial property change refers to geometrical
property change and geometrical dimensionality change. Spatial
object change is related to change of object identity. Spatial